# 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. Divide by 10 on a place value chart to move from thousands to thousandthsB. Multiply a decimal number by 10, 100, or 1,000 using a place value chartC. Multiply a decimal number by 10, 100, or 1,000 (Part 1)D. Multiply a decimal number by 10, 100, or 1,000 (Part 2)E. Divide a whole number by 10, 100, or 1,000 to get a decimal number using a place value chartF. Divide a whole number by 10, 100, or 1,000 to get a decimal number (Part 1)G. Divide a whole number by 10, 100, or 1,000 to get a decimal number (Part 2)H. Represent repeated multiplication of 10 as 10 with an exponentI. Represent 10 with an exponent as repeated multiplicationJ. Multiply a decimal number by 10 with an exponentK. Divide a whole 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. Use <, =, and < to compare numbers to several decimal placesC. Compare numbers to several decimal placesD. 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 to the tenths placeB. Round a number to a given place value using a number line and a midway pointC. Round a number to the hundredths place value using a number line and a midway pointD. Round a number to a given place valueE. Round a number to various given place values

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)

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 equationK. Estimate a quotient of a multi-digit division equation (Level 2)

### 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)