Yr 8 Adding & Subtracting Whole Numbers

Adding & Subtracting Whole Numbers

Number & Place Value Part 1

Key Terms

• Commutative law: two numbers can be added together in any order. Only true for addition.  $a+b=b+a$  but  $a-b\ne b-a$  

• E.g.  $3+2=2+3$  but  $3-2\ne2-3$  

• Associative law: three or more numbers can be added together in any order. Only true for addition.  $\left(a+b\right)+c=a+\left(b+c\right)$  but  $\left(a-b\right)-c\ne a-\left(b-c\right)$  

• E.g.  $\left(9+5\right)+2=9+\left(5+2\right)$  but  $\left(9-5\right)-2\ne9-\left(5-2\right)$  

Multiple Choice

True or false?

 $13+14=14+13$  

• True

• False

Multiple Choice

True or false?
 $17-8=8-17$  

• True

• False

Multiple Choice

True or false?
 $\left(13-8\right)-3\ne13-\left(8-3\right)$ 

• True

• False

Addition Algorithm

• You can use algorithms in order to add larger numbers

• In addition, if we have excess 'tens', we give it to the next number

• We add the numbers in the same column together, then add on top of that value the excess we received from the previous column

Subtraction Algorithm

• You can also use algorithms to subtract larger numbers

• Subtract the number on the bottom from the number on top

• If the top number is smaller than the bottom, we need to 'borrow' a ten from the next column to create a new two-digit number

• This decreases the next value by 1

Mental Strategies

• Partitioning: involves breaking down numbers into place value parts, evaluating each part separately before putting all sections together

• E.g.  $247+121=(200+100)+(40+20)+(7+1)=368$ 

• Compensating: rounding a number to the nearest ten, evaluating these values first, then adding or subtracting the remainder

• E.g.  $134+29=134+30−1=163$  

Mental Strategies

• Doubling or halving: multiplying or dividing a number by 2 then adding or subtracting the remaining amount

• E.g.  $35+37=2×35+2=72$  
  

• E.g.  $240−123=240÷2−3=117$ 

Poll

How do you feel about evaluating addition and subtraction problems using algorithms?

• Confident!

• Good

• Okay

• Not good

• Confused

Poll

Which mental strategy to you find the most comfortable using?

• Partitioning

• Compensating

• Doubling or halving