1 Natural Numbers Learning Outcomes Identify and list

1 Natural Numbers – Learning Outcomes Identify and list natural numbers. Add, subtract, multiply, and divide natural numbers. Use the number line to illustrate arithmetic operations. Use skip counting and area models to illustrate multiplication problems. Solve problems about factors and multiples. Identify prime factors, and prime factorise numbers. Use the order of operations to solve problems. Use the commutative, associative, and distributive properties to solve problems.

2 Identify and List Natural Numbers

3 Identify Natural Numbers

4 Use the Number Line to Illustrate Addition Number lines are used to represent numbers and compare their sizes. Since 1 is the smallest natural number, it goes on the left. Numbers increase as you go to the right. Don’t forget the arrows at both ends! (they mean the line keeps going past what we can see)

5 Use the Number Line to Illustrate Addition

6 Use the Number Line to Illustrate Addition

7 Use the Number Line to Illustrate Addition

8 Subtract Natural Numbers

9 Use the Number Line to Illustrate Subtraction

10 Use the Number Line to Illustrate Subtraction

11 Multiply Natural Numbers

12 Use Area Model to Illustrate Multiplication Area models can also be used to find products. The product of two numbers is the area of a rectangle with those side lengths.

13 Use Area Model to Illustrate Multiplication

14 Use Skip Counting to Illustrate Multiplication

15 Use Skip Counting to Illustrate Multiplication

16 Solve Problems about Factors

17 Solve Problems about Factors The highest common factor (HCF) of a set of numbers is the greatest factor they all share. Outcome check: Find the HCF of these sets of numbers: 1. 12, 18 2. 63, 42 3. 90, 135 4. 3, 5, 9 5. Gheed wants to plant 63 tomato plants and 81 rhubarb plants. She wants to plant them in rows where each row has the same number of tomato plants and the same number of rhubarb plants. What is the greatest number of rows she can plant?

18 Solve Problems about Multiples of a number are the set of that number multiplied by natural numbers. e. g. Multiples of 3 = {3, 6, 9, 12, 15, 18, 21, …} e. g. Multiples of 7 = {7, 14, 21, 28, 35, 42, 49, …} Outcome check: List the first seven multiples of: 1. 4 2. 11 3. 12

19 Solve Problems about Multiples The lowest common multiple (LCM) of a set of numbers is the least multiple they all share. Outcome check: Find the LCM of these sets of numbers: 1. 4, 9 2. 2, 6 3. 12, 8 4. 6, 10, 12 5. Alanah is buying burgers and buns for a barbecue. Burgers come in packs of 4 and buns come in packs of 6. What is the smallest number of burgers that Alanah can buy?

20 Solve Problems about Factors Prime numbers have exactly two factors (itself and 1). e. g. 5 is only divisible by 5 and 1, so 5 is prime. e. g. 12 is divisible by 1, 2, 3, 4, 6, and 12; so 12 is not prime. Outcome check: List all the factors of the following numbers and state whether they are prime: i. 6 ii. 7 iii. 8 iv. 23

21 Solve Problems about Factors

22 Solve Problems about Factors Outcome check: Express each of the following numbers as a product of prime factors (i. e. prime factorise): 1. 12 2. 32 3. 48 4. 59 5. 90

23 Use Order of Operations to Solve Problems

24 Use Order of Operations to Solve Problems To resolve problems, operations are tackled in order of strength – GEMDAS G – groups (operations inside brackets, roots, modulus, numerators, denominators, …) are always strongest. E – exponents (powers, roots) are next. MD – multiplication, division are the same strength. AS – addition, subtraction are the same strength. If a tie would cause different answers, work from left to right.

25 Use Order of Operations to Solve Problems Evaluate G – groups E – exponents MD – multiplication, division AS – addition, subtraction

26 Use Order of Operations to Solve Problems Evaluate G – groups E – exponents MD – multiplication, division AS – addition, subtraction

27 Use Order of Operations to Solve Problems Evaluate G – groups E – exponents MD – multiplication, division AS – addition, subtraction

28 Use Order of Operations to Solve Problems

29 Solve Problems using Commutativity

30 Solve Problems using Commutativity

31 Solve Problems Using Associativity

32 Solve Problems using Associativity

33 Solve Problems using Distribution Multiplication distributes over addition, but not the other way around.

34 Solve Problems Using Distribution