2.3 Problem Solving

Strategies & Keywords

Divide & Conquer the Problem

🟡 Before: Plan

• Read: visualize
• Reread: code
• Sketch: predict

💬 "What is the problem asking? What would a reasonable answer be?"

🔵 During: Solve

• Show my strategies.
• Show my thinking.

💬 "Are my strategies effective and efficient? Is there another way to solve the problem?"

🟢 After: Check

• Check my work.
• Go back to the question.
• Answer in a complete sentence.

💬 "Did I answer the question? Does my answer make sense?"

Keywords

➕ Addition Terms

➖ Subtraction Terms

Problem Solving

Word Problems & Logic

1 John had 24 apples. Lama gave him 16 more. How many apples does John have now?

How many apples:

40 apples (24 + 16)

2 Lee bought 10 books and got 14 more from Joe and another 7 from Jess. How many books does he have altogether?

Books altogether:

31 books (10 + 14 + 7)

3 Find the total of 233,456 and 673?

The total:

234,129 (233,456 + 673)

4 A school has 287 students. 59 students are left at the end of year. How many students are remaining?

Remaining:

228 students (287 - 59)

5 What is the difference between 11786 and 1579?

Difference:

10,207 (11786 - 1579)

6 How much less than 40 is 25?

Less:

15 (40 - 25)

7 Sami subtracted a number from 4000 and got an answer of 1732. What was the number he subtracted?

Subtracted number:

2268 (4000 - 1732)

8 Complete the magic square. The sum of all numbers in every row, column, and diagonal should be 24.

7

6

11

12

8

4

5

10

9

🎯 To solve (not in book): Sum row/col to 24.

Click on dashed pink cells to view step answers!

9 Make up one addition problem and one subtraction problem of your own. Give them to a friend to solve them.

Your addition:

Example: 150 + 250 = 400

Your subtraction:

Example: 500 - 175 = 325

Unit 3: Multiplication

3.1 Multiplication Table

Solve the following products mentally, by hand or by using a pencil and paper:

a) 3 × 4 =

12

b) 7 × 4 =

28

c) 5 × 8 =

40

d) 10 × 3 =

30

e) 4 × 8 =

32

f) 6 × 6 =

36

g) 3 × 9 =

27

- Complete your own multiplication chart:

Only given values are shown below. Click to uncover all blank/empty squares:

3.2 Multiplication without Regrouping

Examples & Exercises

Look at these two examples:

Step (1): 3 × 2 = 6 ones
Step (2): 3 × 3 = 9 tens
Step (3): 90 + 6 = 96

Step (1): 2 × 2 = 4 ones
Step (2): 2 × 4 = 8 tens
Step (3): 2 × 2 = 4 hundreds
Total: 400 + 80 + 4 = 484

Exercise - Multiply:

The below mathematical result are entirely hidden exactly as the original student task page 23.

A-

320

× 3

960

B-

4432

× 2

8864

C-

13142

× 2

26284

3.3 Multiplication with Regrouping

Examples & Exercises

Look at this example: 206 × 3

Step (1): 3 × 6 = 18 ones = 1 ten and 8 ones
Step (2): 3 × 0 = 0 tens
Step (3): 3 × 2 = 6 hundreds
Step (4): 6 hundreds + 1 ten + 8 ones = 600 + 10 + 8 = 618

Exercise - Multiply:

A-

224

× 4

896

B-

429

× 2

858

C-

21347

× 2

42694

D-

244

× 3

732

Exercise: Multiplication Practice

Calculation Task

Multiply mentally or write:

A- 70 × 30 =

2100

B- 32 × 20 =

640

C- 45 × 11 =

495

Column Multiply Exercises:

D-

155

× 3

465

E-

256

× 2

512

F-

342

× 4

1368

G-

72

× 33

2376

H-

56

× 32

1792

I-

132

× 20

2640

J-

425

× 31

13175

3.4 Problem Solving

Task 1 - 5

1 Silva has 4 boxes of pins, each box contains 112 pins. How many pins does she have altogether?

Result:

448 pins (4 × 112)

2 I multiplied two numbers and got 324. What could the two numbers be? Do you have another solution?

Pairs that multiply to 324:

18 × 18 OR 12 × 27 OR 9 × 36 OR 162 × 2

3 Jill drives 50 people every day. He works 6 days a week. How many people will he drive in 3 weeks?

Total:

900 people (50 × 6 × 3)

4 There are 130 rows of 15 chairs in a hall. How many people can be seated?

Total seats:

1950 people (130 × 15)

5 In a library, a rack can hold 166 books. How many books can 14 racks hold?

Altogether:

2324 books (166 × 14)

3.4 Problem Solving (Continued)

Task 6 - 9

6 336 soldiers are lined up in each row. How many soldiers are there in 8 rows?

Soldiers:

2688 soldiers (336 × 8)

7 43 students are seated in each class. How many students are there in 10 classes?

Total:

430 students (43 × 10)

8 A book has 76 pages. How many pages are there in 46 books?

Pages:

3496 pages (76 × 46)

9 A box has 30 apples. How many apples are there in 35 boxes?

Amount:

1050 apples (30 × 35)