Unit 2: Place value

3.NR.1.1 Read, write, and represent whole numbers through the thousands period (0 to 999,999) on a number line and in standard, base ten language, word, and equations in expanded form.

1. Compare and order numbers using number lines

2. Write numbers in words

3. Convert from expanded form

3.NR.1.2 Compose and decompose 4-digit whole numbers in multiple ways using thousands, hundreds, tens, and ones.

1. Place value models up to thousands

2. Convert to/from a number

3. Convert between place values

4. Convert between standard and expanded form

5. Regroup thousands, hundreds, tens, and ones - ways to make a number

3.NR.1.3 Compare two whole numbers up to 999,999 based on the place value of the digits using the symbols for is equal to (=), is less than (<), or is greater than (>).

1. Compare numbers

2. Which number is greatest/least?

3. Order numbers up to one million

3.NR.1.4 Round whole numbers from 0 to 1,000 to the nearest 10 or 100.

1. Round to the nearest ten or hundred using a number line

2. Round to the nearest ten or hundred

3. Round to the nearest ten or hundred in a table

Unit 2: Rounding, Addition, Subtraction 

PAFR.1.1 Use a strategy to compute sums and differences up to 1,000.

Addition

1. Use number lines to add three-digit numbers

2. Use compensation to add: up to three digits

3. Use expanded form to add three-digit numbers

4. Add two numbers up to three digits: without regrouping

5. Add two numbers up to three digits: with regrouping

6. Add two numbers up to three digits

7. Add two numbers up to three digits: word problems

8. Addition up to three digits: fill in the missing digits

9. Add three numbers up to three digits each

10. Add three numbers up to three digits each: word problems

Subtraction

1. Use number lines to subtract three-digit numbers

2. Use compensation to subtract: up to three digits

3. Use expanded form to subtract three-digit numbers

4. Subtract numbers up to three digits: without regrouping

5. Subtract three-digit numbers: with regrouping

6. Subtract numbers up to three digits

7. Subtract across zeros

8. Subtract numbers up to three digits: word problems

9. Subtraction up to three digits: fill in the missing digits

Addition and subtraction

1. Use number lines to add and subtract three-digit numbers

2. Use compensation to add or subtract: up to three digits

3. Add and subtract three-digit numbers

4. Addition and subtraction word problems: up to three digits

Properties of operations

1. Properties of addition

2. Complete the equation using properties of addition\

3. Add using properties

Relationship between addition and subtraction

1. Complete the addition sentence: up to three digits

2. Balance addition equations: up to three digits

3. Complete the subtraction sentence: up to three digits

4. Balance subtraction equations: up to three digits

5. Relate addition and subtraction sentences

6. Complete the addition or subtraction sentence: up to three digits

Unit 3: Multiplication and Division

3.PAFR.1.2 Multiply whole numbers (factors 0–10) and divide whole numbers (divisors 1–10) using a model and write a corresponding equation. 

Multiplication

1. Identify multiplication expressions for equal groups

2. Write multiplication sentences for equal groups

3. Identify multiplication expressions for arrays

4. Write multiplication sentences for arrays

5. Write multiplication sentences for number lines

6. Write two multiplication sentences for an array

Division

1. Write division sentences for groups

2. Write division sentences for arrays

3. Make arrays to model division

4. Divide using number lines

Multiplication and division

1. Relate multiplication and division for groups

2. Relate multiplication and division for arrays

3. Relate multiplication and division

3.PAFR.2.1 Determine the unknown whole number in a multiplication or division real-world situation relating three whole numbers when the unknown is a missing factor, product, dividend, divisor, or quotient.

Word problems

1. Use equal groups and arrays to solve multiplication word problems

2. Use strip models to solve multiplication word problems

3. Multiplication word problems with factors up to 10

4. Multiplication word problems with factors up to 10: find the missing number

5. Use strip models to solve division word problems

6. Division word problems

7. Multiplication and division word problems

8. Two-step multiplication and division word problems

Variable equations

1. Write equations with unknown numbers to represent word problems: multiplication and division only

Unit 4: Using Patterns to Multiply by O, 1, 2, 5, and 10 

3.PAFR.1.3 Multiply two whole numbers from 0 to 10 and divide using related facts flexibly and accurately.

Multiplication facts to 10

1. Multiplication facts up to 10

2. Multiplication facts up to 10: true or false?

3. Multiplication facts up to 10: sorting

4. Multiplication facts up to 10: select the missing factors

5. Multiplication sentences up to 10: true or false?

6. Squares up to 10 x 10

7. Multiplication input/output tables

Division facts to 10

1. Division facts up to 10

2. Division facts up to 10: true or false?

3. Division facts up to 10: sorting

4. Division facts up to 10: select the missing numbers

5. Division sentences up to 10: true or false?

6. Division input/output tables

Relationship between multiplication and division

1. Relate multiplication and division

PAFR.1.2 Multiply whole numbers (factors 0–10) and divide whole numbers (divisors 1–10) using a model and write a corresponding equation. 

Multiplication

1. Identify multiplication expressions for equal groups

2. Write multiplication sentences for equal groups

3. Identify multiplication expressions for arrays

4. Write multiplication sentences for arrays

5. Write multiplication sentences for number lines

6. Write two multiplication sentences for an array

Division

1. Write division sentences for groups

2. Write division sentences for arrays

3. Make arrays to model division

4. Divide using number lines

Multiplication and division

1. Relate multiplication and division for groups

2. Relate multiplication and division for arrays

3. Relate multiplication and division

Unit 5: Use Properties to Multiply 3,4, 6, 7, 8, and 9 

3.PAFR.1.3 Multiply two whole numbers from 0 to 10 and divide using related facts flexibly and accurately.

Multiplication facts to 10

1. Multiplication facts up to 10

2. Multiplication facts up to 10: true or false?

3. Multiplication facts up to 10: sorting

4. Multiplication facts up to 10: select the missing factors

5. Multiplication sentences up to 10: true or false?

6. Squares up to 10 x 10

7. Multiplication input/output tables

Division facts to 10

1. Division facts up to 10

2. Division facts up to 10: true or false?

3. Division facts up to 10: sorting

4. Division facts up to 10: select the missing numbers

5. Division sentences up to 10: true or false?

6. Division input/output tables

Relationship between multiplication and division

1. Relate multiplication and division

PAFR.1.2 Multiply whole numbers (factors 0–10) and divide whole numbers (divisors 1–10) using a model and write a corresponding equation. 

Multiplication

1. Identify multiplication expressions for equal groups

2. Write multiplication sentences for equal groups

3. Identify multiplication expressions for arrays

4. Write multiplication sentences for arrays

5. Write multiplication sentences for number lines

6. Write two multiplication sentences for an array

Division

1. Write division sentences for groups

2. Write division sentences for arrays

3. Make arrays to model division

4. Divide using number lines

Multiplication and division

1. Relate multiplication and division for groups

2. Relate multiplication and division for arrays

3. Relate multiplication and division

Unit 6: Connect Area and Multiplication 

3.MGSR.1.1 Determine the area of squares and rectangles presented in relevant problems by covering the space with square units and counting the total number of units needed.

1. Find the area of figures made of unit squares: customary and metric units

2. Find the area of rectangles made of unit squares

3. Select rectangles with a given area

Unit 7: Fractions

3.NR.2.1 Identify unit fractions as the quantity formed by one part when a whole is partitioned into 2, 3, 4, 6, or 8 equal-sized parts. Express each part as a unit fraction of the whole.

Models

1. Identify equal parts

2. Match fractions to models: halves, thirds, and fourths

3. Match unit fractions to models

Word problems

1. Unit fractions: modeling word problems

2. Unit fractions: word problems

Number lines

1. Fractions of number lines: unit fractions

2. Identify unit fractions on number lines

3. Graph unit fractions on number lines

3.NR.2.2 Represent fractions from 0 to 1 using concrete, set, area, and linear models, and write them in standard form and word form. Limit denominators to 2, 3, 4, 6, and 8.

Understand fractions

1. Understand fractions: fraction bars

2. Understand fractions: area models

Show fractions

1. Show fractions: fraction bars

2. Show fractions: area models

Match fractions and models

1. Match fractions to models: halves, thirds, and fourths

2. Match fractions to models

Word problems

1. Fractions of a whole: modeling word problems

2. Fractions of a whole: word problems

3.NR.2.3 Express whole numbers as fractions and identify fractions that are equivalent to whole numbers. Limit denominators to 1, 2, 3, 4, 6, and 8.

1. Graph fractions equivalent to 1 on number lines

2. Select fractions equivalent to whole numbers using models

3. Select fractions equivalent to whole numbers

4. Find fractions equivalent to whole numbers

3.NR.2.4 Compose fractions between the whole numbers 0 and 5 using unit fractions. Record the composition as a mixed number or fraction greater than 1. Limit denominators to 2, 3, 4, 6, and 8.

1. Match mixed numbers to models

2. Word names for mixed numbers

Unit 8: Fractions Equivalence and Comparison 

3.NR.2.5 Recognize two fractions are equivalent based on the same size whole. Limit denominators to 2, 3, 4, 6, and 8, and fractions should be limited to fractions between 0 and 1.

Model equivalent fractions

1. Find equivalent fractions using fraction strips

2. Find equivalent fractions using area models: two models

3. Find equivalent fractions using area models: one model

4. Graph equivalent fractions on number lines

Find equivalent fractions

1. Identify equivalent fractions

2. Find equivalent fractions

3.NR.2.6 Compare two fractions with the same numerator or same denominator based on the same size whole by reasoning about their size. Use the symbols for is equal to (=), is less than (<), or is greater than (>). Limit denominators to 2, 3, 4, 6, and 8, and fractions should be limited to fractions between 0 and 1.

Compare using models

1. Compare fractions with like denominators using models

2. Compare fractions with like numerators using models

3. Compare fractions using models

Compare using number lines

1. Graph smaller or larger fractions on a number line

2. Graph and compare fractions with like denominators on number lines

3. Graph and compare fractions with like numerators on number lines

4. Compare fractions using number lines

5. Graph and compare fractions on number lines

Compare fractions

1. Compare fractions with like denominators

2. Compare fractions with like numerators

3. Compare fractions

4. Compare fractions and justify your answer

5. Compare fractions in recipes

Unit 9/10: Use Multiplication to Divide

3.PAFR.1.2 Multiply whole numbers (factors 0–10) and divide whole numbers (divisors 1–10) using a model and write a corresponding equation.

Multiplication

1. Identify multiplication expressions for equal groups

2. Write multiplication sentences for equal groups

3. Identify multiplication expressions for arrays

4. Write multiplication sentences for arrays

5. Write multiplication sentences for number lines

6. Write two multiplication sentences for an array

Division

1. Write division sentences for groups

2. Write division sentences for arrays

3. Make arrays to model division

4. Divide using number lines

Multiplication and division

1. Relate multiplication and division for groups

2. Relate multiplication and division for arrays

3. Relate multiplication and division

3.PAFR.1.3 Multiply two whole numbers from 0 to 10 and divide using related facts flexibly and accurately.

Multiplication facts to 10

1. Multiplication facts up to 10

2. Multiplication facts up to 10: true or false?

3. Multiplication facts up to 10: sorting

4. Multiplication facts up to 10: select the missing factors

5. Multiplication sentences up to 10: true or false

6. Squares up to 10 x 10

7. Multiplication input/output tables

Division facts to 10

1. Division facts up to 10

2. Division facts up to 10: true or false?

3. Division facts up to 10: sorting

4. Division facts up to 10: select the missing numbers

5. Division sentences up to 10: true or false?

6. Division input/output tables

Relationship between multiplication and division

1. Relate multiplication and division

Unit 11/12: Perimeter, Measurement, and Data 

3.DPSR.1.1 Collect and organize categorical and numerical data based on observations, surveys, experiments, and investigations with whole number values using tables, scaled picture graphs, scaled bar graphs, or dot plots. Use titles and labels. Limit scales to multiples of 1, 2, 5, and 10.

1. Create scaled bar graphs

2. Create scaled picture graphs

3. Create line plots

3.DPSR.1.2 Solve one-step, real-world situations using whole number data represented in tables, scaled picture graphs, scaled bar graphs, or dot plots. Limit scales to multiples of 1, 2, 5, and 10.

1. Interpret scaled bar graphs

2. Use bar graphs to solve problems

3. Interpret scaled picture graphs

4. Interpret line plots

3.DPSR.2.1 Identify the possible outcomes of a simple event.

1. Certain, probable, unlikely, and impossible

2. Certain, probable, unlikely, and impossible - with spinners

3.MGSR.1.2 Determine the perimeter of regular and irregular triangles and quadrilaterals with known side lengths.

1. Perimeter of figures on grids

2. Perimeter of rectangles

3. Perimeter of rectilinear shapes

4. Perimeter of triangles and quadrilaterals

3.MGSR.1.3 Determine if a real-world situation is an example of the need for finding the area or the perimeter of a figure.

1. Find the area of rectangles: word problems

2. Perimeter: word problems

3. Choose between area and perimeter: word problems

3.MGSR.2.1 Determine the value of any collection of coins, not to exceed $5. Write the amount in the form of dollars and cents using the decimal notation. Limit to penny, nickel, dime, and quarter.

1. Count money - pennies, nickels, dimes, and quarters

2. Count money up to $5: pennies, dimes, and dollar bills only

3.MGSR.2.2 Use analog and digital clocks to tell and record time to 1-minute intervals, identifying AM and PM.

1. Match clocks and times

2. Match analog and digital clocks

3. Read clocks and write times

4. A.M. or P.M.

5. Identify times written in words

3.MGSR.2.3 Solve problems involving addition and subtraction of time intervals to determine elapsed time to the nearest half hour.

1. Find the elapsed time

2. Find the end time: word problems

3. Find the elapsed time: word problems

3.MGSR.2.4 Estimate and measure length/distance to the nearest half inch and nearest whole centimeter.

1. Estimate lengths with inches, feet, and yards

2. Estimate lengths with centimeters and meters

3. Measure using an inch ruler: nearest 1/2 inch

4. Measure using a centimeter ruler

3.MGSR.2.5 Determine which unit of liquid volume is most appropriate to measure in real-world situations. Limit to fluid ounces, cups, pints, quarts, gallons, milliliters, and liters.

1. Measure liquid volumes using half and quarter cups

2. Measure liquid volumes - metric units

3. Which metric unit of volume is appropriate?

4. Which unit of volume is appropriate: ounces, cups, pints, quarts, or gallons?

Unit 13: Geometry 

3.MGSR.3.1 Describe and draw right, acute, obtuse, and straight angles. Identify these angle types in two-dimensional figures including triangles and quadrilaterals.

1. Angles greater than, less than, or equal to a right angle

2. Acute, right, obtuse, and straight angles

3. Acute, obtuse, and right triangles

3.MGSR.3.2 Identify, describe, and draw points, lines, line segments, rays, intersecting lines, perpendicular lines, and parallel lines. Identify these in two-dimensional figures.

1. Parallel, perpendicular, and intersecting lines

2. Name quadrilaterals more than one way

3. Points, lines, line segments, and rays