Chapter 2 · Multiplying and dividing by two-digit numbers

Lesson 2.12 · Dividing two-digit or three-digit numbers by a two-digit number (4)

Hua's Classroom for Shanghai Maths — One Lesson One Exercise (English edition, pages 55–57).

Grade 3 Second Semester Pages 55–57 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. 01Solve reverse multi-step road repair problems. (Question 1)
  2. 02Find total length from partial days and remainder. (Question 2)
  3. 03Apply equal-area rectangle / lawn problems. (Question 3)

Common Core Standards

CodeStandard (focus for this lesson)
3.OA.D.8Multi-step problems.
3.MD.C.7Area applications.

Eureka Math Correspondence

Shanghai MathsFocusEureka Math
ReverseWork backwardsG4 M3
AreaSame area shapesG3 M4

Core Concepts

Multi-step reverse problems: half repaired day 1, etc.

Work Backwards

Day 2 is twice day 3; day 1 is half the road — draw a bar model.

Road Repair

Known remainder + daily amounts → total length.

Equal Area

Same area, different length → find missing width by division.

Key Terms & Definitions (Reference)

Quick glossary for this lesson.

TermDefinition
Reverse problemFind total from parts working backwards.
Bar modelDiagram for multi-step problems.

Key Answers

Quick reference for this lesson’s exercise answers.

1. Greatest in ( )

  • $48\times(4)<205$;\; $34\times(7)<248$;\; $56\times(6)<356$
  • $82\times(5)<483$;\; $78\times(8)<645$;\; $64\times(8)<521$

2. Column method

  • $210\div48=4\cdots18$;\; $325\div38=8\cdots21$;\; $829\div89=9\cdots28$
  • $560\div59=9\cdots29$;\; $260\div28=9\cdots8$;\; $445\div45=9\cdots40$

3. Estimate then calculate

  • $333\div35=9\cdots18$;\; $606\div66=9\cdots12$;\; $515\div59=8\cdots43$

4. Number sentences

  1. Subtract $36$
  2. $8$

5. Application

  1. Road $1080\,\text{m}$
  2. Width $9\,\text{m}$
  3. $4$ days
  4. $14$ bamboo rafts

6. Enhancement

  1. $125$ and $75$
  2. $17.5$ yuan
  3. Last piece white; $89$ white pieces