# Curriculum for Grade 5

## Driven by Pedagogy, Supported by Technology (and not vice versa),

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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)