LESSON PLAN

Multiplication and Division of Decimals

Apothem Team

Grade 6 · Computational Fluency

LESSON AT A GLANCE

Warm-up

5 min

Explore

15 min

Consolidate

10 min

Practice

12 min

Exit ticket

3 min

Warm-up

Quick estimation: 3.8 x 4.2. Approximately 4 x 4 = 16. Actual: 15.96. Close. 8.4 / 7. Approximately 8 / 7 is about 1. Actual: 1.2. Close. The habit of estimating before computing is the single most powerful error-checking tool for decimal operations.

Explore

Base-10 block array: use a 10x10 grid to model 0.4 x 0.3. Shade 4 columns and 3 rows. The overlap is a 4x3 = 12-square region out of 100 total = 12/100 = 0.12. This area model makes 0.4 x 0.3 = 0.12 visually concrete. Extend to 2.3 x 1.4 using multiple grids.

Consolidate

Practice

Students solve 8 decimal multiplication and division problems, showing estimates for each. Exit ticket: estimate then compute 3.6 x 2.5.

Exit ticket

Students solve 8 decimal multiplication and division problems, showing estimates for each. Exit ticket: estimate then compute 3.6 x 2.5.

TIP Require estimation before every decimal computation. Write the estimate, then compute, then compare. If estimate and answer differ by more than a factor of 2, recompute.

WORKED EXAMPLES

Calculate 2.4 x 1.5.

Estimate: 2.5 x 1.5 = 3.75. Compute: 24 x 15 = 360. Decimal places: 1+1=2. Result: 3.60 = 3.6. Reasonable (close to 3.75).

Calculate 6.3 / 7.

Estimate: 7/7 = 1. Compute: 63 tenths / 7 = 9 tenths = 0.9. Check: 0.9 x 7 = 6.3. Correct.

MATERIALS

•Base-10 block arrays for decimal multiplication

•Grid paper (10x10 grids for hundredths)

•Estimation recording sheets

•Real-world context cards

WATCH FOR

!Placing the decimal in the wrong position is the most common error: 2.4 x 1.5 = 36 instead of 3.6. Estimation (3.75) immediately catches this.

!Students may forget that division by a whole number keeps the decimal: 6.3/7 = 0.9, not 9. The quotient must be estimated before computing to anchor the expected magnitude.