Open Sentences – Basic 3 Mathematics Lesson Note (Second Term)

A. counting skill: numbers 1-400, 401-850 and 1-850

Quick review counting:

• By 100s: 100, 200, 300, 400, 500, 600, 700, 800
• By 50s: 400, 450, 500, 550, 600, 650, 700, 750, 800, 850
• By 10s: 810, 820, 830, 840, 850

Practice counting:

• From 395 to 405: _______
• From 795 to 805: _______
• From 845 to 850: _______
• Backwards from 850 to 840: _______

Number patterns:

• 400, 500, 600, _____, _____, _____
• 825, 830, 835, _____, _____, _____
• What comes before 850? _____
• What is 100 less than 850? _____

B. writing skill: writing of the numbers

Review writing numbers:

Write in words:

• 345 = Three hundred and forty-five
• 567 = Five hundred and sixty-seven
• 689 = Six hundred and eighty-nine
• 723 = Seven hundred and twenty-three
• 845 = Eight hundred and forty-five
• 850 = Eight hundred and fifty

Write in figures:

• Four hundred and fifty-six = _______
• Six hundred and twenty-three = _______
• Seven hundred and thirty-four = _______
• Eight hundred and twelve = _______
• Eight hundred and forty-seven = _______

C. open sentences

What are open sentences? Open sentences are math statements with missing numbers (usually shown with a box □ or letter).

Examples of open sentences:

• 5 + □ = 8
• 12 – □ = 7
• □ × 3 = 15
• 16 ÷ □ = 4

How to solve open sentences: Think: “What number makes this sentence true?”

Addition open sentences:

1. 7 + □ = 10 (What plus 7 equals 10? Answer: 3)
2. □ + 6 = 12 (What plus 6 equals 12? Answer: 6)
3. 8 + □ = 15 (Answer: 7)

Practice addition:

1. 9 + □ = 14, so □ = _____
2. □ + 5 = 13, so □ = _____
3. 6 + □ = 11, so □ = _____
4. □ + 8 = 16, so □ = _____

Subtraction open sentences:

1. 10 – □ = 6 (What subtracted from 10 equals 6? Answer: 4)
2. □ – 5 = 8 (What minus 5 equals 8? Answer: 13)
3. 15 – □ = 9 (Answer: 6)

Practice subtraction:

1. 12 – □ = 7, so □ = _____
2. □ – 4 = 9, so □ = _____
3. 18 – □ = 11, so □ = _____
4. □ – 6 = 8, so □ = _____

Multiplication open sentences:

1. □ × 4 = 12 (What times 4 equals 12? Answer: 3)
2. 5 × □ = 20 (What times 5 equals 20? Answer: 4)
3. □ × 3 = 18 (Answer: 6)

Practice multiplication:

1. □ × 2 = 14, so □ = _____
2. 4 × □ = 16, so □ = _____
3. □ × 5 = 25, so □ = _____
4. 3 × □ = 21, so □ = _____

Division open sentences:

1. 12 ÷ □ = 4 (12 divided by what equals 4? Answer: 3)
2. □ ÷ 3 = 5 (What divided by 3 equals 5? Answer: 15)
3. 20 ÷ □ = 5 (Answer: 4)

Practice division:

1. 18 ÷ □ = 6, so □ = _____
2. □ ÷ 4 = 7, so □ = _____
3. 24 ÷ □ = 8, so □ = _____
4. □ ÷ 5 = 6, so □ = _____

D. quantitative reasoning

Word problems with open sentences:

1. Kemi had some marbles. She bought 5 more and now has 12 marbles. How many did she have at first?
   1. Open sentence: □ + 5 = 12
   2. Answer: □ = _____
2. Tolu had 15 sweets. He ate some and has 8 left. How many did he eat?
   1. Open sentence: 15 – □ = 8
   2. Answer: □ = _____
3. A farmer packed eggs in boxes of 6. He used 4 boxes. How many eggs in total?
   1. Open sentence: 6 × 4 = □
   2. Answer: □ = _____
4. 28 pupils are divided into equal groups. There are 4 groups. How many pupils in each group?
   1. Open sentence: 28 ÷ 4 = □
   2. Answer: □ = _____

Missing number patterns:

1. 345, 350, □, 360, 365, so □ = _____
2. 800, 810, □, 830, 840, so □ = _____
3. 12, 15, 18, □, 24, so □ = _____

Two-step open sentences:

1. □ + 7 – 3 = 12, so □ = _____
2. 5 × □ + 2 = 17, so □ = _____
3. 20 – □ + 4 = 18, so □ = _____

Check your answers: Substitute your answer back into the sentence to check if it’s correct. Example: If □ + 8 = 15 and you think □ = 7, check: 7 + 8 = 15 ✓

CLASS EXERCISES

1. Count by 100s from 100 to 850:
2. Write in words:
   1. 456 = _______
   2. 678 = _______
   3. 834 = _______
3. Write in figures:
   1. Five hundred and forty-three = _______
   2. Seven hundred and sixty-seven = _______
4. Solve these open sentences:
   1. 8 + □ = 13, so □ = _____
   2. 15 – □ = 9, so □ = _____
   3. □ × 4 = 20, so □ = _____
   4. 18 ÷ □ = 6, so □ = _____
5. More open sentences:
   1. □ + 9 = 17, so □ = _____
   2. □ – 7 = 12, so □ = _____
   3. 6 × □ = 24, so □ = _____
   4. □ ÷ 5 = 8, so □ = _____
6. Word problems:
   1. Ada had some books. She gave away 6 and has 14 left. How many books did she have originally? (□ – 6 = 14)
   2. A box has 5 rows of cookies. There are 25 cookies in total. How many cookies in each row? (5 × □ = 25)
7. Pattern completion:
   1. 567, 577, □, 597, so □ = _____
   2. 750, 760, 770, □, so □ = _____
8. Check these solutions:
   1. If □ + 12 = 20 and □ = 8, is this correct? _____
   2. If 24 ÷ □ = 6 and □ = 4, is this correct? _____
9. Two-step problems:
   1. □ + 5 – 2 = 10, so □ = _____
   2. 3 × □ + 4 = 19, so □ = _____
10. Create your own open sentence and solve it: My open sentence: _______ The answer is: _______