1.1 Small Group · Group 1
Second Practice Form · Re-Teach, Homework or Retake · Same Standard, New Problems
doer of math · math story · Procedural Fluency · Real-World Applications
- Before any new mathematics, the book asks a different question: where does math already live in your day? We'll walk through a worked example, try one together, then you'll try a few with hints right there when you need them.
- The Ferris wheel has 20 cars, and about 4 people fit in each car. About how many people can ride at one time?
- I count the cars: 20. Then I estimate how many riders fit in one car: about 4.
- I do not count every person — an estimate is a reasoned answer that is close enough to be useful.
- 20 × 4 = 80, so I would say “about 80 people.”
- doer of math (persona que hace matemáticas) — Anyone who uses mathematical thinking — which is everyone, every day.
- math story (historia matemática) — Your own history with mathematics — what you have done, felt, and learned so far.
- strength (fortaleza) — Something you already do well and can share with others.
- decompose (descomponer) — To break a number into parts that add, subtract, multiply, or divide back to it.
- estimate (estimar) — A reasoned answer that is close enough to be useful, without counting every one.
- Believing that 'doing math' only counts when it happens on paper in a classroom.
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1 MULTIPLE CHOICE
A different wheel has 22 cars holding about 4 people each. Ana rounds 22 down to 20 and says “about 80.” Ben multiplies 22 × 4 and says “exactly 88.” Which statement describes both approaches fairly?
- AAna's is fast for a quick head count; Ben's is what the operator needs to sell tickets
- BAna is wrong, because she changed a number that was given
- CBen is wrong, because an estimate has to be a round number
- DOnly one of them can be doing real math
✏️ Workspace & Solution Steps
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2 MULTIPLE CHOICE
Tonight the Ferris wheel has 19 cars, and about 4 people fit in each car. Mia rounds 19 up to 20 and says, “About 80 people can ride at one time.” Is Mia's estimate reasonable?
- AYes — 20 is close to 19, and 20 × 4 = 80 is close to the exact 76
- BNo — she has to use 19, so 76 is the only answer allowed
- CNo — rounding up always makes an estimate too big to be useful
- DYes, but only because 80 is a round number
✏️ Workspace & Solution Steps -
3 MULTIPLE CHOICE
You want to estimate 19 × 4 in your head. Which move makes the numbers friendlier without changing the answer much?
- ARound 19 to 20 — then 20 × 4 is a double of a double
- BRound 4 up to 10, because tens are the easiest to multiply
- CAdd 19 + 4 first, then multiply the total by 2
- DRewrite 19 as 19.0 so it looks like a decimal
✏️ Workspace & Solution Steps -
4 MULTIPLE CHOICE
A third student looks at the same 22-car wheel and says, “About 200 people can ride at one time.” Why is that estimate not reasonable?
- AIt would mean about 9 people squeezed into every car, not about 4
- BIt is wrong only because 200 is not a multiple of 4
- CIt is fine — an estimate can be any number you like
- DIt is wrong because 200 is too round to be an estimate
✏️ Workspace & Solution Steps
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5 OPEN RESPONSE
Mia rounded 19 cars up to 20 before multiplying. Explain why that made the math easier — and say what she gave up by rounding.
💬 Sentence Starter: Rounding 19 to 20 made it easier because ___ .<br>Her estimate is ___ riders away from the exact answer.<br>That is a fair trade here because ___ .✏️ Mathematical Justification & Response -
6 OPEN RESPONSE
The same fair has a carousel with 31 horses. About 1 rider fits on each horse, and it runs 3 times an hour. Estimate about how many people ride the carousel in one hour. Use any strategy you like — then name the strategy you used.
💬 Sentence Starter: I estimated by ___ .<br>My estimate is about ___ riders in one hour.<br>I chose that strategy because ___ .✏️ Mathematical Justification & Response
Writing Task: Justify why your mathematical solution is accurate and complete.