GRADE 6 · DECIMAL MULTIPLICATION
The Decimal Press
Build the product first. The decimal point will have one honest place to go.
▶
The press is ready
Start the guided lesson to hear the voice-over as each model is built.
Narration and lesson sounds use the speaker control.
Stage 1 of 10Read the factors
Build
Tenths are pieces of one whole
Six tenths times four tenths is an area, not a decimal-point guess.
CONCRETE · TENTH PIECES
0.6
multiply the two lengths
0.4
0.6 = 6 tenths
0.4 = 4 tenths
0.4 = 4 tenths
Break each factor by place value
2+0.3
1+0.4
multiply every part by every part
1.4 × 3.7
REAL TOPIC EXAMPLE · QUESTION 1186707
Work on the whiteboard, then submit. Your submission unlocks the calculation receipt here.
1Multiply the digits.
2Count both factors' decimal places.
3Estimate to catch a misplaced point.
PICTORIAL · AREA MODEL
6 tenths wide4 tenths tall
24 overlap squares = 24 hundredths
PLACE-VALUE PRESS
0.6
×10
6
0.4
×10
4
product must ÷ 100
2 × 1
= 2
= 2
0.3 × 1
= 0.3
= 0.3
2 × 0.4
= 0.8
= 0.8
0.3 × 0.4
= 0.12
= 0.12
2 + 0.3 + 0.8 + 0.12 = 3.22
23
× 14
92
+ 230
322
3.22
2 × 1≈ 2
2.3 × 1.43.22
3.22 is near 2. A result like 32.2 is not.
ignore points: 14 × 37
14 × 37 = 518
1 + 1 = 2 decimal places
1.4 × 3.7 = 5.18
YOUR RECEIPT
1.4
×
3.7
verified: 5.18
ABSTRACT · NUMBER SENTENCES
0.6 × 0.4
tenths × tenths = hundredths
610 × 410 = 24100
0.6 × 0.4 = 0.24
multiply whole numbers
6 × 4 = 24
restore 1 + 1 places
24 ÷ 100 = 0.24
2.3 × 1.4
(2 + 0.3)(1 + 0.4)
2 + 0.8 + 0.3 + 0.12 = 3.22
2 total decimal places
23 × 14 = 322
322 → 3.22
The area model and the shortcut agree.
estimate before accepting
2.3 ≈ 2 and 1.4 ≈ 1
2 × 1 ≈ 2, so 3.22 is reasonable
1.4 × 3.7 = ?
Multiply 14 × 37, then restore two decimal places.
Digits → places → estimate
No guessing required.
No guessing required.
✓
Decimal placement verified
You built the meaning, used the shortcut, and checked the size.