Problem bits four
These are level 3 number and algebra 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 answers and teachers’ notes 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:
- Continue a sequential pattern (Problem 1).
- Share regions into fractions (Problem 2).
- Explore divisibility rules for 3 (Problem 3).
Problem bits four
Achievement objectives
NA3-1: Use a range of additive and simple multiplicative strategies with whole numbers, fractions, decimals, and percentages.
NA3-8: Connect members of sequential patterns with their ordinal position and use tables, graphs, and diagrams to find relationships between successive elements of number and spatial patterns.
Required materials
- Figure It Out, Levels 2-3, Problem Solving, "Problem bits four", page 24
See Materials that come with this resource to download:
- Problem bits four activity (.pdf)
Activity
Bit 1
Seven is one possible number to follow in the pattern. It is not the only solution.
For example:
Bit 2
Students may need a physical model of the problems, such as paper strips, to represent the problem. There may be a number of solution strategies.
Divide each doughnut into three equal bits and share the bits equally. Each person will end up with five thirds.
Give each person one whole doughnut, and divide the remaining two doughnuts into three equal bits. Each person will get a whole doughnut and two thirds.
Bit 3
Students will need to list the first multiples of three to see whether there is a pattern, that is 0, 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36 ...
If the ones digit pattern is shown on a digit wheel, students will see that every digit is used and that the ones digit pattern recurs (repeats):
Students can check whether the ones digit of a whole number is either 0 or 5 to see whether that number can be divided evenlyby five. They can test the divisibility for three by adding the digits of the number until they get a single-digt number. If this single-digit number is divisible by three, then the orginal number is divisble by three.
For example:
81 → 8 + 1 = 9 (nine is divisible by three and so is 81
74 → 7 + 4 = 11 → 1 + 1 = 2 (two is not divisible by three and nor is 74).
1.
7 is only one possible solution. There are other justifiable solutions, for example, 1, 2, 4, 8 (see notes).
2.
Yes. Different methods can be used to divide the doughnuts, but each person gets 12/3.
3.
One way is to check whether the sum of the digits is divisible by 3.
The quality of the images on this page may vary depending on the device you are using.