Chapter 1 · Revising and improving

Lesson 1.1 · Warm-up revision (1)

Hua's Classroom for Shanghai Maths — One Lesson One Exercise (English edition, pages 1–2).

Grade 3 First Semester Pages 1–2 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:

01Add and subtract hundreds and tens fluently, including finding and using number patterns. (Question 1, 2)
02Use place value to read, write, and combine hundreds and thousands. (Question 3)
03Apply properties of operations (commutative, associative, distributive) to make calculations easier. (Question 3, 4, 7)
04Translate English phrases into number sentences and calculate correctly. (Question 5)
05Solve multi-step application problems involving addition, subtraction, and multiplication. (Question 6)

Common Core Standards

Code	Standard (focus for this lesson)
3.NBT.A.2	Fluently add and subtract within 1000 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. (Question 1, 2, 4, 6)
3.OA.B.5	Apply properties of operations as strategies to multiply and divide. (Question 3, 4, 7)
3.OA.A.3	Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities. (Question 5, 6)
3.OA.D.8	Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. (Question 5, 6, 7)
2.NBT.A.1 (revision)	Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones. (Question 3)
2.NBT.B.8 (revision)	Mentally add 10 or 100 to a given number 100–900, and mentally subtract 10 or 100 from a given number 100–900. (Question 1, 2)

Eureka Math Correspondence

This Shanghai Maths lesson aligns mainly with Eureka Math Grade 3 Modules 1–3, plus Grade 2 Module 5 as warm-up revision.

Shanghai Maths 1.1	Focus	Eureka Math (corresponding)
Questions 1–2	Mental addition/subtraction; number patterns (+10 / −10)	G2 M5 Addition & Subtraction Within 1,000 · G3 M2 Topics D–F (place-value strategies for ± within 1,000)
Question 3	Place value; distributive property	G3 M2 Topic C (place value) · G3 M1 Topic F (distributive property)
Question 4	Regroup to make friendly numbers (commutative / associative)	G3 M2 Topics E–F (addition & subtraction strategies / algorithms)
Questions 5–6	Number sentences; multi-step word problems	G3 M1 Topics D, F · G3 M3 (multiplication & two-step problem solving)
Question 7	Simplify with properties; unknowns (○, △)	G3 M1 Topic F · G3 M3 Topic B (properties; equations with an unknown)

Core Concepts

Place value, parts of +, −, and ×, and the properties used in this lesson.

Diagram: Place Value

Use this diagram when teaching Question 3.

thousands
→ 3000

hundreds
→ 800

tens
→ 20

ones
→ 1

3 thousands = 3000.
8 hundreds = 800.
2 tens = 20.
1 one = 1.
Together: $3000 + 800 + 20 + 1 = 3821$.

Unit Language to Numeral

Use this when teaching Question 3: turn place-value unit language into numerals.

Rule: How many × the value of that place = the number.

Unit language	Think	Number (numeral)
8 one hundreds / 8 hundreds	$8 \times 100$	$800$
3 one thousands / 3 thousands	$3 \times 1000$	$3000$
5 tens	$5 \times 10$	$50$
6 ones	$6 \times 1$	$6$

Parts of an Addition

Use this diagram when teaching Questions 1, 2, and 4 (and any “altogether / in total” problems).

Addition

Sum

5 ↑Addend

2 ↑Addend

7 ↑Value of
the sum

Term	Meaning	In $5 + 2 = 7$
Addend	A number being added	$5$ or $2$
Sum	The addition expression / the result of adding	$5 + 2$
Value of the sum	The answer after adding	$7$
Addition	The whole number sentence	$5 + 2 = 7$
Reading the equation	Read left to right using math words	“5 plus 2 equals 7”

Reading the equation: $5 + 2 = 7$ → “Five plus two equals seven.” You can also say: “Addend plus addend equals the value of the sum.”

Parts of a Subtraction

Use this diagram when teaching Questions 1, 2, and 4 (and any “how many fewer” problems).

Subtraction

Difference

5 ↑Minuend

−

2 ↑Subtrahend

3 ↑Value of the
difference

Term	Meaning	In $5 - 2 = 3$
Minuend	The number you start with (the whole)	$5$
Subtrahend	The number being taken away	$2$
Difference	The subtraction expression / the result of subtracting	$5 - 2$
Value of the difference	The answer after subtracting	$3$
Subtraction	The whole number sentence	$5 - 2 = 3$
Reading the equation	Read left to right using math words	“5 minus 2 equals 3”

Reading the equation: $5 - 2 = 3$ → “Five minus two equals three.” You can also say: “Minuend minus subtrahend equals the value of the difference.”

Parts of a Multiplication

Use this diagram when teaching Questions 3, 5, 6, and 7 (and any “times / product” problems).

Multiplication

Product

5 ↑Factor

2 ↑Factor

10 ↑Value of
the product

Term	Meaning	In $5 \times 2 = 10$
Factor	A number being multiplied	$5$ or $2$
Product	The multiplication expression / the result of multiplying	$5 \times 2$
Value of the product	The answer after multiplying	$10$
Multiplication	The whole number sentence	$5 \times 2 = 10$
Reading the equation	Read left to right using math words	“5 times 2 equals 10”

Reading the equation: $5 \times 2 = 10$ → “Five times two equals ten.” You can also say: “Factor times factor equals the value of the product.”

Properties & Theorems

1. Commutative property

$$a + b = b + a$$

Order of addends can change; the sum stays the same.

2. Associative property

$$(a + b) + c = a + (b + c)$$

Group addends to make “friendly” (round) numbers.

3. Distributive property

$$a(b+c)=ab+ac$$

$$a(b-c)=ab-ac$$

Break apart or factor out a common multiplier.

Key Terms & Definitions (Reference)

Term	Definition
Number pattern	A rule that repeats or changes in a predictable way. If one number changes by the same amount each time (e.g. +10) and the other stays the same, the sum or difference changes by that same amount.
Place value	The value of a digit depends on its place (ones, tens, hundreds, thousands…).
Ones	The place for single units; 1 one = 1.
Tens	The place for groups of ten; 1 ten = 10; 5 tens = 50.
Hundreds	The place for groups of one hundred; 1 hundred = 100; 8 hundreds = 800.
Thousands	The place for groups of one thousand; 1 thousand = 1000; 3 thousands = 3000.
Number sentence / equation	An equation that shows a calculation (e.g. $8 \times 7 - 21 = 35$).
Addend	A number being added.
Sum	The result of addition (or the addition expression).
Minuend	The number you start with in subtraction (the whole).
Subtrahend	The number being taken away in subtraction.
Difference	The result of subtraction (or the subtraction expression).
Factor	A number being multiplied.
Product	The result of multiplication (or the multiplication expression).
Commutative property	Order can change; the result stays the same. For addition: $a + b = b + a$.
Associative property	Grouping can change; the result stays the same. For addition: $(a + b) + c = a + (b + c)$.
Distributive property	A factor can be shared across a sum or difference: $a(b + c) = ab + ac$; $a(b - c) = ab - ac$.

Key Answers

Quick reference for this lesson’s exercise answers.

1. Let’s calculate

$200+300=500$,\; $1000-400=600$,\; $500+500=1000$
$460-230=230$,\; $470-230=240$,\; $480-230=250$
$170+330=500$,\; $660-600=60$,\; $290+110=400$

2. Patterns

$148+152=300$,\; $138+162=300$,\; $128+172=300$,\; $118+182=300$
$855-170=685$,\; $865-170=695$,\; $875-170=705$,\; $885-170=715$
$220+348=568$,\; $220+350=570$,\; $220+352=572$,\; $220+354=574$

3. Fill in — $800$; $3000$; $3800$. Sequence: $3050,3550,4050,4550,5050,5550$. $11\times3-8\times3=9$. $3\times18=54$.

4. Step by step — $1378$; $834$; $356$; $555$.

5. $8\times7-21=35$;\; $5\times6+48=78$.

6. $994$ bags;\; $39$ fewer;\; $122$ yuan.

7. $21\times6-6=20\times6=120$;\; $\bigcirc=280$, $\triangle=190$;\; sum $470$, difference $90$.