Expanding your horizons
This is a level 3 number link activity from the Figure It Out series. It is focused on showing an understanding of place value for ones, tens, hundreds, and thousands. A PDF of the student activity is included.
About this resource
Figure It Out is a series of 80 books published between 1999 and 2009 to support teaching and learning in New Zealand classrooms.
This resource provides the teachers' notes and answers for one activity from the Figure It Out series. A printable PDF of the student activity can be downloaded from the materials that come with this resource.
Specific learning outcomes:
- Show an understanding of place value for ones, tens, hundreds, and thousands.
Expanding your horizons
Achievement objectives
NA3-1: Use a range of additive and simple multiplicative strategies with whole numbers, fractions, decimals, and percentages.
Required materials
- Figure It Out, Link, Number, Book Two, "Expanding your horizons", page 16
- a calculator
See Materials that come with this resource to download:
- Expanding your horizons activity (.pdf)
- Expanding your horizons CM (.pdf)
Activity
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.
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.
a. +820
b. +170
c. +744
d. -2744
e. -1918
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