Cluster 6

Cluster 6: Using Models to Multiply and Divide Whole Numbers, Decimals, and Fractions

5NBT7: Compute and solve real-world problems with multi-digit whole numbers and decimal numbers.

Multiply decimals with a product to thousandths using models, drawings, or strategies based on place value.
Divide a whole number by a decimal and divide a decimal by a whole number, using repeated subtraction or area models. Decimals should be limited to hundredths.
Use estimation strategies to assess reasonableness of answers.

5.NBT.6: Find quotients with remainders when dividing whole numbers with up to four-digit dividends and two-digit divisors using rectangular arrays, area models, repeated subtraction, partial quotients, and/or the relationship between multiplication and division.

Use models to make connections and develop the algorithm.

5.NBT.5: Demonstrate fluency with the multiplication of two whole numbers up to a three-digit number by a two-digit number using the standard algorithm.

5.NF.4: Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction, including mixed numbers.

Use area and length models to multiply two fractions, with the denominators 2, 3, 4.
Explain why multiplying a given number by a fraction greater than 1 results in a product greater than the given number and when multiplying a given number by a fraction less than 1 results in a product smaller than the given number.
Solve one-step word problems involving multiplication of fractions using models to develop the algorithm.

5.NF.7: Solve one-step word problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions using area and length models, and equations to represent the problem.

5.MD.1: Given a conversion chart, use multiplicative reasoning to solve one-step conversion problems within a given measurement system (customary or metric).

5.OA.2: Write, explain, and evaluate numerical expressions involving the four operations to solve up to two- step problems. Include expressions involving: