Chapter 7 · Consolidation and enhancement

Lesson 7.7 · Mathematics plaza — counting apples

Hua's Classroom for Shanghai Maths — One Lesson One Exercise (English edition, pages 145–146).

Grade 3 Second Semester Pages 145–146 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. 01Count discs with more than one method. (Question 1)
  2. 02Count squares / triangles by type. (Question 2–3)
  3. 03Count marked rectangles. (Question 4)

Common Core Standards

CodeStandard (focus for this lesson)
3.OA.D.8Multi-step.
MP.7Structure.

Eureka Math Correspondence

Shanghai MathsFocusEureka Math
CountBy typeG3 plaza

Core Concepts

Multiple counting strategies for discs, squares, triangles, rectangles.

Many Methods

Write different number sentences that give the same total.

Count by Type

1×1, 2×2, … squares; small/medium/large triangles.

Systematic Count

Mark what you have counted to avoid doubles or misses.

Key Terms & Definitions (Reference)

Quick glossary for this lesson.

TermDefinition
Systematic countingOrganise by size/type.
Number sentenceEquation showing a count method.

Key Answers

Quick reference for this lesson’s exercise answers.

Key answers

  1. $1+2+\cdots+6=21$ discs.
  2. Side 1: 21; side 2: 7; side 3: 4.
  3. 15; 20.
  4. $3\times3$ grid: 14 axis-aligned squares (9+4+1).
  5. 18 triangles.
  6. 24 triangles.
  7. 32 rectangles containing *.
  8. Total to 7th layer: 231.