'Multiplication: Building bots' is a reimagining of classic V8 sequence 'Making robots'
- On the 'In this sequence' tab you'll find all the lessons in this sequence, a suggested implementation plan and curriculum alignment.
- The 'Behind this sequence' tab shows how key mathematical ideas develop over the sequence.
- Have you taught this sequence? Use the Feedback button to let us know how it went!
Lessons in this sequence
Task 1 • Making robots
Students think about the number of robots they can make with three heads, three bodies and three types of legs. Students start by making one robot and checking whether anyone else has made the same robot as them.
Task 2 • Robot combinations
Students play a game to make as many unique robots as they can, using three heads, three bodies and three types of legs. They then sort and classify their robots.
Task 3 • Robot production line
Students use the array to sort robot parts and identify the robots that are missing for their group. They develop their understanding of the “for each” idea to find the number of unique robots which can be made for a given number of parts.
Task 4 • More robot combinations
Students build robots using heads, bodies and sets of legs. They find the number of unique robots which can be made for each of these parts.
Suggested implementation
We recommend implementing this teaching sequence over four consecutive days, with the lesson timings provided in the documentation designed to support this approach.
This sequence aligns with the Australian Curriculum: Mathematics Year 3 content descriptors and achievement standard, and it uses the arrays as a model to support students to reason about the multiplicative idea of “for each”.
The sequence uses the arrays as a model to systematically make all possible unique robot part combinations. We suggest students need to be familiar with, and have a sound understanding of, using arrays to reason about multiplication. Therefore, it would be helpful to teach Multiplication: reSolve Market before teaching Multiplication: Building bots.
We also see potential for this sequence to be used with Year 4 students to consolidate their multiplicative understanding of “for each”, to deepen their understanding of the relationship that exists between each of the parts with respect to every possible combinations which can be made.
The Year 5 teaching sequence Multiplication: What is a Plocoroo? further explores the idea of the Cartesian product and the multiplicative idea of “for each”.
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Curriculum and syllabus alignment
Year 3
Students use mathematical modelling to solve practical problems involving single-digit multiplication and division, recalling multiplication facts for twos, threes, fours, fives and tens, and using a range of strategies.
Number
Multiply and divide one- and two-digit numbers, representing problems using number sentences, diagrams and arrays, and using a variety of calculation strategies
Algebra
Recall and demonstrate proficiency with multiplication facts for 3, 4, 5 and 10; extend and apply facts to develop the related division facts
Each task in this sequence uses the Launch-Explore-Connect-Summarise task structure.
Teaching multiplication in the classroom often focuses on creating equal groups and then extends this idea to the use of arrays. The concept of “equal groups” is a very important aspect of multiplication, but multiplication comes in multiple forms, and all should be explored to build fluency with the operation. One of these forms is “for each”. For example, for each cake there are three candles or for each egg use half a cup of flour. This resource explores the concept of “for each” through Cartesian product, although Cartesian product is not specifically mentioned in the Australian Curriculum: Mathematics.
The Cartesian product of two sets is the set of all possible pairs formed by matching each item in one set with every item in the other set. This is a “for each” relationship. It can be represented as an array, where one set labels the rows and the other labels the columns, and each row-column intersection represents one pair. When more than two sets are involved, this extends to all possible combinations, taking one item from each set.
In this sequence, students are presented with three robot heads, three bodies and three types of legs. They are asked to work out how many combinations are possible using these different sets. Students will see that for each head there are three bodies, and that for each body there are three types of legs. An array structure is used to help students work out the total in the collection.
Sequence framework
| Learning goals | Students’ mathematical activity | Representation | Context | |
| Task 1 | Robot parts can be combined in multiple ways. Each robot combination is unique but related to several others. | Students explore making combinations of three heads, three bodies and three types of legs. | Robot body part (head, body and legs) cards to generate robots. | Generating different robots using three different heads, bodies and legs. |
| Task 2 | For each robot head, there are different bodies, and for each body there are different sets of legs which can be combined to create every possible unique robot combination. | Students explore the number of possible combinations of three heads, three bodies and three types of legs. | Robot body part playing cards to generate unique robots. | Playing Robot Go fish to generate unique robots with three different heads, bodies and legs. |
| Task 3 | Arrays make the multiplicative structure in “for each” problems visible by showing combinations as rows and columns. | Students use arrays to organise the robots they have generated based on each body part, to identify missing combinations. | An array to organise robot card combinations. | Identifying the missing robots for each body part. |
| Task 4 | The multiplicative structure in “for each” problems can be represented in systematic ways to find the total number of combinations. | Students use arrays to systematically organise robots generated for a different number of body parts, to find all combinations. They generalise and record these combinations. | Arrays and number sentences to generate and record unique robot combinations, and to generalise the mathematics. | Introduce an extra robot part to find all robots that can be made with a combination of hats, heads, bodies and legs. |
'Multiplication: Building bots' is a reimagining of classic V8 sequence 'Making robots'
- On the 'In this sequence' tab you'll find all the lessons in this sequence, a suggested implementation plan and curriculum alignment.
- The 'Behind this sequence' tab shows how key mathematical ideas develop over the sequence.
- Have you taught this sequence? Use the Feedback button to let us know how it went!