Maryland Math 5.NOS.B.7

5.NOS.B.7 is a cluster heading. These are the individual standards under it.

• 5.NOS.B.7.a

  Apply estimation strategies to estimate products and quotients.

• 5.NOS.B.7.b

  Use concrete models, drawings, and arrays to multiply and divide.

• 5.NOS.B.7.c

  Use strategies based on place value (e.g., partial products, partial quotients) to multiply and divide.

• 5.NOS.B.7.d

  Use properties of operations and/or the inverse relationship between multiplication and division to multiply and divide.

• 5.NOS.B.7.e

  Represent and explain the computation by connecting concrete models, drawings, and/or equations to the meaning of multiplication and division.

01

What Students Need to Do

Students multiply and divide decimals in word problems. They estimate first, then use a grid, drawing, or place-value strategy to calculate. They explain how their model matches the problem.

02

What Mastery Looks Like

A student can show 0.4 × 0.3 as 12 hundredths on a grid and write 0.12. They can group 1.2 into 0.3s, get 4 groups, and check with 0.3 × 4 = 1.2.

03

Common Misconceptions

Students may write 0.4 × 0.3 = 1.2 because they ignore place value. Some think division always makes a number smaller, so they reject 1.2 ÷ 0.3 = 4. Others change the decimal in only one number when dividing.

04

How to Assess It

Ask: A 1.2-meter ribbon is cut into 0.3-meter pieces. Estimate how many pieces you will get, then show the exact answer with a tenths-strip drawing and an equation.

1. 01

   On a hundred grid, shade 4 columns and 3 rows in different colors, then count the overlap to find 0.4 × 0.3.

2. 02

   Ask, “Why is 1.2 ÷ 0.3 greater than 1.2?” Have partners defend their answers with tenths-strip sketches.

3. 03

   Deal cards marked 0.6 ÷ 0.2, 3, 0.4 × 0.3, and 0.12; match pairs and explain each with tenths or hundredths.

4. 04

   Show a grocery label for apples at $1.25 per pound; have students estimate and calculate the cost of 4 pounds.

• 6.NOS.B.3

  Fluently multiply and divide multi-digit decimals to the thousandths in context.

• 5.NOS.B.6

  Apply and extend previous understanding of addition and subtraction of whole numbers to add and subtract decimals to hundredths.

• 6.NOS.B.3.b

  Generalize whole number strategies to multiply and divide decimals.

• 5.NOS.D.16

  Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions in context.