Promoting Number Sense

Bobis, Mulligan and Lowrie (2004) suggest that promoting number sense is critical to the basic understanding of the application of mathematics in real-life situations, which according to Perso (2006) is the basis of being numerate. Bobis, Mulligan and Lowrie (2004) further highlight the concern of many educators, with regards to the lack number sense of many children who are used to performing number operations without a real conceptual understanding of what the operations mean. As a result, they do not assess the reasonableness of their answers when solving algorithms.

My idea of this very simple resource came as a result of one of our workshop activities where we answered questions such as – Without working it out, is the answer of 35 + 17 more or less than 35 + 18? And why? The idea of this resource is that one double sided sign should be given to each child or group of children in a classroom (see below). The idea is that the teacher can call our questions similar to the one above, and ask the children to display if they think the answer will be more or less/ bigger or smaller. Then the teacher asks specific children to justify the position they have taken.

The benefits of using this resource:
· More children can answer the question at once (teacher can gain a wider indication of where each child is at in terms of their level of understanding)
· If everyone is doing it, it is does not put one child on the spot
· It is easier for teachers to take note of each child or small group of children’s answers compared with if the children are simply calling their answers out

The following are some questions which can be used to assess number sense:

Addition
Without working the sums out, tell me...
· 229 + 30, is the answer bigger than 229 or smaller than 229? Why?
· Is 36 + 35 more or less than 39 + 35? Why?
· Is 37 + 35 more or less than 37 + 38? Why?
· Is 27 + 25 more or less than 37 + 25? Why?
· Is 27 + 35 more or less than 37 +39? Why?

Subtraction
Without working out the difference, tell me...
· 14 - 9 is the answer bigger than 14 or smaller than 14?
· Is 28 – 19 more or less than 28-22? Why?
· Is 39 – 25 more or less than 38-25? Why?
· Is 45 – 28 more or less than 45 – 38? Why?
· Is 64 – 18 more or less than 66 – 18? Why?

Multiplication
Without working out the product, tell me...
· Is 105 × 4 more or less than 105? Why?
· 3 × 5 more or less than 9 × 5? Why?
· Is 4 × 7 more or less than 7 × 5? Why?
· Is 6 × 9 more or less than 9 × 5? Why?
· Is 12 × 44 more or less than 13 × 44? Why?

Division
Without finding the quotient, tell me...
· Is 300 ÷ 44 more or less than 300? Why?
· Is 13 ÷ 5 more or less than 12 ÷ 5? Why?
· Is 66 ÷ 3 more or less than 66 ÷ 2? Why?
· Is 49 ÷ 7 more or less than 49 ÷ 9? Why?
· Is 100 ÷ 3 more or less than 100 ÷ 2? Why?

References:

Bobbis, J., Mulligan, J., Lowrie, T. (2004). Mathematics for children: challenging children to think mathematically. Frenchs Forest: Pearson Education Australia.