Chapter 3 · Statistics
Unit Test 3
Hua's Classroom for Shanghai Maths — One Lesson One Exercise (English edition, pages 74–78).
Lesson Alignment
How this unit test connects to learning goals, Common Core, and Eureka Math.
Learning Objectives
Students will be able to (across the test):
- 01Compute mental and column ×÷ with order of operations and remainders.
- 02Write number sentences from language (dividend / quotient / remainder).
- 03Find area of a composite shape by splitting into rectangles.
- 04Read and complete bar charts (Olympic medals; weekly violations).
- 05Solve multi-step application problems (packing, distance, rate).
Common Core Standards
| Code | Standard (focus for this test) |
|---|---|
| 3.MD.B.3 | Scaled bar graphs; one- and two-step problems from graphs. |
| 3.OA.D.8 | Two-step (and multi-step) word problems using the four operations. |
| 3.MD.C.7 | Relate area to multiplication; composite figures. |
| 4.NBT.B.5 / 4.NBT.B.6 (preview) | Multi-digit × and ÷ (Chapter 2 carryover on this paper). |
| 3.MD.A.1 / 3.MD.A.2 | Time, length, mass sense in fill-in items. |
Eureka Math Correspondence
| Strand | Focus | Eureka Math |
|---|---|---|
| Statistics | Bar charts; complete missing bar | G3 M6 |
| Fluency / column | ×÷; remainders | G3 M1–M3 / G4 M3 preview |
| Area | Composite rectangle | G3 M4 |
| Applications | Packing; ship distance | G3 M3 / M7 |
Question–Lesson Map
Where each Unit Test 3 question was taught in Chapter 3 (Lesson 3.1).
| Test question | Focus | Taught in |
|---|---|---|
| 1. Mental calculation | Mixed ops; ×÷ before +−; brackets first (fluency review) | 3.1 |
| 2. Column method | Column ×÷ with remainder check (fluency review) | 3.1 |
| 3. Step by step | Distributive/friendly-pair rewrites in multi-step expressions | 3.1 |
| 4. Number sentences | Dividend = divisor × quotient + remainder | 3.1 |
| 5. Composite area | Split L-shape into rectangles; sum areas (m²) | 3.1 |
| 6. Fill in the spaces | Sensible units; speed table; area conversions; Olympic bar chart; division digit bounds | 3.1 |
| 7. Multiple choice | Greatest remainder when dividing by 25; who skipped fastest | 3.1 |
| 8. Application problems | Packing with leftovers; boxes and parts; ship distance = speed × time + remaining | 3.1 |
| 9. Let's do statistics | Read scale; complete Saturday bar; fewest/most; weekly total; write observation | 3.1 |
Core Concepts
What this paper checks — and teaching moves for review.
Test Structure
| Section | Type | Teaching note |
|---|---|---|
| 1 | Mental mixed ops | ×÷ before +−; brackets first |
| 2 | Column ×÷ (+ check) | Show working; remainder < divisor |
| 3 | Step-by-step | Rewrite with distributive property when helpful |
| 4–5 | Number sentence; composite area | Dividend = divisor × quotient + remainder |
| 6 | Fill-ins (units, speed table, Olympic chart) | Scale × grids; “times as many” |
| 7 | MCQ | Greatest remainder; who is fastest |
| 8 | Applications | Packing leftovers; distance = speed × time + remaining |
| 9 | Let’s do statistics | Complete bar; fewest/most; weekly total; comment |
Statistics Focus
Olympic gold medals chart: compare USA and Japan (“times as many”); identify who ranks first (China).
Drunk-driving weekly chart:
- Each small grid represents a stated number of violations (OCR: about $20$).
- Complete Saturday’s bar when the value is given (e.g. $470$).
- Find fewest / most days; difference; weekly total; write a short observation.
For “complete the chart,” count grids from the scale first, then draw the missing bar to the correct height.
High-Frequency Focus
- Remainder must be less than the divisor (MCQ: dividing by $25$ → greatest remainder $24$).
- Packing: maximum groups + leftover pieces / boxes.
- Ship: distance $= $ speed $\times$ time $+$ remaining distance to Port B.
- Bar chart: read scale before comparing heights.
Key Terms & Definitions (Reference)
| Term | Definition |
|---|---|
| Bar chart | Uses bars to show amounts for categories. |
| Scale | What one grid (or axis mark) represents. |
| Remainder | Amount left after equal groups; must be less than the divisor. |
| Composite shape | A figure made of two or more rectangles. |
| Times as many | Multiplicative comparison of two amounts. |
| Statistics | Collecting, showing, and reading data. |
Key Answers
Quick reference for this lesson’s exercise answers.
1. Mental calculation
- $8\times3\div6=4$;\; $(18+18)\div2=18$;\; $11+15\div3=16$;\; $15\div(5\times3)=1$
- $6\times5\times4=120$;\; $22-(12+10)=0$;\; $48\div8\times8=48$;\; $99\times(99-99)=0$
2. Column method
- $98\times42=4116$;\; $24\times302=7248$;\; $1320\div60=22$
- $452\div56=8\,\mathrm{R}\,4$;\; $7832\div72=108\,\mathrm{R}\,56$
3. Step by step
- $786-278-222=286$;\; $75\times55\div11=375$;\; $555\times20\div5=2220$
- $(438-362)\div19=4$;\; $25\times16+25\times13+25=750$;\; $(379-193)\times15=2790$
4–5
- Number: $(330-7)\div19=17$.
- Composite area: $33\,\mathrm{m}^{2}$.
6. Fill in
- Height: cm; dictionary: cm; bicycle: km/h.
- Speed $56\,\mathrm{km/h}$. Table: $392$; $336$; $504$; $13$ hours.
- $450\,\mathrm{cm}=45\,\mathrm{dm}$;\; $30\,\mathrm{m}^{2}=3000\,\mathrm{dm}^{2}$;\; $2\,\mathrm{dm}^{2}\,4\,\mathrm{cm}^{2}=204\,\mathrm{cm}^{2}$.
- USA is $4$ times Japan; China ranks first; China has $28$ more golds than Russia.
- $4068\div46$: quotient is a two-digit number; highest place is tens.
- Greatest leading digit for 2-digit quotient: $6$; least for 3-digit: $7$.
- $1250$.
- Xiao Nan skipped faster.
- $2999\,\mathrm{g}<3\,\mathrm{kg}$;\; $500\,\mathrm{m}>5000\,\mathrm{cm}$.
7. Multiple choice
(1) C $24$;\; (2) C Xiao Ya;\; (3) B $120$.
8. Application
- $216\div30=7\,\mathrm{R}\,6$ → $7$ notepads, $6$ pieces left.
- $6960\div8=870$ boxes used; $30$ boxes left; $0$ parts left.
- $28\times12+120=456\,\mathrm{km}$.
9. Statistics
- $1$ grid $=20$ violations; Saturday bar $=470$.
- Fewest: Mon; $104$ fewer than Wed (largest); total $3349$.
- Open comment (e.g. Wed highest / Mon lowest; weekend still high).