In this unit students explore the number patterns created when tins are stacked in different arrangements and keep track of the numbers involved by drawing up a table of values.
Patterns are an important part of mathematics. It is valuable to be able to recognise the relationships between things. This enhances understanding of how things are interrelated and allows us to make predictions.
Patterns also provide an introduction to algebra. The rules for simple patterns can be discovered in words and then written using more concise algebraic notation. There are two useful rules that we concentrate on here.
It should be noted that there are many rules operating in these more complicated patterns. Encourage students to look for any relation between the numbers involved.
In this unit we ask students to construct tables so that they can keep track of the numbers in the patterns. The tables will also make it easier for the students to look for patterns.
In addition to the algebraic focus of the unit there are many opportunities to extend the students computational strategies. By encouraging the students to explain their calculating strategies we can see where the students are in terms of the Number Framework. As the numbers become larger expect the students to use a range of part-whole strategies in combination with their knowledge of the basic number facts.
This unit can be differentiated by varying the scaffolding provided or altering the difficulty of the tasks to make the learning opportunities accessible to a range of learners. For example:
The context in this unit can be adapted to recognise diversity and student interests to encourage engagement. For example:
Today we look at the number patterns in a tower of tins (tini).
Show the students the arrangement:
How many tins are in this arrangement?
How many tins will be in the next row (kapa)?
Then how many tins will there be altogether?
How did you work that out?
Encourage the students to share the strategy they used to work out the number of tins. “I can see 4 tins and know that you need 5 more on the bottom. 4 + 5 = 9”
“I know that 1 + 3 + 5 = 9 because 5+3= 8 and 1 more is 9.”
[These strategies illustrate the student’s knowledge of basic addition facts.]
Show the students the next arrangement of tins. They can check that their predictions were correct.
How many tins will be in the next row?
Then how many tins will there be altogether?
How did you work that out?
Add seven tins to the arrangement and ask the same questions. As the numbers are becoming larger expect the range of strategies used to be more varied.
“16 + 9 = 25. I counted on from 16.” [advanced counting strategy]
“16 + 10 = 26 so it is one less which is 25.” [part-whole strategy]
Over the next 2-3 sessions the students work with a partner to investigate the patterns in other stacking problems. Consider pairing together students with mixed mathematical abilities (tuakana/teina). We suggest the following introduction to each problem.
Write the following questions on the board for the students to consider as they solve the problem.
How many tins are in the first row?
How many are in the second row?
By how much is the number of tins changing as the rows increase?
What patterns do you notice?
Can you predict how many tins would be needed for the bottom row if the stack was 15 rows high?
Explain the strategy you are using to count the tins to your partner?
Did you use the same strategy?
Which strategy do you find the easiest?
Problem 1:
A supermarket assistant was asked to make a display of sauce tins. The display has to be 10 rows high.
How many tins are needed altogether?
What patterns do you notice?
Problem 2:
A supermarket assistant was asked to make a display of sauce tins. The display has to be 10 rows high.
How many tins are needed altogether?
What patterns do you notice?
Problem 3:
A food demonstrator likes her products displayed using a cross pattern. The display has to be 10 products wide.
How many products are needed altogether?
What patterns do you notice?
In this session the students create their own “growth” pattern for others to solve.
Dear parents and whānau,
In maths this week we have been looking at patterns. Patterns are an important part of mathematics. It is always valuable to be able to recognise the relationships between things to help us see how things are interrelated and allow us to make predictions.
The patterns below are to do with buildings. We have been learning about how patterns like these can be continued. An important part of this has been learning to use tables to keep track of the pattern and the relationships between terms.
Ask your child if they can continue the pattern below and say what patterns they notice in the numbers. Can they draw or fill out a table to show how the pattern would progress? Can you work out how many crosses would be in the triangle with 15 crosses along the bottom?
Number of crosses high | Number of crosses along bottom | Number altogether |
1 | 1 | 1 |
2 | 2 | 3 |
3 | 3 | 6 |
Printed from https://nzmaths.co.nz/resource/supermarket-displays at 6:32pm on the 29th April 2024