Explinations
Explain why lining up the decimal points is important when adding decimals.
Because lining up the decimals ensures that the digits in each place value (tenths, hundredths, thousandths) are added correctly.
3.2 + 4.85 = 3.685
They didn’t line up the decimals, so they added digits from different place values. 3.2 + 4.85 = 8.05
4.3 + 2.27
6.57
5.6 + 1.49
7.09
A granola bar weighs 1.25 g more with the wrapper.
The wrapper weighs 0.07 g.
How much does the granola bar weigh without the wrapper?
1.25 – 0.07 = 1.18 g
Why do we add extra zeros when adding or subtracting decimals.
Adding extra zeros to a decimal so both numbers have the same number of digits after the decimal, making addition/subtraction easier.
9.6 – 2.48 = 7.52
They subtracted without annexing a zero to make 9.60, and they incorrectly subtracted the decimal places. 9.60 – 2.48 = 7.12
8.05 – 3.6
4.45
12.05 – 7.68
4.37
Ben walked 2.4 km in the morning and 3.85 km in the afternoon. How far did he walk?
2.4 + 3.85 = 6.25 km
Explain why multiplying a number by 0.1 moves the digits one place to the right.
Multiplying by 0.1 makes the number ten times smaller, so each digit shifts one place to the right to show division by 10.
A student solved 0.7 × 0.5 = 0.35 and said “multiplying makes numbers bigger.”
Their reasoning is wrong because multiplying by a number less than 1 makes the product smaller. Their numerical answer is correct: 0.35.
0.24 × 0.3
0.072
0.348 × 0.6
0.2088
Sara bought 3.5 m of ribbon. Each project uses 0.25 m. How many projects can she make?
3.5 ÷ 0.25 = 14 projects
Why do we need to "jump decimals" when dividing a decimal by a decimal.
Because dividing by a decimal requires you to “make the divisor a whole number.” Whole-number divisors make division consistent. You shift the decimal in both numbers the same amount so the divisor becomes a whole number while keeping the quotient the same.
4.2 ÷ 0.7 = 0.06
They misplaced the decimal — dividing by less than 1 should make the answer bigger. 4.2 ÷ 0.7 = 6
4.8 ÷ 0.12
40
6.25 ÷ 0.125
50
A tank holds 18.75 L of water. Each bucket removes 2.5 L. How many full buckets are needed?
18.75 ÷ 2.5 = 7.5
Explain how you know where to place the decimal point when multiplying two decimals via stacking.
Count the total number of decimal places in both factors. The product must have that same total number of decimal places.
12.5 ÷ 0.25 = 0.5
They failed to shift the decimals correctly to make the divisor whole. 12.5 ÷ 0.25 = 50
3.275 × 0.04
0.131
(3.27 × 0.4) + (9.5 ÷ 0.5)
1.308 + 19 = 20.308
A bakery sells cookies for $0.65 each. The class buys 32 cookies. How much does the class spend?
0.65 × 32 = $20.80