Expanding Your Horizons

A copymaster of compact numeral cards is provided at the end of these notes.
Make sure that the students know how to use the cards. The arrow on the cards helps the students to align the numeral cards correctly so that the compact number is visible. You may need to show some students how to organise the cards to make a number by placing the card with the largest number on the bottom and then
the other cards on top in ascending order. Have the students organise their set of cards in place value order and in size order.
Before the students attempt the questions, have them experiment with the cards to make numbers using different combinations. Ensure that they vary the number of cards so that they see the “0” used as a placeholder. Watch out for students who try to use two cards from the same column because this shows that they do not understand the cards.
Question 1 is a good activity to develop a sense of number size and place value.
You could extend question 2 by challenging the students to find all the possible ways to make the numbers.
This would encourage them to use a systematic approach to finding all the combinations. In question 3, the students need to work out the quantity as well as the operation required to change the display. Have them estimate a sensible answer before calculating the result.

Answers to Activity
1. a. 78
b. 278
c. 170
d. 3 978
e. 5 978
f. 5 000
2. a. 56 + 34 or 54 + 36
b. 178 + 254, 174 + 258, 158 + 274, or 154 + 278
c. 3 170 + 5 930, 3 130 + 5 970, 3 970 + 5 130, or 3 930 + 5 170
d. 7 206 + 5 904, 7 204 + 5 906, 7 906 + 5 204, 7 904 + 5 206, 7 136 + 5 974, 7 134 + 5 976, 7 176 + 5 934, 7 174 + 5 936, 7 936 + 5 174, 7 934 + 5 176, 7 976 + 5 134, or 7 974 + 5 136
3.