Mi Math Standards


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1

Picture of Troy Patterson

1.G.A

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 
Grade 1 » Geometry » Reason with shapes and their attributes.

Picture of Troy Patterson

1.G.A.1

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Distinguish between defining attributes (e.g., triangles are closed and three-sided) versus non-defining attributes (e.g., color, orientation, overall size); build and draw shapes to possess defining attributes.

Grade levels
01


Picture of Troy Patterson

1.G.A.2

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, and quarter-circles) or three-dimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) to create a composite shape, and compose new shapes from the composite shape.1

Grade levels
01


Picture of Troy Patterson

1.G.A.3

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Partition circles and rectangles into two and four equal shares, describe the shares using the words halves, fourths, and quarters, and use the phrases half of, fourth of, and quarter of. Describe the whole as two of, or four of the shares. Understand for these examples that decomposing into more equal shares creates smaller shares.

Grade levels
01


Picture of Troy Patterson

1.MD.A

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 
Grade 1 » Measurement & Data » Measure lengths indirectly and by iterating length units.

Picture of Troy Patterson

1.MD.A.1

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Order three objects by length; compare the lengths of two objects indirectly by using a third object.

Grade levels
01


Picture of Troy Patterson

1.MD.A.2

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Express the length of an object as a whole number of length units, by laying multiple copies of a shorter object (the length unit) end to end; understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps. Limit to contexts where the object being measured is spanned by a whole number of length units with no gaps or overlaps.

Grade levels
01


Picture of Troy Patterson

1.MD.B

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 
Grade 1 » Measurement & Data » Tell and write time.

Picture of Troy Patterson

1.MD.B.3

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Tell and write time in hours and half-hours using analog and digital clocks.

Grade levels
01


Picture of Troy Patterson

1.MD.C

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 
Grade 1 » Measurement & Data » Represent and interpret data.

Picture of Troy Patterson

1.MD.C.4

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another.

Grade levels
01


Picture of Troy Patterson

1.NBT.A

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 
Grade 1 » Number & Operations in Base Ten » Extend the counting sequence.

Picture of Troy Patterson

1.NBT.A.1

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Count to 120, starting at any number less than 120. In this range, read and write numerals and represent a number of objects with a written numeral.

Grade levels
01


Picture of Troy Patterson

1.NBT.B

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 
Grade 1 » Number & Operations in Base Ten » Understand place value.

Picture of Troy Patterson

1.NBT.B.2

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Understand that the two digits of a two-digit number represent amounts of tens and ones. Understand the following as special cases:

Grade levels
01


Picture of Troy Patterson

1.NBT.B.2a

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

10 can be thought of as a bundle of ten ones — called a "ten."

Grade levels
01


Picture of Troy Patterson

1.NBT.B.2b

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

The numbers from 11 to 19 are composed of a ten and one, two, three, four, five, six, seven, eight, or nine ones.

Grade levels
01


Picture of Troy Patterson

1.NBT.B.2c

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

The numbers 10, 20, 30, 40, 50, 60, 70, 80, 90 refer to one, two, three, four, five, six, seven, eight, or nine tens (and 0 ones).

Grade levels
01


Picture of Troy Patterson

1.NBT.B.3

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <.

Grade levels
01


Picture of Troy Patterson

1.NBT.C

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 
Grade 1 » Number & Operations in Base Ten » Use place value understanding and properties of operations to add and subtract.

Picture of Troy Patterson

1.NBT.C.4

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Understand that in adding two-digit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten.

Grade levels
01


Picture of Troy Patterson

1.NBT.C.5

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used.

Grade levels
01


Picture of Troy Patterson

1.NBT.C.6

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Subtract multiples of 10 in the range 10-90 from multiples of 10 in the range 10-90 (positive or zero differences), using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.

Grade levels
01


Picture of Troy Patterson

1.OA.A

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 
Grade 1 » Operations & Algebraic Thinking » Represent and solve problems involving addition and subtraction.

Picture of Troy Patterson

1.OA.A.1

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.1

Grade levels
01


Picture of Troy Patterson

1.OA.A.2

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.

Grade levels
01


Picture of Troy Patterson

1.OA.B

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 
Grade 1 » Operations & Algebraic Thinking » Understand and apply properties of operations and the relationship between addition and subtraction.

Picture of Troy Patterson

1.OA.B.3

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Apply properties of operations as strategies to add and subtract.2Examples: If 8 + 3 = 11 is known, then 3 + 8 = 11 is also known. (Commutative property of addition.) To add 2 + 6 + 4, the second two numbers can be added to make a ten, so 2 + 6 + 4 = 2 + 10 = 12. (Associative property of addition.)

Grade levels
01


Picture of Troy Patterson

1.OA.B.4

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Understand subtraction as an unknown-addend problem. For example, subtract 10 - 8 by finding the number that makes 10 when added to 8.

Grade levels
01


Picture of Troy Patterson

1.OA.C

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 
Grade 1 » Operations & Algebraic Thinking » Add and subtract within 20.

Picture of Troy Patterson

1.OA.C.5

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Relate counting to addition and subtraction (e.g., by counting on 2 to add 2).

Grade levels
01


Picture of Troy Patterson

1.OA.C.6

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 - 4 = 13 - 3 - 1 = 10 - 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 - 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13).

Grade levels
01


Picture of Troy Patterson

1.OA.D

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 
Grade 1 » Operations & Algebraic Thinking » Work with addition and subtraction equations.

Picture of Troy Patterson

1.OA.D.7

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false. For example, which of the following equations are true and which are false? 6 = 6, 7 = 8 - 1, 5 + 2 = 2 + 5, 4 + 1 = 5 + 2.

Grade levels
01


Picture of Troy Patterson

1.OA.D.8

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Determine the unknown whole number in an addition or subtraction equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 + ? = 11, 5 = _ - 3, 6 + 6 = _.

Grade levels
01


2

Picture of Troy Patterson

2.G.A

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 
Grade 2 » Geometry » Reason with shapes and their attributes.

Picture of Troy Patterson

2.G.A.1

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces.1 Identify triangles, quadrilaterals, pentagons, hexagons, and cubes.

Grade levels
02


Picture of Troy Patterson

2.G.A.2

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Partition a rectangle into rows and columns of same-size squares and count to find the total number of them.

Grade levels
02


Picture of Troy Patterson

2.G.A.3

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half of, a third of, etc., and describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape.

Grade levels
02


Picture of Troy Patterson

2.MD.A

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 
Grade 2 » Measurement & Data » Measure and estimate lengths in standard units.

Picture of Troy Patterson

2.MD.A.1

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes.

Grade levels
02


Picture of Troy Patterson

2.MD.A.2

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Measure the length of an object twice, using length units of different lengths for the two measurements; describe how the two measurements relate to the size of the unit chosen.

Grade levels
02


Picture of Troy Patterson

2.MD.A.3

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Estimate lengths using units of inches, feet, centimeters, and meters.

Grade levels
02


Picture of Troy Patterson

2.MD.A.4

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard length unit.

Grade levels
02


Picture of Troy Patterson

2.MD.B

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 
Grade 2 » Measurement & Data » Relate addition and subtraction to length.

Picture of Troy Patterson

2.MD.B.5

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Use addition and subtraction within 100 to solve word problems involving lengths that are given in the same units, e.g., by using drawings (such as drawings of rulers) and equations with a symbol for the unknown number to represent the problem.

Grade levels
02


Picture of Troy Patterson

2.MD.B.6

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Represent whole numbers as lengths from 0 on a number line diagram with equally spaced points corresponding to the numbers 0, 1, 2, ..., and represent whole-number sums and differences within 100 on a number line diagram.

Grade levels
02


Picture of Troy Patterson

2.MD.C

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 
Grade 2 » Measurement & Data » Work with time and money.

Picture of Troy Patterson

2.MD.C.7

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m.

Grade levels
02


Picture of Troy Patterson

2.MD.C.8

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and ¢ symbols appropriately. Example: If you have 2 dimes and 3 pennies, how many cents do you have?

Grade levels
02


Picture of Troy Patterson

2.MD.D

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 
Grade 2 » Measurement & Data » Represent and interpret data.

Picture of Troy Patterson

2.MD.D.10

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories. Solve simple put-together, take-apart, and compare problems1 using information presented in a bar graph.

Grade levels
02


Picture of Troy Patterson

2.MD.D.9

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Generate measurement data by measuring lengths of several objects to the nearest whole unit, or by making repeated measurements of the same object. Show the measurements by making a line plot, where the horizontal scale is marked off in whole-number units.

Grade levels
02


Picture of Troy Patterson

2.NBT.A

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 
Grade 2 » Number & Operations in Base Ten » Understand place value.

Picture of Troy Patterson

2.NBT.A.1

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. Understand the following as special cases:

Grade levels
02


Picture of Troy Patterson

2.NBT.A.1a

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

100 can be thought of as a bundle of ten tens — called a "hundred."

Grade levels
02


Picture of Troy Patterson

2.NBT.A.1b

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

The numbers 100, 200, 300, 400, 500, 600, 700, 800, 900 refer to one, two, three, four, five, six, seven, eight, or nine hundreds (and 0 tens and 0 ones).

Grade levels
02


Picture of Troy Patterson

2.NBT.A.2

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Count within 1000; skip-count by 5s, 10s, and 100s.

Grade levels
02


Picture of Troy Patterson

2.NBT.A.3

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Read and write numbers to 1000 using base-ten numerals, number names, and expanded form.

Grade levels
02


Picture of Troy Patterson

2.NBT.A.4

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using >, =, and < symbols to record the results of comparisons.

Grade levels
02


Picture of Troy Patterson

2.NBT.B

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 
Grade 2 » Number & Operations in Base Ten » Use place value understanding and properties of operations to add and subtract.

Picture of Troy Patterson

2.NBT.B.5

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.

Grade levels
02


Picture of Troy Patterson

2.NBT.B.6

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Add up to four two-digit numbers using strategies based on place value and properties of operations.

Grade levels
02


Picture of Troy Patterson

2.NBT.B.7

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds.

Grade levels
02


Picture of Troy Patterson

2.NBT.B.8

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Mentally add 10 or 100 to a given number 100-900, and mentally subtract 10 or 100 from a given number 100-900.

Grade levels
02


Picture of Troy Patterson

2.NBT.B.9

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Explain why addition and subtraction strategies work, using place value and the properties of operations.1

Grade levels
02


Picture of Troy Patterson

2.OA.A

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 
Grade 2 » Operations & Algebraic Thinking » Represent and solve problems involving addition and subtraction.

Picture of Troy Patterson

2.OA.A.1

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.1

Grade levels
02


Picture of Troy Patterson

2.OA.B

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 
Grade 2 » Operations & Algebraic Thinking » Add and subtract within 20.

Picture of Troy Patterson

2.OA.B.2

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Fluently add and subtract within 20 using mental strategies.2 By end of Grade 2, know from memory all sums of two one-digit numbers.

Grade levels
02


Picture of Troy Patterson

2.OA.C

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 
Grade 2 » Operations & Algebraic Thinking » Work with equal groups of objects to gain foundations for multiplication.

Picture of Troy Patterson

2.OA.C.3

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Determine whether a group of objects (up to 20) has an odd or even number of members, e.g., by pairing objects or counting them by 2s; write an equation to express an even number as a sum of two equal addends.

Grade levels
02


Picture of Troy Patterson

2.OA.C.4

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends.

Grade levels
02


3

Picture of Troy Patterson

3.G.A

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 
Grade 3 » Geometry » Reason with shapes and their attributes.

Picture of Troy Patterson

3.G.A.1

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories.

Grade levels
03


Picture of Troy Patterson

3.G.A.2

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. For example, partition a shape into 4 parts with equal area, and describe the area of each part as 1/4 of the area of the shape.

Grade levels
03


Picture of Troy Patterson

3.MD.A

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 
Grade 3 » Measurement & Data » Solve problems involving measurement and estimation.

Picture of Troy Patterson

3.MD.A.1

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Tell and write time to the nearest minute and measure time intervals in minutes. Solve word problems involving addition and subtraction of time intervals in minutes, e.g., by representing the problem on a number line diagram.

Grade levels
03


Picture of Troy Patterson

3.MD.A.2

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l).1 Add, subtract, multiply, or divide to solve one-step word problems involving masses or volumes that are given in the same units, e.g., by using drawings (such as a beaker with a measurement scale) to represent the problem.2

Grade levels
03


Picture of Troy Patterson

3.MD.B

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 
Grade 3 » Measurement & Data » Represent and interpret data.

Picture of Troy Patterson

3.MD.B.3

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step "how many more" and "how many less" problems using information presented in scaled bar graphs. For example, draw a bar graph in which each square in the bar graph might represent 5 pets.

Grade levels
03


Picture of Troy Patterson

3.MD.B.4

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units— whole numbers, halves, or quarters.

Grade levels
03


Picture of Troy Patterson

3.MD.C

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 
Grade 3 » Measurement & Data » Geometric measurement: understand concepts of area and relate area to multiplication and to addition.

Picture of Troy Patterson

3.MD.C.5

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Recognize area as an attribute of plane figures and understand concepts of area measurement.

Grade levels
03


Picture of Troy Patterson

3.MD.C.5a

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

A square with side length 1 unit, called "a unit square," is said to have "one square unit" of area, and can be used to measure area.

Grade levels
03


Picture of Troy Patterson

3.MD.C.5b

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

A plane figure which can be covered without gaps or overlaps by n unit squares is said to have an area of n square units.

Grade levels
03


Picture of Troy Patterson

3.MD.C.6

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units).

Grade levels
03


Picture of Troy Patterson

3.MD.C.7

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Relate area to the operations of multiplication and addition.

Grade levels
03


Picture of Troy Patterson

3.MD.C.7a

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Find the area of a rectangle with whole-number side lengths by tiling it, and show that the area is the same as would be found by multiplying the side lengths.

Grade levels
03


Picture of Troy Patterson

3.MD.C.7b

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Multiply side lengths to find areas of rectangles with whole-number side lengths in the context of solving real world and mathematical problems, and represent whole-number products as rectangular areas in mathematical reasoning.

Grade levels
03


Picture of Troy Patterson

3.MD.C.7c

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b + c is the sum of a × b and a × c. Use area models to represent the distributive property in mathematical reasoning.

Grade levels
03


Picture of Troy Patterson

3.MD.C.7d

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Recognize area as additive. Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts, applying this technique to solve real world problems.

Grade levels
03


Picture of Troy Patterson

3.MD.D

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 
Grade 3 » Measurement & Data » Geometric measurement: recognize perimeter.

Picture of Troy Patterson

3.MD.D.8

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters.

Grade levels
03


Picture of Troy Patterson

3.NBT.A

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 
Grade 3 » Number & Operations in Base Ten » Use place value understanding and properties of operations to perform multi-digit arithmetic.¹

Picture of Troy Patterson

3.NBT.A.1

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Use place value understanding to round whole numbers to the nearest 10 or 100.

Grade levels
03


Picture of Troy Patterson

3.NBT.A.2

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction.

Grade levels
03


Picture of Troy Patterson

3.NBT.A.3

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Multiply one-digit whole numbers by multiples of 10 in the range 10-90 (e.g., 9 × 80, 5 × 60) using strategies based on place value and properties of operations.

Grade levels
03


Picture of Troy Patterson

3.NF.A

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 
Grade 3 » Number & Operations—Fractions¹ » Develop understanding of fractions as numbers.

Picture of Troy Patterson

3.NF.A.1

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b.

Grade levels
03


Picture of Troy Patterson

3.NF.A.2

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Understand a fraction as a number on the number line; represent fractions on a number line diagram.

Grade levels
03


Picture of Troy Patterson

3.NF.A.2a

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Represent a fraction 1/b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts. Recognize that each part has size 1/b and that the endpoint of the part based at 0 locates the number 1/b on the number line.

Grade levels
03


Picture of Troy Patterson

3.NF.A.2b

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Represent a fraction a/b on a number line diagram by marking off a lengths 1/b from 0. Recognize that the resulting interval has size a/b and that its endpoint locates the number a/b on the number line.

Grade levels
03


Picture of Troy Patterson

3.NF.A.3

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.

Grade levels
03


Picture of Troy Patterson

3.NF.A.3a

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line.

Grade levels
03


Picture of Troy Patterson

3.NF.A.3b

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Recognize and generate simple equivalent fractions, e.g., 1/2 = 2/4, 4/6 = 2/3. Explain why the fractions are equivalent, e.g., by using a visual fraction model.

Grade levels
03


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3.NF.A.3c

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. Examples: Express 3 in the form 3 = 3/1; recognize that 6/1 = 6; locate 4/4 and 1 at the same point of a number line diagram.

Grade levels
03


Picture of Troy Patterson

3.NF.A.3d

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.

Grade levels
03


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3.OA.A

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 
Grade 3 » Operations & Algebraic Thinking » Represent and solve problems involving multiplication and division.

Picture of Troy Patterson

3.OA.A.1

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 × 7.

Grade levels
03


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3.OA.A.2

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Interpret whole-number quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. For example, describe a context in which a number of shares or a number of groups can be expressed as 56 ÷ 8.

Grade levels
03


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3.OA.A.3

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.1

Grade levels
03


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3.OA.A.4

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Determine the unknown whole number in a multiplication or division equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 × ? = 48, 5 = _ ÷ 3, 6 × 6 = ?

Grade levels
03


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3.OA.B

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 
Grade 3 » Operations & Algebraic Thinking » Understand properties of multiplication and the relationship between multiplication and division.

Picture of Troy Patterson

3.OA.B.5

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Apply properties of operations as strategies to multiply and divide.2Examples: If 6 × 4 = 24 is known, then 4 × 6 = 24 is also known. (Commutative property of multiplication.) 3 × 5 × 2 can be found by 3 × 5 = 15, then 15 × 2 = 30, or by 5 × 2 = 10, then 3 × 10 = 30. (Associative property of multiplication.) Knowing that 8 × 5 = 40 and 8 × 2 = 16, one can find 8 × 7 as 8 × (5 + 2) = (8 × 5) + (8 × 2) = 40 + 16 = 56. (Distributive property.)

Grade levels
03


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3.OA.B.6

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Understand division as an unknown-factor problem. For example, find 32 ÷ 8 by finding the number that makes 32 when multiplied by 8.

Grade levels
03


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3.OA.C

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 
Grade 3 » Operations & Algebraic Thinking » Multiply and divide within 100.

Picture of Troy Patterson

3.OA.C.7

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers.

Grade levels
03


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3.OA.D

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 
Grade 3 » Operations & Algebraic Thinking » Solve problems involving the four operations, and identify and explain patterns in arithmetic.

Picture of Troy Patterson

3.OA.D.8

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.3

Grade levels
03


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3.OA.D.9

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. For example, observe that 4 times a number is always even, and explain why 4 times a number can be decomposed into two equal addends.

Grade levels
03


4

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4.G.A

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 
Grade 4 » Geometry » Draw and identify lines and angles, and classify shapes by properties of their lines and angles.

Picture of Troy Patterson

4.G.A.1

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures.

Grade levels
04


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4.G.A.2

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles.

Grade levels
04


Picture of Troy Patterson

4.G.A.3

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry.

Grade levels
04


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4.MD.A

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 
Grade 4 » Measurement & Data » Solve problems involving measurement and conversion of measurements.

Picture of Troy Patterson

4.MD.A.1

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. For example, know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...

Grade levels
04


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4.MD.A.2

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale.

Grade levels
04


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4.MD.A.3

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Apply the area and perimeter formulas for rectangles in real world and mathematical problems. For example, find the width of a rectangular room given the area of the flooring and the length, by viewing the area formula as a multiplication equation with an unknown factor.

Grade levels
04


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4.MD.B

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 
Grade 4 » Measurement & Data » Represent and interpret data.

Picture of Troy Patterson

4.MD.B.4

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots. For example, from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection.

Grade levels
04


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4.MD.C

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 
Grade 4 » Measurement & Data » Geometric measurement: understand concepts of angle and measure angles.

Picture of Troy Patterson

4.MD.C.5

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement:

Grade levels
04


Picture of Troy Patterson

4.MD.C.5a

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

An angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. An angle that turns through 1/360 of a circle is called a "one-degree angle," and can be used to measure angles.

Grade levels
04


Picture of Troy Patterson

4.MD.C.5b

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

An angle that turns through n one-degree angles is said to have an angle measure of n degrees.

Grade levels
04


Picture of Troy Patterson

4.MD.C.6

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure.

Grade levels
04


Picture of Troy Patterson

4.MD.C.7

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure.

Grade levels
04


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4.NBT.A

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 
Grade 4 » Number & Operations in Base Ten¹ » Generalize place value understanding for multi-digit whole numbers.

Picture of Troy Patterson

4.NBT.A.1

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. For example, recognize that 700 ÷ 70 = 10 by applying concepts of place value and division.

Grade levels
04


Picture of Troy Patterson

4.NBT.A.2

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.

Grade levels
04


Picture of Troy Patterson

4.NBT.A.3

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Use place value understanding to round multi-digit whole numbers to any place.

Grade levels
04


Picture of Troy Patterson

4.NBT.B

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 
Grade 4 » Number & Operations in Base Ten¹ » Use place value understanding and properties of operations to perform multi-digit arithmetic.

Picture of Troy Patterson

4.NBT.B.4

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Fluently add and subtract multi-digit whole numbers using the standard algorithm.

Grade levels
04


Picture of Troy Patterson

4.NBT.B.5

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

Grade levels
04


Picture of Troy Patterson

4.NBT.B.6

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

Grade levels
04


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4.NF.A

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 
Grade 4 » Number & Operations—Fractions¹ » Extend understanding of fraction equivalence and ordering.

Picture of Troy Patterson

4.NF.A.1

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions.

Grade levels
04


Picture of Troy Patterson

4.NF.A.2

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.

Grade levels
04


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4.NF.B

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 
Grade 4 » Number & Operations—Fractions¹ » Build fractions from unit fractions.

Picture of Troy Patterson

4.NF.B.3

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Understand a fraction a/b with a > 1 as a sum of fractions 1/b.

Grade levels
04


Picture of Troy Patterson

4.NF.B.3a

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.

Grade levels
04


Picture of Troy Patterson

4.NF.B.3b

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model. Examples: 3/8 = 1/8 + 1/8 + 1/8 ; 3/8 = 1/8 + 2/8 ; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8.

Grade levels
04


Picture of Troy Patterson

4.NF.B.3c

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction.

Grade levels
04


Picture of Troy Patterson

4.NF.B.3d

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem.

Grade levels
04


Picture of Troy Patterson

4.NF.B.4

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Apply and extend previous understandings of multiplication to multiply a fraction by a whole number.

Grade levels
04


Picture of Troy Patterson

4.NF.B.4a

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Understand a fraction a/b as a multiple of 1/b. For example, use a visual fraction model to represent 5/4 as the product 5 × (1/4), recording the conclusion by the equation 5/4 = 5 × (1/4).

Grade levels
04


Picture of Troy Patterson

4.NF.B.4b

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number. For example, use a visual fraction model to express 3 × (2/5) as 6 × (1/5), recognizing this product as 6/5. (In general, n × (a/b) = (n × a)/b.)

Grade levels
04


Picture of Troy Patterson

4.NF.B.4c

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Solve word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction models and equations to represent the problem. For example, if each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?

Grade levels
04


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4.NF.C

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 
Grade 4 » Number & Operations—Fractions¹ » Understand decimal notation for fractions, and compare decimal fractions.

Picture of Troy Patterson

4.NF.C.5

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100.2For example, express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100.

Grade levels
04


Picture of Troy Patterson

4.NF.C.6

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Use decimal notation for fractions with denominators 10 or 100. For example, rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram.

Grade levels
04


Picture of Troy Patterson

4.NF.C.7

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual model.

Grade levels
04


Picture of Troy Patterson

4.OA.A

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 
Grade 4 » Operations & Algebraic Thinking » Use the four operations with whole numbers to solve problems.

Picture of Troy Patterson

4.OA.A.1

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations.

Grade levels
04


Picture of Troy Patterson

4.OA.A.2

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison.1

Grade levels
04


Picture of Troy Patterson

4.OA.A.3

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.

Grade levels
04


Picture of Troy Patterson

4.OA.B

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 
Grade 4 » Operations & Algebraic Thinking » Gain familiarity with factors and multiples.

Picture of Troy Patterson

4.OA.B.4

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Find all factor pairs for a whole number in the range 1-100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1-100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1-100 is prime or composite.

Grade levels
04


Picture of Troy Patterson

4.OA.C

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 
Grade 4 » Operations & Algebraic Thinking » Generate and analyze patterns.

Picture of Troy Patterson

4.OA.C.5

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. For example, given the rule "Add 3" and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.

Grade levels
04


5

Picture of Troy Patterson

5.G.A

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 
Grade 5 » Geometry » Graph points on the coordinate plane to solve real-world and mathematical problems.

Picture of Troy Patterson

5.G.A.1

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate).

Grade levels
05


Picture of Troy Patterson

5.G.A.2

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation.

Grade levels
05


Picture of Troy Patterson

5.G.B

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 
Grade 5 » Geometry » Classify two-dimensional figures into categories based on their properties.

Picture of Troy Patterson

5.G.B.3

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles.

Grade levels
05


Picture of Troy Patterson

5.G.B.4

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Classify two-dimensional figures in a hierarchy based on properties.

Grade levels
05


Picture of Troy Patterson

5.MD.A

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 
Grade 5 » Measurement & Data » Convert like measurement units within a given measurement system.

Picture of Troy Patterson

5.MD.A.1

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems.

Grade levels
05


Picture of Troy Patterson

5.MD.B

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 
Grade 5 » Measurement & Data » Represent and interpret data.

Picture of Troy Patterson

5.MD.B.2

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally.

Grade levels
05


Picture of Troy Patterson

5.MD.C

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 
Grade 5 » Measurement & Data » Geometric measurement: understand concepts of volume.

Picture of Troy Patterson

5.MD.C.3

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Recognize volume as an attribute of solid figures and understand concepts of volume measurement.

Grade levels
05


Picture of Troy Patterson

5.MD.C.3a

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

A cube with side length 1 unit, called a "unit cube," is said to have "one cubic unit" of volume, and can be used to measure volume.

Grade levels
05


Picture of Troy Patterson

5.MD.C.3b

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

A solid figure which can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units.

Grade levels
05


Picture of Troy Patterson

5.MD.C.4

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units.

Grade levels
05


Picture of Troy Patterson

5.MD.C.5

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume.

Grade levels
05


Picture of Troy Patterson

5.MD.C.5a

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Find the volume of a right rectangular prism with whole-number side lengths by packing it with unit cubes, and show that the volume is the same as would be found by multiplying the edge lengths, equivalently by multiplying the height by the area of the base. Represent threefold whole-number products as volumes, e.g., to represent the associative property of multiplication.

Grade levels
05


Picture of Troy Patterson

5.MD.C.5b

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Apply the formulas V = l × w × h and V = b × h for rectangular prisms to find volumes of right rectangular prisms with whole-number edge lengths in the context of solving real world and mathematical problems.

Grade levels
05


Picture of Troy Patterson

5.MD.C.5c

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Recognize volume as additive. Find volumes of solid figures composed of two non-overlapping right rectangular prisms by adding the volumes of the non-overlapping parts, applying this technique to solve real world problems.

Grade levels
05


Picture of Troy Patterson

5.NBT.A

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 
Grade 5 » Number & Operations in Base Ten » Understand the place value system.

Picture of Troy Patterson

5.NBT.A.1

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left.

Grade levels
05


Picture of Troy Patterson

5.NBT.A.2

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10.

Grade levels
05


Picture of Troy Patterson

5.NBT.A.3

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Read, write, and compare decimals to thousandths.

Grade levels
05


Picture of Troy Patterson

5.NBT.A.3a

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000).

Grade levels
05


Picture of Troy Patterson

5.NBT.A.3b

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.

Grade levels
05


Picture of Troy Patterson

5.NBT.A.4

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Use place value understanding to round decimals to any place.

Grade levels
05


Picture of Troy Patterson

5.NBT.B

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 
Grade 5 » Number & Operations in Base Ten » Perform operations with multi-digit whole numbers and with decimals to hundredths.

Picture of Troy Patterson

5.NBT.B.5

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Fluently multiply multi-digit whole numbers using the standard algorithm.

Grade levels
05


Picture of Troy Patterson

5.NBT.B.6

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

Grade levels
05


Picture of Troy Patterson

5.NBT.B.7

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.

Grade levels
05


Picture of Troy Patterson

5.NF.A

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 
Grade 5 » Number & Operations—Fractions » Use equivalent fractions as a strategy to add and subtract fractions.

Picture of Troy Patterson

5.NF.A.1

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.)

Grade levels
05


Picture of Troy Patterson

5.NF.A.2

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2.

Grade levels
05


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5.NF.B

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 
Grade 5 » Number & Operations—Fractions » Apply and extend previous understandings of multiplication and division.

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5.NF.B.3

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie?

Grade levels
05


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5.NF.B.4

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.

Grade levels
05


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5.NF.B.4a

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.)

Grade levels
05


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5.NF.B.4b

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas.

Grade levels
05


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5.NF.B.5

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Interpret multiplication as scaling (resizing), by:

Grade levels
05


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5.NF.B.5a

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication.

Grade levels
05


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5.NF.B.5b

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n × a)/(n × b) to the effect of multiplying a/b by 1.

Grade levels
05


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5.NF.B.6

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem.

Grade levels
05


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5.NF.B.7

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions.1

Grade levels
05


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5.NF.B.7a

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3.

Grade levels
05


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5.NF.B.7b

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4.

Grade levels
05


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5.NF.B.7c

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins?

Grade levels
05


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5.OA.A

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 
Grade 5 » Operations & Algebraic Thinking » Write and interpret numerical expressions.

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5.OA.A.1

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.

Grade levels
05


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5.OA.A.2

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, express the calculation "add 8 and 7, then multiply by 2" as 2 × (8 + 7). Recognize that 3 × (18932 + 921) is three times as large as 18932 + 921, without having to calculate the indicated sum or product.

Grade levels
05


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5.OA.B

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 
Grade 5 » Operations & Algebraic Thinking » Analyze patterns and relationships.

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5.OA.B.3

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For example, given the rule "Add 3" and the starting number 0, and given the rule "Add 6" and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so.

Grade levels
05


6

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6.EE.A

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 
Grade 6 » Expressions & Equations » Apply and extend previous understandings of arithmetic to algebraic expressions.

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6.EE.A.1

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Write and evaluate numerical expressions involving whole-number exponents.

Grade levels
06


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6.EE.A.2

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Write, read, and evaluate expressions in which letters stand for numbers.

Grade levels
06


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6.EE.A.2a

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation "Subtract y from 5" as 5 - y.

Grade levels
06


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6.EE.A.2b

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity. For example, describe the expression 2 (8 + 7) as a product of two factors; view (8 + 7) as both a single entity and a sum of two terms.

Grade levels
06


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6.EE.A.2c

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations). For example, use the formulas V = s3 and A = 6 s2 to find the volume and surface area of a cube with sides of length s = 1/2.

Grade levels
06


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6.EE.A.3

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y.

Grade levels
06


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6.EE.A.4

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for..

Grade levels
06


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6.EE.B

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 
Grade 6 » Expressions & Equations » Reason about and solve one-variable equations and inequalities.

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6.EE.B.5

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.

Grade levels
06


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6.EE.B.6

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.

Grade levels
06


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6.EE.B.7

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers.

Grade levels
06


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6.EE.B.8

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams.

Grade levels
06


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6.EE.C

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 
Grade 6 » Expressions & Equations » Represent and analyze quantitative relationships between dependent and independent variables.

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6.EE.C.9

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time.

Grade levels
06


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6.G.A

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 
Grade 6 » Geometry » Solve real-world and mathematical problems involving area, surface area, and volume.

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6.G.A.1

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.

Grade levels
06


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6.G.A.2

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = l w h and V = b h to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems.

Grade levels
06


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6.G.A.3

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems.

Grade levels
06


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6.G.A.4

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.

Grade levels
06


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6.NS.A

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 
Grade 6 » The Number System » Apply and extend previous understandings of multiplication and division to divide fractions by fractions.

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6.NS.A.1

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?.

Grade levels
06


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6.NS.B

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 
Grade 6 » The Number System » Compute fluently with multi-digit numbers and find common factors and multiples.

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6.NS.B.2

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Fluently divide multi-digit numbers using the standard algorithm.

Grade levels
06


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6.NS.B.3

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.

Grade levels
06


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6.NS.B.4

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1-100 with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express 36 + 8 as 4 (9 + 2)..

Grade levels
06


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6.NS.C

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 
Grade 6 » The Number System » Apply and extend previous understandings of numbers to the system of rational numbers.

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6.NS.C.5

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation.

Grade levels
06


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6.NS.C.6

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates.

Grade levels
06


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6.NS.C.6a

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g., -(-3) = 3, and that 0 is its own opposite.

Grade levels
06


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6.NS.C.6b

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes.

Grade levels
06


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6.NS.C.6c

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane.

Grade levels
06


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6.NS.C.7

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Understand ordering and absolute value of rational numbers.

Grade levels
06


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6.NS.C.7a

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. For example, interpret -3 > -7 as a statement that -3 is located to the right of -7 on a number line oriented from left to right.

Grade levels
06


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6.NS.C.7b

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Write, interpret, and explain statements of order for rational numbers in real-world contexts. For example, write -3 oC > -7 oC to express the fact that -3 oC is warmer than -7 oC.

Grade levels
06


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6.NS.C.7c

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real-world situation. For example, for an account balance of -30 dollars, write |-30| = 30 to describe the size of the debt in dollars.

Grade levels
06


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6.NS.C.7d

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Distinguish comparisons of absolute value from statements about order. For example, recognize that an account balance less than -30 dollars represents a debt greater than 30 dollars.

Grade levels
06


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6.NS.C.8

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate.

Grade levels
06


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6.RP.A

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 
Grade 6 » Ratios & Proportional Relationships » Understand ratio concepts and use ratio reasoning to solve problems.

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6.RP.A.1

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, "The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak." "For every vote candidate A received, candidate C received nearly three votes."

Grade levels
06


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6.RP.A.2

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0, and use rate language in the context of a ratio relationship. For example, "This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar." "We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger."1

Grade levels
06


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6.RP.A.3

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.

Grade levels
06


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6.RP.A.3a

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.

Grade levels
06


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6.RP.A.3b

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?

Grade levels
06


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6.RP.A.3c

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.

Grade levels
06


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6.RP.A.3d

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.

Grade levels
06


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6.SP.A

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 
Grade 6 » Statistics & Probability » Develop understanding of statistical variability.

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6.SP.A.1

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. For example, "How old am I?" is not a statistical question, but "How old are the students in my school?" is a statistical question because one anticipates variability in students' ages.

Grade levels
06


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6.SP.A.2

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape.

Grade levels
06


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6.SP.A.3

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number.

Grade levels
06


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6.SP.B

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 
Grade 6 » Statistics & Probability » Summarize and describe distributions.

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6.SP.B.4

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Display numerical data in plots on a number line, including dot plots, histograms, and box plots.

Grade levels
06


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6.SP.B.5

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Summarize numerical data sets in relation to their context, such as by:

Grade levels
06


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6.SP.B.5a

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Reporting the number of observations.

Grade levels
06


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6.SP.B.5b

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Describing the nature of the attribute under investigation, including how it was measured and its units of measurement.

Grade levels
06


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6.SP.B.5c

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.

Grade levels
06


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6.SP.B.5d

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered.

Grade levels
06


7

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7.EE.A

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 
Grade 7 » Expressions & Equations » Use properties of operations to generate equivalent expressions.

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7.EE.A.1

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.

Grade levels
07


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7.EE.A.2

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. For example, a + 0.05a = 1.05a means that "increase by 5%" is the same as "multiply by 1.05."

Grade levels
07


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7.EE.B

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 
Grade 7 » Expressions & Equations » Solve real-life and mathematical problems using numerical and algebraic expressions and equations.

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7.EE.B.3

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation.

Grade levels
07


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7.EE.B.4

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.

Grade levels
07


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7.EE.B.4a

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width?

Grade levels
07


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7.EE.B.4b

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. For example: As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions.

Grade levels
07


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7.G.A

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 
Grade 7 » Geometry » Draw construct, and describe geometrical figures and describe the relationships between them.

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7.G.A.1

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.

Grade levels
07


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7.G.A.2

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.

Grade levels
07


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7.G.A.3

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids.

Grade levels
07


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7.G.B

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 
Grade 7 » Geometry » Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.

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7.G.B.4

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.

Grade levels
07


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7.G.B.5

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure.

Grade levels
07


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7.G.B.6

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.

Grade levels
07


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7.NS.A

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 
Grade 7 » The Number System » Apply and extend previous understandings of operations with fractions.

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7.NS.A.1

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.

Grade levels
07


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7.NS.A.1a

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Describe situations in which opposite quantities combine to make 0. For example, a hydrogen atom has 0 charge because its two constituents are oppositely charged.

Grade levels
07


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7.NS.A.1b

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Understand p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts.

Grade levels
07


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7.NS.A.1c

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Understand subtraction of rational numbers as adding the additive inverse, p - q = p + (-q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts.

Grade levels
07


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7.NS.A.1d

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Apply properties of operations as strategies to add and subtract rational numbers.

Grade levels
07


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7.NS.A.2

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.

Grade levels
07


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7.NS.A.2a

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (-1)(-1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts.

Grade levels
07


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7.NS.A.2b

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers, then -(p/q) = (-p)/q = p/(-q). Interpret quotients of rational numbers by describing real-world contexts.

Grade levels
07


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7.NS.A.2c

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Apply properties of operations as strategies to multiply and divide rational numbers.

Grade levels
07


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7.NS.A.2d

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats.

Grade levels
07


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7.NS.A.3

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Solve real-world and mathematical problems involving the four operations with rational numbers.1

Grade levels
07


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7.RP.A

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 
Grade 7 » Ratios & Proportional Relationships » Analyze proportional relationships and use them to solve real-world and mathematical problems.

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7.RP.A.1

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction 1/2/1/4 miles per hour, equivalently 2 miles per hour.

Grade levels
07


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7.RP.A.2

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Recognize and represent proportional relationships between quantities.

Grade levels
07


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7.RP.A.2a

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin.

Grade levels
07


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7.RP.A.2b

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.

Grade levels
07


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7.RP.A.2c

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Represent proportional relationships by equations. For example, if total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn.

Grade levels
07


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7.RP.A.2d

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate.

Grade levels
07


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7.RP.A.3

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.

Grade levels
07


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7.SP.A

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 
Grade 7 » Statistics & Probability » Use random sampling to draw inferences about a population.

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7.SP.A.1

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences.

Grade levels
07


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7.SP.A.2

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. For example, estimate the mean word length in a book by randomly sampling words from the book; predict the winner of a school election based on randomly sampled survey data. Gauge how far off the estimate or prediction might be.

Grade levels
07


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7.SP.B

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 
Grade 7 » Statistics & Probability » Draw informal comparative inferences about two populations.

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7.SP.B.3

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability. For example, the mean height of players on the basketball team is 10 cm greater than the mean height of players on the soccer team, about twice the variability (mean absolute deviation) on either team; on a dot plot, the separation between the two distributions of heights is noticeable.

Grade levels
07


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7.SP.B.4

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. For example, decide whether the words in a chapter of a seventh-grade science book are generally longer than the words in a chapter of a fourth-grade science book.

Grade levels
07


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7.SP.C

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 
Grade 7 » Statistics & Probability » Investigate chance processes and develop, use, and evaluate probability models.

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7.SP.C.5

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around 1/2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event.

Grade levels
07


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7.SP.C.6

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability. For example, when rolling a number cube 600 times, predict that a 3 or 6 would be rolled roughly 200 times, but probably not exactly 200 times.

Grade levels
07


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7.SP.C.7

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy.

Grade levels
07


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7.SP.C.7a

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events. For example, if a student is selected at random from a class, find the probability that Jane will be selected and the probability that a girl will be selected.

Grade levels
07


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7.SP.C.7b

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process. For example, find the approximate probability that a spinning penny will land heads up or that a tossed paper cup will land open-end down. Do the outcomes for the spinning penny appear to be equally likely based on the observed frequencies?

Grade levels
07


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7.SP.C.8

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.

Grade levels
07


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7.SP.C.8a

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs.

Grade levels
07


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7.SP.C.8b

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. For an event described in everyday language (e.g., "rolling double sixes"), identify the outcomes in the sample space which compose the event.

Grade levels
07


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7.SP.C.8c

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Design and use a simulation to generate frequencies for compound events. For example, use random digits as a simulation tool to approximate the answer to the question: If 40% of donors have type A blood, what is the probability that it will take at least 4 donors to find one with type A blood?

Grade levels
07


8

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8.EE.A

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 
Grade 8 » Expressions & Equations » Expressions and Equations Work with radicals and integer exponents.

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8.EE.A.1

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 32 × 3-5 = 3-3 = 1/33 = 1/27.

Grade levels
08


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8.EE.A.2

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Use square root and cube root symbols to represent solutions to equations of the form x2 = p and x3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational.

Grade levels
08


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8.EE.A.3

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. For example, estimate the population of the United States as 3 times 108 and the population of the world as 7 times 109, and determine that the world population is more than 20 times larger.

Grade levels
08


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8.EE.A.4

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology

Grade levels
08


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8.EE.B

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 
Grade 8 » Expressions & Equations » Understand the connections between proportional relationships, lines, and linear equations.

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8.EE.B.5

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed.

Grade levels
08


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8.EE.B.6

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.

Grade levels
08


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8.EE.C

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 
Grade 8 » Expressions & Equations » Analyze and solve linear equations and pairs of simultaneous linear equations.

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8.EE.C.7

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Solve linear equations in one variable.

Grade levels
08


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8.EE.C.7a

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers).

Grade levels
08


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8.EE.C.7b

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.

Grade levels
08


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8.EE.C.8

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Analyze and solve pairs of simultaneous linear equations.

Grade levels
08


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8.EE.C.8a

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously.

Grade levels
08


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8.EE.C.8b

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection. For example, 3x + 2y = 5 and 3x + 2y = 6 have no solution because 3x + 2y cannot simultaneously be 5 and 6.

Grade levels
08


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8.EE.C.8c

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Solve real-world and mathematical problems leading to two linear equations in two variables. For example, given coordinates for two pairs of points, determine whether the line through the first pair of points intersects the line through the second pair.

Grade levels
08


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8.F.A

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 
Grade 8 » Functions » Define, evaluate, and compare functions.

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8.F.A.1

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output.1

Grade levels
08


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8.F.A.2

by Troy Patterson - Monday, July 31, 2017, 1:48 PM
 

Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a linear function represented by a table of values and a linear function represented by an algebraic expression, determine which function has the greater rate of change.

Grade levels
08