Add and subtract two-place decimals without a calculator

What you will learn

• Add and subtract two-place decimals without a calculator

Models used: number sentences, stories, tables.

Before you start

• Round decimals

Join pieces of the same size

Twenty-five hundredths means 25 little squares.

1. The whole grid has 100 equal squares. One full row is 10 hundredths, or one tenth.

   Twenty-five hundredths means 25 little squares.

   0.25

   One small square is one hundredth of the whole. Ten small squares make one tenth, so the same shaded amount can be described in more than one way.

   25/100 = 0.25 = 25%

2. The whole grid has 100 equal squares. One full row is 10 hundredths, or one tenth.

   Add 30 hundredths first. There are now 55 shaded squares.

   0.25 + 0.30 = 0.55

   One small square is one hundredth of the whole. Ten small squares make one tenth, so the same shaded amount can be described in more than one way.

   55/100 = 0.55 = 55%

3. The whole grid has 100 equal squares. One full row is 10 hundredths, or one tenth.

   Add the remaining 8 hundredths. The whole has 63 shaded squares.

   0.25 + 0.38 = 0.63

   One small square is one hundredth of the whole. Ten small squares make one tenth, so the same shaded amount can be described in more than one way.

   63/100 = 0.63 = 63%

4. The whole grid has 100 equal squares. One full row is 10 hundredths, or one tenth.

   Taking away those same 38 squares brings us back to 25.

   0.63 − 0.38 = 0.25

   One small square is one hundredth of the whole. Ten small squares make one tenth, so the same shaded amount can be described in more than one way.

   25/100 = 0.25 = 25%

Worked example: A new example, together

Calculate 9.44 + 0.8.

1. Track the value of the units, not just the digit strings. Read each value with the heading above its column.

   Say the name of each column and track any exchange between neighbouring columns.

   Both lengths must use the same-sized units. Join hundredths with hundredths; a hundred hundredths makes one whole.

   Track the value of the units, not just the digit strings.

   Starting amount	Amount added
   9.44	0.8

2. Track the value of the units, not just the digit strings. Read each value with the heading above its column.

   Line up decimal points so equal places meet.

   Track the value of the units, not just the digit strings.

   Starting amount	Amount added
   9.44	0.8

   Calculate 9.44 + 0.8.

   10.24 m

3. Track the value of the units, not just the digit strings. Read each value with the heading above its column.

   Work in hundredths: 944 + 80.

   Track the value of the units, not just the digit strings.

   Starting amount	Amount added
   9.44	0.8

4. Track the value of the units, not just the digit strings. Read each value with the heading above its column.

   Convert the result back: 10.24.

   Track the value of the units, not just the digit strings.

   Starting amount	Amount added
   9.44	0.8

5. Track the value of the units, not just the digit strings. Read each value with the heading above its column.

   Check the result against the question we started with.

   10.24 − 0.8 = 9.44. Removing the added length restores the start.

   We found 10.24 m. Both lengths must use the same-sized units. Join hundredths with hundredths; a hundred hundredths makes one whole.

   Track the value of the units, not just the digit strings.

   Starting amount	Amount added
   9.44	0.8

Common mistakes to discuss

• Lining up the right-hand ends. Align the decimal points, not the last digits. 5.4 + 3.47 is 8.87: the 4 is 4 tenths and must sit above the 4 tenths.

Check your understanding

• Add and subtract two-place decimals without a calculator
• explain decimal addition and subtraction using like units
• check the answer against the original quantities and units

Explain your reasoning to an adult, then try a fresh question in the interactive lesson. A result from one attempt is not proof of lasting mastery.