Solve addition and subtraction problems by compensating with tidy numbers.
Number Framework Stage 5
Number lines (Material Master 5-12)
Using Materials
Problem: Freddo the frog lives at number 28 on the number line. He wants to visit his friend at number 81. How far does he have to jump to get there? Stick the large number line on the board and record 28 + ? = 81.
Suggest Freddo will first jump to 30 because it is a “nice” or “tidy” number. Show this jump with an arrow and ring the jump of 2. Discuss how far Freddo has to go. Some students will jump by tens to 80 then go 1 more. Some will jump 50 then 1 more, and a few will jump 51 directly to 81. Show these jumps with arrows and ring the numbers. In all cases focus attention on the ringed numbers always giving the answer 53. Discuss which way is best. The students now do individual work with you observing their methods.
Examples. Give the students the first sheet from Material Master 5-12 and get them to write the following 7 problems down against each number line. 39 + ? = 61, 48 + ? = 81, 57 + ? = 85, 29 + ? 78, 18 + ? = 60, 27 + ? = 93, 36 + ? = 90
The students do the problems then discuss the answers back as a whole group.
Using Imaging
Problem: Solve 18 + ? = 73
Draw a large empty number line on the board and discuss where to place the 18 and 73. Without adding 30, 40, 50, 60 and 70 to the empty number line discuss how to jump from 18 to 20 then to 73 in two steps. So the only numbers on the number line are 18, 20 and 73. Record the answer 55.
Examples. Get the students to turn over their sheet to use the empty number lines. It has 7 empty number lines. Get them to write the following 7 problems down against each number line; 29 + ? = 62, 58 + ? =93, 27 + ? = 86, 29 + ? = 78, 48 + ? = 70, 29 + ? = 83, 46 + ? = 83