Solve problems that involve adding and subtracting decimals.
Number Framework Stage 7
Unilink cubes
Using Materials
Problem: Hina has 4.3 metres of fabric and uses 1.7 metres to make a skirt. How much fabric does Hina have left over?
Students model 4.3 as four wrapped bars (wholes) and three small pieces (tenths). Students may do 4.3 – 1 = 3.3 at first. Then they may unwrap one bar, add the ten tenths to the three tenths, and remove seven tenths to leave six tenths: 4.3 – 1.7 = 2.6. Alternatively, they may unwrap one bar first to take away the seven tenths and then take away the one whole.
Notice whether students understand that the number after the decimal point always represents tenths, that the maximum digit in any place is 9, and that to perform subtraction calculations, it is usually necessary to break one whole into ten tenths.
Examples:
4.6 – 1.7 3.3 – 1.6 5 – 3.6 4.2 – 0.4
3.6 – 2.9 2.3 – 1.8 3 – 2.9 3.3 – 0.6
7.2 – 3.5 9.2 – 7.3 11 – 1.6 12.8 – 0.9
15.8 – 8.9 15.1 – 1.8 16 – 3.9 10.3 – 0.8
Using imaging
Problem: Work out 1.5 – 0.8.
Place one wrapped bar and five small pieces where the students can see but not touch them. Listen to see who talks the language of place value as they break the one whole into ten tenths and then subtract the eight tenths from the fifteen tenths. Students who are unable to solve the problem by imaging may need to fold back to “Using materials”.
Examples:
3 – 2.9 3.3 – 0.6 7.2 – 3.5 9.2 – 7.3 11 – 1.6 12.8 – 0.9 …
Using number properties
Students need to repeat this kind of problem until they can predict the answer and explain their reasoning without using or referring to materials.
Examples:
15.8 – 8.9 15.1 – 1.8 16 – 3.9 10.3 – 0.8 …
When teachers make up their own examples, the digit in the tenths column of the number being subtracted needs to be greater than the digit in the tenths column of the number it is being subtracted from. Thus 3.3 – 1.7 is suitable, but 5.6 – 3.4 is not.