# Curriculum for Grade 5

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### MODULE 1. Place Value and Decimal Fractions

Relying on solid understanding of the place value chart and powers of ten, students multiply and divide to solve problems with a decimal number as a factor or quotient.

A. Multiply by 10 with and without a place value chartB. Multiply by 100 with and without a place value chartC. Multiply by 1,000 with and without a place value chartD. Multiply by 10, 100, and 1,000E. Complete a pattern of multiplication by 10 or 100F. Divide by 10 with and without a place value chartG. Divide by 100 with and without a place value chartH. Divide by 1,000 with and without a place value chartI. Divide by 10, 100, and 1,000J. Identify and complete a pattern of division by 10 or 100K. Factor out powers of 10 to multiply numbers with a single non-zero digitL. Multiply numbers with a single non-zero digitM. Record the relationship between hundredths and thousandths using a place value chartN. Convert between ones, tenths, hundredths, and thousandthsO. Multiply a decimal number by 10 with and without a place value chartP. Multiply a decimal number by 100 with and without a place value chartQ. Multiply a decimal number by 1,000 with and without a place value chartR. Multiply a decimal number by 10, 100, and 1,000S. Complete a pattern of multiplication by 10, 100, and 1,000T. Convert between ones, tenths, hundredths, and thousandths in division problemsU. Divide a decimal number by 10 with and without a place value chartV. Divide a decimal number by 100 with and without a place value chartW. Divide a decimal number by 1,000 with and without a place value chartX. Divide a number by 10, 100, and 1,000Y. Complete a pattern of division by 10, 100, and 1,000Z. Represent repeated multiplication of 10 as 10 with an exponentAA. Represent 10 with an exponent as repeated multiplicationAB. Multiply a decimal number by 10 with an exponentAC. Divide a number by 10 with an exponent

Students use familiar symbols (<, =, >) to compare numbers to the thousandths place. They identify, compose, and arrange numbers of equal and unequal length.

A. Record a decimal number in expanded notationB. Compare numbers to the hundredths place with and without a place value chartC. Complete inequalities that compare numbers to the hundredths placeD. Arrange decimal numbers in order from smallest to greatest (Level 1)E. Arrange decimal numbers in order from smallest to greatest (Level 2)F. Arrange decimal numbers in order from smallest to greatest (Level 3)

Using a number line to provide context, students first determine the midway point between two decimal numbers. They then progress to rounding using the number line and the midway point. Finally, students round decimal numbers to any given place value without use of the number line.

A. Determine the midway point between two decimal numbers on a number lineB. Determine whether a decimal number is greater or less than halfway between two points on a number lineC. Compose and apply a rule for rounding numbersD. Determine whether a decimal number rounds up or downE. Round a given number by first determining its nearest tenthsF. Round a given number to the hundredths, tenths, and ones placeG. Round a decimal number to a given place value (Level 1)H. Round a decimal number to a given place value (Level 2)I. Round a decimal number to a given place value (Level 3)J. Round a decimal number to a given place value (Level 4)

Based on the familiar disk model, students add and subtract numbers to the thousands place. They add and subtract in equations that require regrouping and learn to use the standard algorithm (column addition and column subtraction).

A. Add numbers to the hundredths place with regrouping using a disk modelB. Add numbers to the thousandths place with regrouping using a disk modelC. Add numbers to the thousandths place with regrouping using column addition and a disk modelD. Add numbers to the thousandths place with regrouping using column additionE. Subtract numbers to the hundredths place with regrouping using a disk modelF. Subtract numbers to the thousandths place with regrouping using a disk modelG. Subtract numbers to the thousandths place with regrouping using column subtraction and a disk modelH. Subtract numbers of different lengths to the thousandths place with regrouping using column subtraction and a disk modelI. Subtract numbers to the thousandths place with regrouping using column subtraction

Students take the first steps in understanding multiplication of a decimal number. Working with a single-digit whole number and a decimal number, students work step-by-step through the process using the familiar disk model. They trade disks to model regrouping and explore the importance of decimal point placement.

A. Multiply a decimal number with regrouping using a disk modelB. Multiply a decimal number with regrouping using a disk model and the standard algorithmC. Compare multiplying a whole number with multiplying a digit number with the same digitsD. Multiply a decimal number by converting it to a whole number and converting the product back to a decimal

Students rely on familiar models and procedures to apply their division knowledge to decimals. Step-by-step, they learn to correctly work through regrouping, using a new place value, using zeros, and placing a decimal in their quotient.

A. Divide a decimal number by a single-digit number based on a modelB. Divide a decimal number by a single-digit number with and without regrouping based on a modelC. Divide a decimal number by a single-digit number with and without regrouping based on a modelD. Divide a decimal number by a single-digit number with regrouping to a new place value based on a modelE. Divide a decimal number by a single-digit number with and without regrouping using long division and a modelF. Use long division to divide a decimal number by a single-digit number with and without regroupingG. Use long division to divide a decimal number by a single-digit number with quotients that include 0H. Use long division to divide a decimal number by a single-digit number with regrouping to a new place value

### MODULE 2. Multi-Digit Whole Number and Decimal Fraction Operations

Students work with round numbers in the tens, hundreds, and thousands to see how factoring out can make mental multiplication easier. In doing so, they apply properties of multiplication.

A. Factor out 10, 100, or 1,000 from a given numberB. Solve multiplication problems using the associative and commutative propertiesC. Solve a multi-digit multiplication problem using factoring out and properties of multiplication (Level 1)D. Solve a multi-digit multiplication problem mentallyE. Solve a multi-digit multiplication problem using factoring out and properties of multiplication (Level 2)F. Round multi-digit numbers to estimate the area of a rectangleG. Round multi-digit numbers to estimate the product

Students hone their use of the standard algorithm for multiplication, working with multi-digit numbers. They master the use of regrouping and working across zeros. To further their conceptual understanding, the standard algorithm is presented alongside other strategies, such as the area model and factoring out powers of 10.

A. Identify sum, difference, product, and quotient in equationsB. Compose simple numerical expressions from textC. Compose addition and multiplication expressions with multiple addends or factorsD. Compose complex numerical expressions based on a model (Part 1)E. Compose complex numerical expressions based on a model (Part 2)F. Compose complex numerical expressions based on a model (Part 3)G. Multiply using the standard algorithm (1-digit by 3-digit)H. Multiply using the standard algorithm (1-digit by 4-digit)I. Factor out powers of 10 to simplify multiplication expressionsJ. Solve related multiplication expressions after factoring out powers of 10K. Multiply by a number with a power of 10 mentallyL. Multiply by a number with a power of 10 using the standard algorithmM. Multiply using an area model and the standard algorithmN. Multiply using the standard algorithm (3-digit by 3-digit) (Part 1)O. Multiply using the standard algorithm (3-digit by 3-digit) (Part 2)P. Multiply using the standard algorithm (3-digit by 4-digit) (Part 1)Q. Multiply using the standard algorithm (3-digit by 4-digit) (Part 2)R. Multiply using the standard algorithm (2-digit by 5-digit)

Students further their understanding multiplication of a decimal number by increasing the number of digits in factors. Working with a 2- or 3-digit whole number and a decimal number in the tenths or hundredths, students work step-by-step through the process using the standard algorithm. They learn how to place a decimal in their answer and how to estimate to check the reasonableness of their answer.

A. Multiply a 2-digit decimal number by a 2-digit whole number using partial products with an area modelB. Multiply a 2-digit decimal number by a 2-digit whole number using the standard algorithm (Level 1)C. Multiply a 3-digit decimal number by a 2-digit whole number using the standard algorithm (Level 1)D. Multiply a 2- or 3-digit decimal number by a 2-digit whole number using the standard algorithm (Level 2)E. Multiply a 2- or 3-digit decimal number by a 2-digit whole number using the standard algorithm (Level 3)F. Multiply a decimal number by a round number by factoring out powers of 10G. Multiply a decimal number by a round numberH. Estimate the product of a decimal number and a 3-digit whole number (Part 1)I. Estimate the product of a decimal number and a 3-digit whole number (Part 2)J. Estimate the product of a decimal number and a 3-digit whole number then solve using the standard algorithm

Students rely on their understanding of powers of 10, division, place value, and rounding to divide multi-digit whole numbers mentally.

A. Divide round numbers by powers of 10B. Divide by factoring out powers of 10 from the divisorC. Divide multi-digit round numbers mentallyD. Round a multi-digit number to a given place (Level 1)E. Round a multi-digit number to a given place (Level 2)F. List the multiples of a given 2-digit round numberG. Round a 3-digit number to the nearest multiple of a given 2-digit round number (Level 1)H. Round a 3-digit number to the nearest multiple of a given 2-digit round number (Level 2)I. Estimate a quotient by finding the nearest multipleJ. Estimate a quotient of a multi-digit division equation (Level 1)K. Estimate a quotient of a multi-digit division equation (Level 2)

Students look under the hood of division to really understand the concept of a remainder as well as the steps involved in long division. Students work with one- or two- and three-digit dividends and one- and two-digit divisors. They use the standard algorithm for long division, but approach it in different ways to build math flexibility.

A. Divide a group of objects into groups of given size with a remainderB. Find the quotient and remainder by using multiples of the divisorC. Find the quotient and remainder by subtracting the divisor from the dividend (Part 1)D. Find the quotient and remainder by subtracting the divisor from the dividend (Part 2)E. Estimate the quotient, then solve using long division with a 1-digit quotient (Part 1)F. Estimate the quotient, then solve using long division with a 1-digit quotient (Part 2)G. Solve using long division with a 1-digit quotientH. Solve using long division with a 1-digit quotient (overestimate)I. Solve using long division with a 1-digit quotient (underestimate)J. Solve using long division with a 1-digit quotientK. Solve using long division with a 2-digit quotient (Part 1)L. Solve using long division with a 2-digit quotient (over and underestimate)M. Solve using long division with a 2-digit quotient (Part 2)N. Solve using long division with a 3-digit quotientO. Solve using long division with a 3-digit quotient (over and underestimate) (Part 1)P. Solve using long division with a 3-digit quotient (over and underestimate) (Part 2)

Students look under the hood of division to really understand the concept of a remainder as well as the steps involved in long division. Students work with one- or two- and three-digit dividends and one- and two-digit divisors. They use the standard algorithm for long division, but approach it in different ways to build math flexibility.

A. Rename decimal numbers in unit formB. Rename a number in unit form as a decimal numberC. Rename a whole number in unit form and decimal formD. Divide a decimal by a whole number (with and without using unit form)E. Divide a decimal number by 10 or 100F. Divide a decimal number by a multiple of 10 or 100G. Estimate the quotient of a decimal number divided by a 2-digit number (Level 1)H. Estimate the quotient of a decimal number divided by a 2-digit number (Level 2)I. Solve long division to the tenths placeJ. Solve long division to the hundredths placeK. Solve long division of a decimal number (Level 1)L. Solve long division of a decimal number (Level 2)M. Solve long division of a decimal number (over and underestimate)N. Solve long division of a decimal number (Level 3)O. Use long division to solve a word problem with a decimal quotientP. Use long division to solve area problems with a decimal quotient

### MODULE 3. Addition and Subtraction of Fractions

Students are introduced to the basics of fraction equivalency. They learn to multiply to find an equivalent fraction and to divide to reduce a fraction. The concepts of common factors and greatest common factor are also introduced and applied.

A. Label the numerator and denominator in a fractionB. Write an equivalent fraction (larger) based on a given multiple or denominatorC. Write an equivalent fraction (smaller) based on a given divisor, numerator, or denominatorD. Complete equivalent fractionsE. Identify common factors of two given numbersF. Identify a common factor of two given numbers and divide both by the common factorG. Reduce a fraction to its simplest form by dividing by the greatest common factor

Students rely on their knowledge of fraction equivalence to work through all aspects of adding and subtracting with fractions and mixed numbers. With plenty of visual support and step-by-step prompting, they work with like and unlike denominators. Students learn to convert between mixed numbers and fractions to solve problems, write their answer in simplest form, and solve word problems.

A. Add fractions with like denominatorsB. Rewrite an improper fraction as a mixed numberC. Add fractions with like denominators and rewrite the sum as a mixed numberD. Divide shapes into an equal number of parts (precursor to finding common denominators)E. Add fractions with unlike denominators (multiply denominators to find a common denominator)F. Rename fractions with unlike denominators (Level 1)G. Rename fractions with unlike denominators (Level 2)H. Add fractions with unlike denominators and rewrite the sum as a mixed numberI. Add fractions with unlike denominators and rewrite the sum in simplest form (Part 1)J. Add fractions with unlike denominators and rewrite the sum in simplest form (Part 2)K. Subtract fractions with like denominatorsL. Subtract fractions with unlike denominators (multiply denominators to find a common denominator)M. Subtract fractions with unlike denominatorsN. Rewrite a mixed number as an improper fractionO. Subtract a fraction from a mixed number with like denominators (rename the mixed number as a fraction)P. Subtract a fraction from a mixed number with unlike denominators (rename the mixed number as a fraction)Q. Subtract a fraction from a mixed number with unlike denominators and rewrite the difference in simplest formR. Subtract a fraction from a mixed number with unlike denominators to solve a word problemS. Subtract a fraction from 1 whole to solve a word problemT. Subtract two fractions from 1 whole to solve a word problemU. Add fractions to solve a word problem

Students increase the complexity of the addition and subtraction operations they can solve by using mixed numbers. They reinforce and apply their understanding of number equivalence as they rename numbers to solve problems.

A. Add a mixed number and a whole number with like denominatorsB. Subtract a fraction or a mixed number from a whole number with like denominators with and without a number lineC. Add a mixed number and a fraction with like denominatorsD. Add mixed numbers with like denominatorsE. Add mixed numbers with unlike denominators (Level 1)F. Add mixed numbers with unlike denominators (Level 2)G. Subtract mixed numbers with like denominatorsH. Subtract mixed numbers with unlike denominators (Level 1)I. Subtract a fraction from a mixed number with like denominators (rename the mixed number)J. Subtract mixed numbers with unlike denominators (Level 2)K. Subtract mixed numbers with unlike denominators (Level 3)

To support more complex understanding of operations with fractions, students are supported by visual models, the number line, and diagrams. They apply their knowledge of fractions to estimate sums and differences and solve multi-step word problems with mixed numbers.

A. Compare fractions with unlike denominators to ½ to estimate the sumB. Compare fractions with unlike denominators to a missing unit to estimate the sumC. Compare fractions with unlike denominators to estimate the difference of a mixed number minus a fractionD. Add multiple mixed numbers and fractionsE. Solve a multi-step word problem with mixed numbers with unlike denominators (Part 1)F. Solve a multi-step word problem with mixed numbers with unlike denominators (Part 2)

### MODULE 4. Multiplication and Division of Fractions and Decimal Fractions

Students combine their knowledge of measurement, rounding, and mixed numbers to create line plots. They then analyze the data, requiring them to perform operations with mixed numbers.

A. Round to the nearest half inch on a rulerB. Round to the nearest half inch on a ruler to create a line plot and analyze the dataC. Round to the nearest quarter inch on a rulerD. Round to the nearest quarter inch on a ruler to create a line plot and analyze the dataE. Round to the nearest eighth of a foot on a rulerF. Round to the nearest eighth of an inch on a ruler to create a line plot and analyze the data

To solidify their understanding of fractions as division, students work to convert between the two, using fractions greater than and less than one. They then work step by step to make sense of the remainder of a division problem as a fraction. Equipped with this understanding, students solve increasingly complex division word problems.

A. Rewrite division of whole numbers as a fraction based on a modelB. Rewrite division of whole numbers as a fraction and match a fraction to its related division equationC. Relate division to fractionsD. Relate division to fractions greater than oneE. Divide and report the remainder as a fraction based on a modelF. Rename a fraction greater than one as a mixed number (Level 1)G. Rename a fraction greater than one as a mixed number (Level 2)H. Solve fraction word problems based on a model (Level 1)I. Solve fraction word problems based on a model (Level 2)J. Solve fraction word problems based on a model (Level 3)K. Solve fraction word problems based on a model (Level 4)L. Solve fraction word problems based on a model (Level 5)

Students begin by finding a unit fraction of a whole number and other fractions of a whole number using familiar models. They then relate that process to multiplication. To multiply a whole number by a fraction, students learn to find common factors and reduce either before or after multiplying.

A. Determine fractions of a whole number based on a model (Level 1)B. Determine fractions of a whole number based on a model to solve a word problemC. Determine fractions of a whole number based on a model (Level 2)D. Determine fractions of a whole number based on a model (Level 3)E. Determine a whole number given a fraction of that number based on a modelF. Multiply a whole number by a fractionG. Relate a fraction of a whole number to multiplication and solveH. Determine a fraction of a measurement by converting units and multiplyingI. Determine common factors of two whole numbersJ. Divide whole numbers by a common factorK. Reduce a fraction by dividing by a common factorL. Reduce factors before multiplying a whole number by a fraction (Level 1)M. Reduce factors before multiplying a whole number by a fraction (Level 2)N. Multiply a whole number by a fraction by reducing before or after multiplying

Students synthesize their understanding of fractions and operations to build and solve expressions. Familiar models support their learning, and word problems put the skills in context.

A. Match operations to the terms sum, difference, product, and quotientB. Compose an expression based on textC. Compose a compound expression based on text (Part 1)D. Compose a compound expression based on text (Part 2)E. Compose a compound expression based on text (Part 3)F. Compose a compound equation based on a model and solve (Part 1)G. Compose a compound equation based on a model and solve (Part 2)H. Solve compound equations with parentheses and fractionsI. Solve a word problem by multiplying a whole number by a fraction (Level 1)J. Solve a word problem by multiplying a whole number by a fraction (Level 2)

Students learn to multiply fractions by starting with unit fractions and the support of an area model. They then progress to multiplication that involves mixed numbers, reducing, and units of measure.

A. Multiply unit fractions using an area modelB. Multiply fractions using an area modelC. Multiply fractions (reduce before multiplying)D. Multiply fractions (reduce before or after multiplying)E. Solve word problems by multiplying fractions using an area modelF. Rename a mixed number as a fraction to multiply by a fractionG. Convert measurements by multiplying a whole number by a fractionH. Convert measurements by multiplying fractionsI. Convert multiplication by a decimal to multiplication by a fraction and solveJ. Multiply by 0.1 using a place value chartK. Multiply by 0.01 using a place value chartL. Multiply by 0.1 or 0.01M. Decompose a decimal number to multiplyN. Determine the placement of the decimal point in the product of two decimal numbersO. Multiply two decimal numbers using column multiplication (Part 1)P. Multiply two decimal numbers using column multiplication (Part 2)Q. Multiply two decimal numbers using column multiplication (Part 3)

Students explore the effects of multiplying by less than, equal to, and greater than 1. They solve multiplication problems, provide missing factors, and complete inequalities to solidify their understanding.

A. Multiply a fraction by a fraction equal to 1B. Identify a missing factor as a fraction equal to 1C. Identify patterns in multiplying by fractions less than, equal to, and greater than 1D. Use <, =, and > to compare the result of multiplying by fractions less than, equal to, and greater than 1E. Identify a fraction that will complete a multiplication inequalityF. Convert a fraction less than one to decimal form (Level 1)G. Convert a fraction greater than one to decimal formH. Convert a fraction less than one to decimal form (Level 2)I. Convert a fraction less than one to decimal form using divisionJ. Convert a fraction greater than one to decimal form using divisionK. Determine the outcome of multiplication using <, =, or > (Part 1)L. Complete inequalities involving multiplication by a decimal numberM. Determine the outcome of multiplication using <, =, or > (Part 2)N. Determine the outcome of multiplication using <, =, or > (Part 3)

Students rely upon their understanding of multiplying fractions to learn how to divide fractions. With the assistance of familiar models such as tape diagrams and area models, they learn different ways to approach dividing with fractions. At this stage, they use unit fractions with whole numbers and unit fractions with unit fractions.

A. Rewrite an equation with multiplication by a fraction as a division equation based on a modelB. Compose a division equation with a fraction based on a modelC. Divide a whole number by a unit fraction based on a tape diagramD. Relate division by a unit fraction to multiplication by the denominatorE. Divide a whole number by a unit fraction by multiplying by the denominatorF. Divide a whole number by a unit fractionG. Divide a unit fraction by a whole number based on a tape diagram (Part 1)H. Divide a unit fraction by a whole number based on a tape diagram (Part 2)I. Divide a unit fraction by a whole numberJ. Multiply a unit fraction by a unit fraction with and without an area model (Part 1)K. Multiply a unit fraction by a unit fraction with and without an area model (Part 2)L. Relate division by a whole number to multiplication by a unit fractionM. Solve division equations with unit fractions and whole numbersN. Multiply a decimal number by a power of tenO. Simplify a fraction using the basic property of fractionsP. Convert a fraction to a given denominator using the basic property of fractionsQ. Convert between division expressions and fractionsR. Complete fraction expressions using the basic property of fractionsS. Convert fractions with decimal denominators to fractions with whole number denominators (Level 1)T. Convert fractions with decimal denominators to fractions with whole number denominators (Level 2)U. Convert fractions with decimal denominators to fractions with whole number denominators (Level 3)V. Convert fractions with decimal denominators to fractions with whole number denominators (Level 4)W. Convert division expressions with decimal divisors to expressions with whole number divisors (Level 1)X. Convert division expressions with decimal divisors to expressions with whole number divisors (Level 2)

### MODULE 5: Algebraic Expressions

Topic Description: Students solve increasingly complex missing addend equations. In these pre-algebra equations, the challenge is not in the number values but in the logic of how numbers and equations can be combined to solve for numbers represented by symbols.

A. Solve missing addend equationsB. Solve multi-step missing addend equationsC. Solve for missing addends in paired equations (Level 1)D. Solve for missing addends in a set of three equationsE. Solve for missing addends in paired equations (Level 2)F. Solve missing addend equations containing a 0G. Solve for missing addends in paired equations containing a 0