1.6 Small Group · Group 1
Second Practice Form · Re-Teach, Homework or Retake · Same Standard, New Problems
make sense of a problem · representation · Procedural Fluency · Real-World Applications
- Problem solving is not one lightning bolt — it is a process you can name, practice, and share. And when the process stalls, getting stuck is part of doing math, not a sign you can't. We'll walk through a worked example, try one together, then you'll try a few with hints right there when you need them.
- First I make sense of it: one rack holds 8 bikes, each bike has 2 wheels, so this rack has 8 × 2 = 16 wheels. The other rack has 6 times as many wheels — that is what I don't know yet.
- I choose a representation: 6 equal groups of 16. Then I make a plan: multiply.
- 16 × 6 = 96, so the other rack has about 96 wheels. I check my progress: 96 is 6 groups of 16, and 16 × 6 = 96, so my answer matches my plan.
- make sense of a problem (comprender un problema) — To figure out what a problem is asking — what you know, and what you don't know yet.
- representation (representación) — A way of showing a problem — a drawing, table, equation, or model — that helps you see it.
- strategy (estrategia) — A plan of attack for a problem — and something you can switch when you get stuck.
- critique (criticar constructivamente) — To examine an idea and say what is convincing or not — about the idea, never about the person.
- community agreement (acuerdo comunitario) — A rule the whole class agrees to so that everyone can learn together.
- Treating 'stuck' as a stop sign instead of a signal — waiting silently instead of trying a strategy: asking a question, drawing the problem, or recalling a similar problem.
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1 MULTIPLE CHOICE
You decided to find 16 × 6 for the second rack. Which representation matches the problem?
- A6 equal groups of 16 wheels
- B6 wheels shared equally among 16 bikes
- C16 groups of 6 bikes
- DOne group of 16 wheels plus one group of 6 wheels
✏️ Workspace & Solution Steps
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2 MULTIPLE CHOICE
A rack holds 8 bikes, and each bike has 2 wheels. Another rack has 6 times as many wheels. Before computing anything: what do you need to find FIRST?
- AHow many bikes are in the whole school
- BThe answer 96, because that is what the book says
- CNothing — you can multiply 8 × 6 right away and be done
- DHow many wheels the first rack has — 6 times as many needs a starting number
✏️ Workspace & Solution Steps -
3 MULTIPLE CHOICE
Carry out the plan: 16 × 6 = ___. Then check your progress — which check actually tests the answer?
- A22 — because 16 + 6 = 22
- B48 — because 8 × 6 = 48
- C96 — and 96 ÷ 6 = 16 brings back the first rack's wheels
- D96 — and 96 looks like a big number, so it must be right
✏️ Workspace & Solution Steps -
4 MULTIPLE CHOICE
You read: 'The second rack has 96 wheels. How many BIKES is that?' — and you freeze. Which move is one of this lesson's get-unstuck strategies?
- ASkip it and answer the next one instead
- BCopy what the student next to you wrote
- CDraw the situation — one bike per 2 wheels — or think of a problem like it you already solved
- DMultiply the two numbers you see, because that worked last time
✏️ Workspace & Solution Steps
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5 OPEN RESPONSE
Describe your problem-solving process for the rack problem, in order. Use the phrases make sense of, try a strategy, and check.
💬 Sentence Starter: First I make sense of the problem: I know ___ and I need ___ .<br>Then I try a strategy: ___ .<br>Last I check by ___ .✏️ Mathematical Justification & Response -
6 OPEN RESPONSE
A classmate is stuck on the rack problem and says, 'I'm just bad at math.' Write what you would say and do — one sentence that helps them re-enter the problem, and one question you would ask instead of giving the answer.
💬 Sentence Starter: I would say: '___' .<br>Instead of the answer, I would ask: '___?' <br>That helps because ___ .✏️ Mathematical Justification & Response
Writing Task: Justify why your mathematical solution is accurate and complete.