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:  $85-22=(80-20)+(5-2)=63$  

Fill in the Blank

Use partitioning to solve:

 $146+241=$  

Fill in the Blank

Use partitioning to solve:

 $146+241=$  

Strategy 2: Compensating

• Borrow from one number to make an easier calculation  

• Eg 1:  $134+29=134+30-1=163$  

• Eg 2:  $322-40=320-40+2=282$  

Fill in the Blank

Use compensating to solve:

 $273+19=$  

Fill in the Blank

Use compensating to solve:

 $347-39=$  

Strategy 3: Doubling

• Works if the numbers are close together 

• Eg:  $35+37=2\times35+2=72$  

Fill in the Blank

Use doubling to solve:

 $60+62=$  

Algorithms: Addition & Subtraction

Fill in the Blank

Using the algorithm strategy and working out on a piece of paper, evaluate:

 $938+217=$  

Fill in the Blank

Using the algorithm strategy and working out on a piece of paper, evaluate:

 $141-86=$  

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:  $5\times40=5\times4\times10=20\times10=200$  

Fill in the Blank

Evaluate

 $40\times300=$  
Hint: think carefully about how many 0s you need to include

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

Fill in the Blank

Working out on paper, solve using the associative law:

 $4\times368\times25=$ 

Hint: you could actually do this without paper

Strategy 2: Splitting into Factors

• Split a number into more manageable factors:

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

Fill in the Blank

Working out on paper, split into factors to evaluate $24\times3=$  

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:  $96÷3=(90÷3)+(6÷3)=30+2=32$  

Fill in the Blank

Working out on paper, use the distributive law to solve

 $7\times89=$  
Hint: make 89 into an easier number

Fill in the Blank

Working out on paper, use the distributive law to solve

 $93\div3=$  

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  $3\times3\times3=27$  

Fill in the Blank

Evaluate  $\sqrt{121}=$  

Fill in the Blank

Expand (not solve)  $6^3=$  

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  $2\times3=6$  

Fill in the Blank

Draw factor trees on a piece of paper to work out the Lowest Common Multiple of 16 and 36

Fill in the Blank

Using the factor trees you have already drawn, now find the Highest Common Multiple of 16 and 36

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

Fill in the Blank

Work out on a piece of paper showing each new step, the answer to the following:

 $\left(4^2-\left(-4\times7\right)+9\right)+55\div\left(-11\right)=$ 

Remember start with the innermost brackets

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

Fill in the Blank

Evaluate $a^2+b^2$ where  $a=5$  and  $b=-4$   

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