474
↑Dividend
Chapter 1 · Revising and improving
Lesson 1.2 · Warm-up revision (2)
Hua's Classroom for Shanghai Maths — One Lesson One Exercise (English edition, pages 3–5).
Lesson Alignment
How this Shanghai Maths lesson connects to learning goals, Common Core, and Eureka Math.
Learning Objectives
Students will be able to:
- 01Calculate mixed +, −, ×, ÷ using the correct order of operations. (Question 1)
- 02Use the column method for multi-digit addition and subtraction. (Question 2)
- 03Write number sentences using minuend, subtrahend, and difference. (Question 3)
- 04Simplify multi-step calculations with order of operations and properties. (Question 4)
- 05Solve multi-step application problems with diagrams and tables. (Question 5)
- 06Find missing digits and use the division relationship (dividend, divisor, quotient, remainder). (Question 6, 7)
Common Core Standards
| Code | Standard (focus for this lesson) |
|---|---|
| 3.OA.D.8 | Solve two-step word problems using the four operations. (Question 3, 5, 7) |
| 3.NBT.A.2 | Fluently add and subtract within 1000 using strategies and algorithms. (Question 2, 4, 5) |
| 3.OA.A.3 | Use multiplication and division within 100 to solve word problems. (Question 5, 7) |
| 3.OA.B.5 | Apply properties of operations as strategies. (Question 4) |
| 3.OA.A.4 (related) | Determine the unknown whole number in a multiplication or division equation. (Question 7) |
| 4.OA.A.3 (preview / enrichment) | Solve multi-step problems; interpret remainders. (Question 7) |
Eureka Math Correspondence
| Shanghai Maths 1.2 | Focus | Eureka Math (corresponding) |
|---|---|---|
| Question 1 | Order of operations (× ÷ before + −) | G3 M1 / M3 fluency; properties of operations |
| Question 2 | Column method (standard algorithm) | G3 M2 Topics E–F (addition & subtraction algorithms) |
| Question 3 | Minuend / subtrahend / difference language | G2 M5 / G3 M2 subtraction relationships |
| Question 4 | Regroup + order of operations | G3 M2 strategies; G3 M1 properties |
| Question 5 | Multi-step word problems, tape/bar models, tables | G3 M1 / M3 / M7 application problems |
| Questions 6–7 | Missing digits; dividend = divisor × quotient + remainder | G3 M1 Topic B (division as unknown factor); remainder language |
Core Concepts
Order of operations, column method, division relationship, and reading equations for this lesson.
Order of Operations
When a number sentence has more than one operation:
Step 1
Do multiplication and division first (left to right).
Step 2
Then do addition and subtraction (left to right).
Examples from Question 1:
| Number sentence | Think | Answer |
|---|---|---|
| $42 + 15 \div 3$ | $15 \div 3 = 5$, then $42 + 5$ | $47$ |
| $27 - 4 \times 6$ | $4 \times 6 = 24$, then $27 - 24$ | $3$ |
| $24 + 0 \div 6$ | $0 \div 6 = 0$, then $24 + 0$ | $24$ |
Note: $0 \div 6 = 0$ is allowed. Division by zero (e.g. $6 \div 0$) is not.
Column Method
Line up digits by place value (ones under ones, tens under tens…).
| Problem | Answer |
|---|---|
| $462 + 6079$ | $6541$ |
| $10101 - 5872$ | $4229$ |
| $631 - 79 + 557$ | Regroup: $(631 + 557) - 79 = 1188 - 79 = 1109$ |
Parts of a Division
Use for Question 7.
dividend
÷
78
↑Divisor
=
6 R 6
↑Quotient & remainder
| Term | Meaning | In this problem |
|---|---|---|
| Divisor | The number you divide by | $78$ |
| Quotient | How many equal groups (result of division) | $6$ |
| Remainder | What is left over | $6$ |
| Dividend | The number being divided | unknown |
Relationship
$$\text{dividend} = \text{divisor} \times \text{quotient} + \text{remainder}$$
Example: divisor $78$, quotient $6$, remainder $6$:
$$78 \times 6 + 6 = 468 + 6 = 474$$
Reading the Equation (review)
| Operation | Example | Read as |
|---|---|---|
| Addition | $5 + 2 = 7$ | “5 plus 2 equals 7” |
| Subtraction | $5 - 2 = 3$ | “5 minus 2 equals 3” |
| Multiplication | $5 \times 2 = 10$ | “5 times 2 equals 10” |
| Division | $474 \div 78 = 6\ \text{R}\ 6$ | “474 divided by 78 equals 6 remainder 6” |
Properties & Theorems (used in Question 4)
1. Commutative property of addition
$$a + b = b + a$$
2. Associative property of addition
$$(a + b) + c = a + (b + c)$$
3. Order of operations with parentheses
Multiply/divide first, or use parentheses to show that step clearly:
$$774 - 9 \times 6 = 774 - (9 \times 6) = 774 - 54 = 720$$
Key Terms & Definitions (Reference)
Quick glossary for Lesson 1.2 language.
| Term | Definition |
|---|---|
| Order of operations | Multiply and divide before add and subtract (left to right in each level). |
| Column method | Vertical calculation with digits lined up by place value. |
| Number sentence / equation | An equation that shows a calculation. |
| Addend | A number being added. |
| Minuend | The number you start with in subtraction. |
| Subtrahend | The number being taken away. |
| Difference | The result of subtraction. |
| Factor | A number being multiplied. |
| Product | The result of multiplication. |
| Dividend | The number being divided. |
| Divisor | The number you divide by. |
| Quotient | The result of division (how many groups). |
| Remainder | What is left after dividing into equal groups. |
| Commutative property | Order can change; result stays the same ($a + b = b + a$). |
| Associative property | Grouping can change; result stays the same ($(a+b)+c = a+(b+c)$). |
Key Answers
Quick reference for this lesson’s exercise answers.
1. Let’s calculate — $47$, $3$, $30$, $51$, $20$, $70$, $44$, impossible ($24\div0\div6$), $20$.
2. Column method — $6541$;\; $4229$;\; $1109$.
3. $4006-418=3588$;\; $8559+8559=17118$.
4. Step by step — $720$;\; $1489$;\; $166$;\; $2100$.
5. Applications — $420$ boxes; yes ($15$ yuan, has $20$); $370$ m; (a) $720$ orders, (b) $60$ more.
6. $788+126=914$;\; $2593-1384=1209$.
7. Dividend $=78\times6+6=474$.