Chapter 4 · Introduction to fractions (I)

Unit Test 4

Hua's Classroom for Shanghai Maths — One Lesson One Exercise (English edition, pages 91–95).

Grade 3 Second Semester Pages 91–95 ECNU Press

Lesson Alignment

How this Shanghai Maths lesson connects to learning goals, Common Core, and Eureka Math.

Learning Objectives

Students will be able to:

  1. 01Demonstrate fraction understanding. (Parts A–B)
  2. 02Apply fraction stories and diagrams. (Part C)

Common Core Standards

CodeStandard (focus for this lesson)
3.NF.A.1Fractions.
3.OA.D.8Multi-step problems.

Eureka Math Correspondence

Shanghai MathsFocusEureka Math
Unit testChapter 4G3 M5

Question–Lesson Map

Where each Unit Test 4 question was taught in Chapter 4 (Lessons 4.1–4.5).

Test questionFocusTaught in
1. Mental calculation ×÷ fluency review alongside fraction unit 4.5
2. Column method Large × and ÷ column review 4.5
3. Step by step Multi-step computation review 4.5
4. Number sentences Write and evaluate division sentences from language 4.5
5. Fill in the spaces Unit fractions of length; colour parts; name fractions; compare fractions; fraction of a set 4.1, 4.2, 4.3, 4.4, 4.5
6. True or false Equal parts; unit vs non-unit fractions; comparing denominators 4.1, 4.2, 4.4
7. Multiple choice Choose shaded fraction; equivalent representations 4.2, 4.3, 4.4
8. Diagrams / circle Shade to show a fraction; circle a fraction of a set 4.2, 4.3, 4.4, 4.5
9. Application problems Date-span rate; equal groups; speed; boys/girls fraction of class; tangram piece fractions 4.4, 4.5

Core Concepts

Fractions + fluency + applications.

Test Structure

Mental; fill-ins; true/false; circle by fraction; applications.

High-Frequency Focus

  • Equal parts.
  • Unit vs non-unit fractions.
  • Fraction of a set.

Key Terms & Definitions (Reference)

Quick glossary for this lesson.

TermDefinition
Unit testEnd-of-chapter assessment.

Key Answers

Quick reference for this lesson’s exercise answers.

1. Mental

  • $48\div12=4$;\; $400\times20=8000$;\; $70-70\div7=60$;\; $48\div9=5\,\mathrm{R}\,3$
  • $25\times80=2000$;\; $3600\div60=60$;\; $540\div90=6$;\; $25+75\times2=175$

2. Column

$160\times4200=672\,000$;\; $2064\div57=36\,\mathrm{R}\,12$.

3. Step by step

  • $(1000-244)\div42=18$;\; $105\times87-87\times5=8700$
  • $1152\div36\times39=1248$;\; $(316-16\times16)\times20=1200$

4. Number sentences

  1. $(34\times34)\div17=68$.
  2. $(388-298)\div90=1$.

5. Fill in

  1. $\frac{1}{10}$, $\frac{1}{10}\,\mathrm{m}$;\; $\frac{1}{10}$ of $10\,\mathrm{m}$, that is $1\,\mathrm{m}$.
  2. $4$ parts; $1$ part not coloured.
  3. $\frac{1}{6}$; four sixths; $\frac{7}{8}$.
  4. $4$ triangles; $12$ stars.
  5. $\frac{2}{2}=\frac{4}{4}$;\; $\frac{1}{12}<\frac{1}{8}$;\; $\frac{4}{5}>\frac{2}{5}$.
  6. $14$ shapes; circles $\frac{3}{14}$; squares $\frac{4}{14}$; triangles $\frac{7}{14}$.
  7. bigger; more.

6. True / false

✕, ✕, ✓, ✓, ✕.

7. Multiple choice

(1) C $\frac{5}{8}$;\; (2) B $\frac{4}{12}$ and C $\frac{2}{3}$.

8. Diagrams / circle

  • Shaded: $\frac{1}{2}$;\; $\frac{4}{6}$ (or $\frac{2}{3}$).
  • Circle $5$ of $6$ smileys; $6$ of $8$ suns.

9. Application

  1. $25$ Mar–$17$ Apr $=24$ days; $125\,040\div24=5210$ thousand yuan/day.
  2. $1980\times4+90=8010$ bins.
  3. Return speed $225\div5=45\,\mathrm{km/h}$.
  4. Boys $\frac{8}{17}$; girls $\frac{9}{17}$.
  5. Tangram: ① $\frac{1}{4}$; ④ $\frac{1}{8}$; ⑦ $\frac{1}{8}$; ⑤ $\frac{1}{16}$; ③ $\frac{1}{16}$ (⑥ $\frac{1}{8}$).