UK K12 GCSE/A-Level: Year 1 KS1 Mathematics - Addition and Subtraction, within 20

Learning Objectives

By the end of this topic, students will be able to: - Add and subtract numbers within 20 using a range of strategies, including counting on and counting back. - Use mental and written methods to solve addition and subtraction problems within 20. - Demonstrate an understanding of the concept of place value and how it relates to addition and subtraction.

Core Concepts

Addition and subtraction are fundamental mathematical operations that involve combining or separating numbers. In this topic, we will focus on adding and subtracting numbers within 20, which is a critical building block for more complex mathematical concepts.

• Counting on: This involves starting with a known number and adding a certain amount to find the total. For example, if we have 5 pencils and we add 3 more, we can count on from 5 to find the total: 5, 6, 7, 8.
• Counting back: This involves starting with a known number and subtracting a certain amount to find the difference. For example, if we have 8 pencils and we take away 3, we can count back from 8 to find the difference: 8, 7, 6, 5.
• Place value: This refers to the value of a digit in a number based on its position. In the number 14, the 1 is in the tens place and the 4 is in the ones place. Understanding place value is essential for adding and subtracting numbers within 20.

Worked Examples

Example 1: Counting on

Sarah has 5 pencils in her pencil case. She adds 2 more pencils to her case. How many pencils does Sarah have now?

To solve this problem, we can count on from 5: 5, 6, 7. Sarah now has 7 pencils in her case.

Example 2: Counting back

Tom has 12 pencils in his pencil case. He gives 4 pencils to his friend. How many pencils does Tom have left?

To solve this problem, we can count back from 12: 12, 11, 10, 9. Tom now has 9 pencils left in his case.

Example 3: Place value

Emily has 17 pencils in her pencil case. How many tens and ones does Emily have?

To solve this problem, we need to understand place value. The 1 is in the tens place and the 7 is in the ones place. Emily has 1 ten and 7 ones.

Common Misconceptions

• Some students may confuse counting on and counting back. For example, if we have 5 pencils and we add 3 more, some students may count back from 5 instead of counting on.
• Some students may not understand the concept of place value and may struggle to identify the tens and ones in a number.

Exam Tips

• Make sure to read the question carefully and understand what is being asked.
• Use a range of strategies, including counting on and counting back, to solve addition and subtraction problems.
• Pay attention to the place value of the numbers involved in the problem.

MCQs

MCQ 1: [F]

What is the result of adding 5 and 3?

A) 7 B) 8 C) 10 D) 12

Correct answer: A) 8 Why the distractors fail: Option B is one more than the correct answer, option C is two more than the correct answer, and option D is four more than the correct answer.

MCQ 2: [H]

What is the result of subtracting 2 from 14?

A) 12 B) 13 C) 16 D) 18

Correct answer: A) 12 Why the distractors fail: Option B is one less than the correct answer, option C is two less than the correct answer, and option D is four less than the correct answer.

MCQ 3: [F]

What is the place value of the digit 5 in the number 15?

A) Tens B) Ones C) Hundreds D) Thousands

Correct answer: B) Ones Why the distractors fail: Option A is incorrect because the digit 5 is in the ones place, not the tens place. Option C and D are incorrect because the number 15 does not have hundreds or thousands.

MCQ 4: [H]

What is the result of adding 7 and 9?

A) 15 B) 16 C) 18 D) 20

Correct answer: C) 16 Why the distractors fail: Option A is one less than the correct answer, option B is one more than the correct answer, and option D is four more than the correct answer.

MCQ 5: [F]

What is the result of subtracting 1 from 10?

A) 9 B) 8 C) 11 D) 12

Correct answer: A) 9 Why the distractors fail: Option B is one less than the correct answer, option C is one more than the correct answer, and option D is two more than the correct answer.

Short-answer questions

Question 1

Emily has 17 pencils in her pencil case. How many tens and ones does Emily have?

Question 2

Tom has 12 pencils in his pencil case. He gives 4 pencils to his friend. How many pencils does Tom have left?

Question 3

Sarah has 5 pencils in her pencil case. She adds 2 more pencils to her case. How many pencils does Sarah have now?

Question 4

What is the place value of the digit 3 in the number 35?

Question 5

What is the result of adding 9 and 5?