Teaching with Thinking Adventures
🍎 Teacher’s guide
Each place on a game’s map is called a stop. It focuses on one maths idea, taught in five levels, with a matching worksheet. Choose a stop that matches your lesson. Use its examples to teach the idea, its questions for practice and its thinking task for group discussion.
Turn a stop into a lesson
Begin together with the number string, develop and practise the concept, then finish with a group thinking task.
- 1Begin together 🔗Level 1Number stringFind the connections
- 2Build understanding 🧠Level 2KnowledgeUnderstand the idea 🧭Level 3ApplicationUse the maths 💬Level 4ReasoningExplain how you know
- 3Think together 🧩Level 5Problem of the dayChoose, test and rethink
Before teaching, preview the stop and its worksheet. Have paper and any objects you need ready. A stop can extend over several lessons.
Begin together
Lead the number string
Show one calculation at a time. Give everyone thinking time, then ask, “How did you work it out?” Record their methods and keep earlier working visible. With the next question, ask, “Which earlier calculation can help us? Why?”
10 × 8 = 80 → 5 × 8 = 40 → 15 × 8 = 120.
Five groups are half of ten groups. Fifteen groups combine ten groups and five groups. Make those connections explicit as learners explain.
Why it matters: a carefully chosen string helps learners build a calculation strategy from facts they already know. The discussion shows you whether they can use the relationship between questions.
Draws on Pam Harris’s problem strings.
Build understanding
Develop the concept, then practise it
Use the Knowledge activity to teach the idea. Connect objects learners can handle, pictures they can draw, and the numbers and symbols they write. This is the concrete–pictorial–abstract (CPA) approach, drawing on Bruner’s work on representing ideas through actions, images and symbols.
- Objects: share 12 counters into four equal groups. Select three groups.
- Picture: draw the same four groups and circle three of them.
- Symbols: write 12 ÷ 4 = 3, then 3 × 3 = 9. Connect this to 34 × 12 = 9.
Ask learners to show where each number appears in the objects and drawing.
Why it matters: connecting these representations gives meaning to the calculation. Add real objects to the game’s pictures, and return to them when a step is unclear.
Model an example, complete a similar question together, then let learners practise in the game or on the worksheet. In Application, ask what the word problem requires and why the chosen method fits. In Reasoning, ask learners to explain or check a method. Use their working and explanations to decide what needs teaching again.
Teaching ideas: Bruner and CPA; Kirschner, Clark and Sweller on guidance; Sherrington on modelling, practice and checking understanding.
Think together
Investigate the final challenge
Use Problem of the day for learners to decide how to approach a problem together. Explain the challenge and check that the wording is understood.
- Set up groups: use a visible random method, such as drawing cards, to make groups of three. Give each group a shared erasable surface, ideally an upright whiteboard.
- Let learners begin: ask them to choose an approach and show their thinking. Leave the solution method for them to work out.
- Help them move forward: listen first. Ask, “What have you tried?” or “Could you test a simpler case?” Give a small hint when needed; explain missing knowledge if it prevents a start.
- Bring the learning together: select group work to discuss, starting with an accessible approach. Connect the methods and ask learners why they work. Finish with a short individual question to check each learner’s understanding.
Why it matters: learners make decisions, test ideas and revise them. The shared working lets them compare and build on one another’s reasoning.
Uses selected practices from Liljedahl’s Building Thinking Classrooms.
The educational thinking behind this approach
This teaching sequence brings together approaches that support different aspects of mathematical learning. Pam Harris’s connected calculations use a carefully chosen sequence of related problems to help learners notice patterns and use known facts to work out unfamiliar calculations. For example, knowing that 10 × 6 = 60 can help learners reason that 9 × 6 = 54 by subtracting one group of six. Harris’s approach
Bruner’s representations help learners connect actions, images and symbols. Learners can explore an idea using objects, represent it through drawings or diagrams, and connect these representations to written numbers and equations. Linking these forms helps learners understand what the mathematical symbols mean. Bruner’s account
Guided instruction supports new learning through clear explanations, modelled examples and supported practice. Teachers explain their reasoning, check learners’ understanding and provide feedback, gradually reducing support as learners become ready to work independently. Principles of instruction
Jo Boaler’s work on number sense informs the emphasis on flexible thinking about numbers. Learners are given time to consider a calculation, explain their methods and compare strategies, helping them recognise relationships and choose approaches that make sense for the numbers involved. Number sense
Peter Liljedahl’s collaborative thinking practices inform the final challenge at each stop. Learners can work in small, randomly formed groups at shared upright whiteboards, where they discuss ideas, make their reasoning visible and revise their solutions together. Although his wider model also uses thinking tasks to introduce new learning, this sequence draws on these practices to help learners apply and extend their understanding. Building Thinking Classrooms
How MathsConnected supports the lesson
Where each part of that lesson lives on the site: setting the stop, what learners see, the paper beside it, and how every level went.
Set the stop
In Thinking adventures, choose the grade and the term, then find the stop that matches your lesson: tap its town on the map, or pick it from the list under the map. Press Set and all five levels are set for your class.
Open the stop to set only some of its levels, or to add a date or a note. If you lead the number string and the problem of the day with the whole class, set the three levels in the middle.
Preview it as a learner
Preview as a learner shows the adventures exactly as a child sees them. Play the stop’s five levels before you teach it: nothing is saved, and no learner’s record changes.
What learners see
The stop is at the top of each learner’s own page, under Your work. Do my work opens the game at the next level they have not finished. When that level is done, the game takes them to the next one.
A learner who is stuck can ask for a hint, and after two wrong tries Max shows the answer. Both are noted in that learner’s record.
The worksheet beside every stop
Every stop has a matching worksheet, with space to draw models, record calculations and explain thinking. For you there is the same worksheet with its answer pages, which learners cannot open.
Each term also has a learner workbook, with all of its worksheets in one book, and an answer book. The revision games have a workbook and a teacher guide of their own.
See how each level went
Work set lists each piece of work and who has done it. Your class page shows every learner’s levels. A finished level is marked from what the learner did: secure when nearly all of it was right first time, needs help when under half was, or when Max kept having to show the answer. The wrong tries and hints are listed with it.
SecureGetting thereNeeds help
One stop may take more than one lesson
A stop is one maths idea, not one period. Lead the number string today and come back for the rest tomorrow, or give the problem of the day a lesson of its own.
Finished levels are kept, and Do my work opens at the next one.
🎬 Strategy videos
The thinking behind the visual models, the number strings and the problems of the day — for sharing with your team, or watching before you teach an idea for the first time. Add the links your school uses.
Kept in this browser. Links you add here stay on this device and are not yet shared with the rest of the school.