Chapter 4 · Introduction to fractions (I)

Lesson 4.5 · Non-unit fractions (2)

Hua's Classroom for Shanghai Maths — One Lesson One Exercise (English edition, pages 88–90).

Grade 3 Second Semester Pages 88–90 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. 01Fill in non-unit fractions from diagrams and measures. (Question 1–2)
  2. 02Compare fractions with $>$, $<$, $=$. (Question 3)
  3. 03Reason about possible fractional shares. (Question 4–5)

Common Core Standards

CodeStandard (focus for this lesson)
3.NF.A.1Fractions.
3.NF.A.3Compare fractions.

Eureka Math Correspondence

Shanghai MathsFocusEureka Math
CompareSame denominator / wholeG3 M5
ApplyStoriesG3 M5

Core Concepts

Fill, compare, and reason with non-unit fractions.

Fill Fractions

10 one-tenths = 1 whole; connect to metres and decimetres.

Compare

Same denominator → larger numerator is larger; same numerator → larger denominator is smaller.

Reason

Can Xiao Dingding take away $\frac{3}{4}$? Check against what remains.

Key Terms & Definitions (Reference)

Quick glossary for this lesson.

TermDefinition
Compare fractionsUse same whole and equal parts.
Equivalent idea10 tenths make 1 whole.

Key Answers

Quick reference for this lesson’s exercise answers.

1. Fill in

  1. $12$ cans; $\frac{12}{12}$ box; that is $1$ box.
  2. Number line: $\frac{3}{10}$;\; $\frac{1}{10}$;\; $\frac{7}{10}$.

2. Shaded circles

$\frac{4}{8}=\frac{1}{2}$;\; $\frac{15}{15}=1$;\; $\frac{8}{12}=\frac{2}{3}$.

3. Circle items

$\frac{3}{4}$ of $16$ → $12$;\; $\frac{5}{8}$ of $16$ → $10$.

4. Fill in

  1. $\frac{10}{10}$ yuan $=1$ yuan.
  2. $\frac{1}{10}\,\mathrm{m}=1\,\mathrm{dm}$.
  3. $\frac{1}{12}<\frac{1}{8}$;\; $\frac{4}{10}>\frac{2}{10}$;\; $\frac{3}{3}=\frac{9}{9}$.
  4. $\frac{4}{4}=1$.
  5. $\frac{1}{4}$ of $8=2$ chocolates.
  6. $\frac{4}{6}$;\; $\frac{1}{5}$;\; $1$.
  7. Hens $\frac{5}{8}$ of the total.

5. Shaded diagrams

(1) $\frac{1}{4}$;\; (2) $\frac{1}{2}$ (or $\frac{9}{18}$).

6. Coke bottles

  1. $6$;\; $8$.
  2. Xiao Hong takes more ($18>16$).
  3. No — $48$ is not divisible by $5$.
  4. Any fraction whose denominator divides $48$ (e.g. $\frac{1}{2},\frac{1}{3},\frac{1}{4},\frac{1}{6},\frac{1}{8},\frac{1}{12},\ldots$); remaining after (2) is $\frac{14}{48}=\frac{7}{24}$.

7. Multiple choice

C — originally longer than $1$ metre.