Setting up swaps
These are level 2 number problems from the Figure It Out series. 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:
- Use addition facts to solve problems (Problems 1 and 2).
- Skip count in 2 s and 3 s (Problem 3).
Setting up swaps
Achievement objectives
NA2-1: Use simple additive strategies with whole numbers and fractions.
Required materials
- Figure It Out, Levels 2–3, Problem Solving, "Setting up swaps", page 19
See Materials that come with this resource to download:
- Setting up swaps (.pdf)
Activity
It is easy for students to draw a model of the problem using cards with the numerals 1 to 6, which they can then use to try out different possible solutions.
Taking account of the clues will limit the possibilities and make the problem quicker to solve.
The top block is 3:
The middle tower numbers add up to 5:
Students cannot make 10 with the remaining numbers if they arrange the middle tower like this:
The bottom blocks add up to 11:
Students may enjoy making up their own problems with these digits.
The first step is to work out which amounts of change are possible with two coins.
A table or tree diagram showing the change would be useful:
|
5 c |
10 c |
20 c |
50 c |
$1 |
|---|---|---|---|---|---|
5 c |
✓ |
|
|
|
|
10 c |
✓ |
✓ |
|
|
|
20 c |
✓ |
✓ |
✓ |
|
|
50 c |
✓ |
✓ |
✓ |
✓ |
|
$1 |
✓ |
✓ |
✓ |
✓ |
|
So the following amounts could be given as change:
10 c, 15 c, 20 c, 25 c, 30 c, 40 c, 55 c, 60 c, 70 c, $1, $1.05, $1.10, $1.20, or $1.50, in which case the article could cost $1.90, $1.85, $1.80, $1.75, $1.70, $1.60, $1.45, $1.40, $1.30, $1, 95 c, 90 c, 80 c, or 50 c, respectively.
You could discuss with students which of these amounts the chippies are more likely to cost.
A table is a good way to keep track of the amount that each person has saved:
|
Start |
Jan |
Feb |
Mar |
Apr |
May |
Jun |
Jul |
Aug |
Sep |
Oct |
Nov |
Dec |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Kuini |
$12 |
$14 |
$16 |
$18 |
$20 |
$22 |
$24 |
$26 |
$28 |
$30 |
$32 |
$34 |
$36 |
Romi |
$4 |
$7 |
$10 |
$13 |
$16 |
$19 |
$22 |
$25 |
$28 |
$31 |
$34 |
$37 |
$40 |
Students can quickly calculate each person’s savings by using the constant function on a calculator.
Kuini 12 + 2 = = = … (12 times)
Romi 4 + 3 = = = … (12 times)
(On some calculators, you have to press + twice to make the constant function work.)
As an extension, ask students:
- What would have happened if Romi had saved only $2 per month?
- Would the amounts in their piggy banks ever have been the same?
Students can act out the problem by making up three sets of A, B, C, and D cards. A good place to start is with the cards that are not wanted in each player’s hand. These cards are Simon (A), Cathy (C and D), and Beth (B). The players need to make two swaps to get the cards they need:
Simon (A) ↔ (D) Cathy, and Beth (B) ↔ (C) Cathy.
Students might investigate more complex swap situations, such as:
AAAB CCCB DDDB
Beth Cathy Simon
or where there are five cards in a set:
AAAEE CCCBB DDDEE
Beth Cathy Simon
1.
2.
$1.90, $1.85, $1.80, $1.75, $1.70, $1.60, $1.45, $1.40, $1.30, $1, 95 c, 90 c, 80 c, or 50 c
3.
August
4.
2
The quality of the images on this page may vary depending on the device you are using.