Multiplication: Building bots
View Sequence overviewFor 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.
Whole class
Building bots Slides
Each group
Robot playing cards printed onto A3 card and cut along the lines
Each student
Robot parts pictures
2 sheets of Robot templates
Glue stick
Two different colour counters (e.g. one red and one green counter)
Task
Revise: In the last task we made our own robots and estimated the number of different robots we think we can make with three different heads, bodies and legs.
Show students Slide 5 of the Building bots Slides, which contains the rules for playing Robot Go Fish!. Explain how to play Robot Go Fish!.
- Shuffle the cards and deal 7 cards to each player. Place remaining cards in a pile in the centre.
- Take turns to build a new robot or go fish:
- Build a new robot
- To build a new robot you must have a head, body and legs. The robot must be different to any others already built. Place the completed robot in front of you, then take 3 new cards from the pile.
- Go fish
- Pick another player and ask if they have a head, body or legs card. If they do, they must hand it over.
If they don’t have the correct parts card, they say “Go fish!” and you take one new card from the pile.
- Pick another player and ask if they have a head, body or legs card. If they do, they must hand it over.
- Build a new robot
- The game ends when there are no more cards left or when no more unique robots can be made.
- The winner is the player who makes the most unique robots.
- After each game, use the robot part pictures and your templates to create copies of each unique robot you’ve built.
Ask students to keep in mind their estimate for the number of different possible robots while they are playing.
Pose the task: Play Robot Go Fish! and make as many unique robots as you can.
Ask students to work in groups of 3-4. Provide each group with a set of Robot playing cards. Provide each student with a set of Robot parts pictures, a glue stick, and two sheets of Robot templates.
Allow students time to play Robot Go Fish! a couple of times. After their first game ask the students to use the Robot parts pictures and Robot templates to make copies of each of the robots that they have built in the game. After the second game, ask them to make copies of any new robots that they have built.
In preparation for a gallery walk, ask each group to sort and organise their robot combinations so that they are easy to see. This is an opportunity for students to describe what they notice about their robots, rather than the teacher explaining ways of sorting and organising.
Focus students’ attention on:
- ways of organising robots to make it clear to see related robots, for example:
- grouping by one body part.
- same robot combinations grouped together.
- organised in a line showing each change.
- organised in rows.
- ways of organising robots to see which ones still need to be made, for example:
- organising in rows, where each robot shows one part changed.
- organising in arrays to see the gap where a robot has not been made.
Context in mathematics
Context provides a ‘hook’ or entry point for students to begin solving the problem, and for them to think and talk about the mathematics in a meaningful way.
The robot-building context works well as it is hands-on, visual, and naturally invites comparison. Students can:
- physically manipulate parts, which supports reasoning without needing symbolic language.
- see gaps in the pattern (“We haven’t made any robots with the square head and the long legs yet!”).
- work socially—noticing that someone else has made a robot they haven’t thought of.
The purpose of this game is to allow students to use their informal knowledge as a starting point to explore the “for each” idea. The multiplicative structure becomes more visible as students focus on building unique robots as the game progresses. The game supports students in developing relational thinking, to notice connections between combinations, rather than simply counting them individually.
Engaging in collaborative play through games develops students’ language within an authentic context and deepens their understanding of concepts in a fun and encouraging environment.
Context provides a ‘hook’ or entry point for students to begin solving the problem, and for them to think and talk about the mathematics in a meaningful way.
The robot-building context works well as it is hands-on, visual, and naturally invites comparison. Students can:
- physically manipulate parts, which supports reasoning without needing symbolic language.
- see gaps in the pattern (“We haven’t made any robots with the square head and the long legs yet!”).
- work socially—noticing that someone else has made a robot they haven’t thought of.
The purpose of this game is to allow students to use their informal knowledge as a starting point to explore the “for each” idea. The multiplicative structure becomes more visible as students focus on building unique robots as the game progresses. The game supports students in developing relational thinking, to notice connections between combinations, rather than simply counting them individually.
Engaging in collaborative play through games develops students’ language within an authentic context and deepens their understanding of concepts in a fun and encouraging environment.
The purpose of this Connect phase is for students to have a chance to:
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Review the task that was posed and ask students to think about what they expect to see as they look at how other groups organised their robots. Ask students to consider the following questions as they look at others’ work:
- What do you notice about other robot sorts that is similar or different to how your group organised your robots?
- What ways of organising the robots make it clearer to see robots that might be missing?
Provide each student with two different coloured counters (e.g. one red and one green counter). Explain that they should place the green counter next to work that surprised them or showed them something they hadn’t thought of, and the red counter next to work where the organisation made the pattern particularly easy to see.
Conduct a class gallery walk.
Afterwards, discuss what students noticed and any useful ways of organising the robots to be able to clearly see missing ones. Use the counters that have been placed to guide the discussion. Student noticings may include the following useful strategies:
- organising the robots in rows, where each robot shows one part changed. For example:
- Making three robots with the same head and three different bodies.
- Making three robots with the same head and body and then changing the legs to make new robots.
- organising in arrays to see the gap where a possible combination has not been made.
These are the early seeds of multiplicative thinking and systematic counting.
Show Slides 6-7 and discuss the sorting strategy used on each slide, considering:
- How have the groups of robots been sorted?
- How can sorting robots by one body part the same (head, body or legs) help to find missing robots?
Gallery walk
A gallery walk is used here as a tool for students to have the opportunity to view and review:
- the variety of robot combinations made by the class.
- how organising related combinations makes it easier to see what is missing.
- how missing robots can be found by looking at connections between combinations.
The teacher encourages the students to notice how their work is similar or different to the work of other students. Students place coloured counters next to work that struck them as surprising or particularly well-organised. They reflect on other students’ work and make connections to their own thinking. They may also see missing combinations that they have not made, as well as notice how different robot combinations are related to each other.
The counters left during the gallery walk will be used to inform the discussion about the mathematics they noticed.
A gallery walk is used here as a tool for students to have the opportunity to view and review:
- the variety of robot combinations made by the class.
- how organising related combinations makes it easier to see what is missing.
- how missing robots can be found by looking at connections between combinations.
The teacher encourages the students to notice how their work is similar or different to the work of other students. Students place coloured counters next to work that struck them as surprising or particularly well-organised. They reflect on other students’ work and make connections to their own thinking. They may also see missing combinations that they have not made, as well as notice how different robot combinations are related to each other.
The counters left during the gallery walk will be used to inform the discussion about the mathematics they noticed.
Show Slide 8 in preparation for the next task and ask students to think about which robots are missing.
Explain: We can make the problem simpler by making it smaller. We could just focus on using one type of robot head and find every combination only using this head and three bodies and three types of legs.