Chapter 1 Test Revision

Chapter 1 Test Revision

Number & Place Value

This revision task has 50 slides so should take 2 periods to complete

1A Whole Number Addition & Subtraction

• Commutative Law:  $2+3$  is the same as  $3+2$  (doesn't work for subtraction, only addition)

• Associative Law: Three or more numbers can be added in any order (but not subtracted)

Strategy 1: Partitioning

• Solve for the hundreds, tens and ones separately then combine altogether 

• Eg 1:  $247+121=(200+100)+(40+20)+(7+1)=368$  

• Eg 2:  $85-22=(80-20)+(5-2)=63$  

Strategy 2: Compensating

• Borrow from one number to make an easier calculation  

• Eg 1:  $134+29=134+30-1=163$  

• Eg 2:  $322-40=320-40+2=282$  

Strategy 3: Doubling

• Works if the numbers are close together 

• Eg:  $35+37=2\times35+2=72$  

Algorithms: Addition & Subtraction

1B Whole Number Multiplication & Division

• Commutative Law: $4\times5$ is the same as $5\times4$ (doesn't work for division, only multiplication)

• Associative Law: Three or more numbers can be multiplied in any order (but not divided)

Multiples of 10, 100, 1000...

• When multiplying by one of these numbers, just add the number of zeroes onto the end of the number

• Eg 1: $45\times1000=45000$  

• Eg 2:  $150\times10=1500$  (there is one 0 from the 150 and another from the 10)

Multiples of 10, 100, 1000...

• If the the first digit is something other than one (such as 200 instead of 100) multiply by that digit first then add the zeroes

• Eg 1: $23\times200=23\times2\times100=26\times100=2600$  

• Eg 2:  $5\times40=5\times4\times10=20\times10=200$  

Strategy 1: Commutative & Associative Laws

• Rearrange into an easier order

• Eg:  $5\times17\times4=5\times4\times17=20\times17=340$  

• Working left to right, it is easier to do 5x4 than 5x17

Strategy 2: Splitting into Factors

• Split a number into more manageable factors:

• Eg:  $5\times18\ =\ 5\times6\times3=30\times3=90$  

Strategy 3: Distributive Law

• Splitting a number into parts that add together

• Eg 1:  $4+87=(4\times80)+(4\times7)=320+28=348$ 

• Eg 2:  $96÷3=(90÷3)+(6÷3)=30+2=32$  

Algorithms: Multiplication & Division

1C Number Properties

• A multiple of a number is made by multiplying the number by all the counting numbers

• Eg: Multiples of 3 are 3, 6, 9, 12, 15, 18, 21...

• A factor is a number that can be divided into the given number with no remainder

• Eg: Factors of 12 are 1, 2, 3, 4, 6 & 12.

Prime & Composite Numbers

• A prime number only has factors 1 and itself

• A composite number has more than two factors

• Eg: Some primes include 2, 3, 5, 7 & 11

• Eg: Composites include all even numbers greater than 2, as well as 9, 15, 21 and so on

Multiple Select

Select all the prime numbers:

• 3

• 5

• 7

• 9

• 11

Squares & Square Roots

• Square numbers are a number multiplied by itself, and have an index power of 2

• Eg: $3^2=3\times3=9$  

• Square roots can be found by determining which number multiplied by itself gives the number under the square root symbol

• Eg:  $\sqrt{49}=7$  because  $7\times7=49$  

Cubes & Cube Roots

• Cube numbers are a number multiplied by itself, and then itself again, and have an index power of 3

• Eg: $2^3=2\times2\times2=4\times2=8$  

• Cube roots can be found by determining which number multiplied by itself twice gives the number under the cube root symbol

• Eg:  $^3\sqrt{27}=3$  because  $3\times3\times3=27$  

Writing numbers in Prime Factor Form

Lowest Common Multiple using Factor Trees

• Write both numbers in prime factor form then multiply together all the DIFFERENT primes raised to the HIGHEST power

• Eg: Find the LCM of 12 and 30

   $12=2^2\times3$ and  $30=2\times3\times5$  
   LCM is  $2^2\times3\times5=60$  

Highest Common Factor using Factor Trees

• Write both numbers in prime factor form then multiply together all the COMMON (same) primes raised to the LOWEST power

• Eg: Find the LCM of 12 and 30

   $12=2^2\times3$ and  $30=2\times3\times5$  
   HCF is  $2\times3=6$  

Multiple Choice

Using the divisibility rules, determine which of the following numbers is divisible by 2, 4 & 9

• 32

• 36

• 249

• 270

1E Negative Integers

• Negative numbers lie to the left of the number line

• Adding or subtracting a positive integer can result in wither a negative or a positive

1F Adding & Subtracting Negative Integers

• Adding a negative is the same as subtracting its opposite

• Eg: $2+\left(-3\right)=2-3$ 

• Subtracting a negative is the same as adding its opposite

• Eg:  $5-\left(-4\right)=5+4$  

Multiple Select

Which of the following are equal to 3? 

Hint: work each one out on paper - slow down!

•  $-1-2$  

•  $-2+5$  

•  $4-\left(-1\right)$  

•  $2-\left(-1\right)$  

•  $-5-\left(-8\right)$  

1G Multiplication & Division of Integers

• Same sign gives a positive answer

• Opposite sign gives a negative answer

Multiple Select

Which of the following are equal to –12? 

Hint: work each one out on paper - slow down!

•  $-24\div\left(-2\right)$  

•  $-3\times4$  
  

•  $144\div\left(-12\right)$  
  

•  $-6\times\left(-2\right)$  
  

•  $-36\div3$  
  

1H Order of Operations and Substitution

• B I MD AS

• Work through in BIMDAS order, then left to right

• Remember in an equation like $3-\left(-2\right)\times4=$  the  $\left(-2\right)$  can't be done first as there is no sum to compute inside the brackets, it is just a number

Substitution

• A letter that stands in the place of a number is called a pronumeral

• You can solve $-2a+b$ if you know the values of  $a$  and  $b$   

  
  

• Eg: If  $a=3$  and  $b=7$  , then:

•  $-2a+b=-2\left(3\right)+7=-6+7=1$  

• Remember  $-2\left(3\right)$  means  $-2\times3$  

• When you substitute, always write the number in brackets whererever you see the pronumeral

You made it! 🙌

• That is everything from chapter 1

• Please ensure you have completed all the fluency questions from each chapter, plus the end of chapter review questions on p55-57