Mental Math Strategies

Mental Math Strategies

With a solid part-whole understanding students learn about numbers as they compose and decompose them.  They can add the parts together to make the whole (total). They can subtract one part from the whole to find the other part.  When our students can fluently take numbers apart and flexibly put them back together, they truly have developed number sense.

For example,

Count on  and  Counting back (addition & subtraction)

  • Say one number’s amount and then continue counting

6+4=10   say 6, then continue counting up 4 more, 7,8,9,10 (students may need to track their counting using their fingers)

  • Start at one number and count backwards by the number being subtracted

9 – 2 =   7, in your head, count back two, 8,7 (students may need to track their counting using their fingers)

 

Making Tens (addition & subtraction)

  • Identify tens within numbers and add

9 + 7=?         7 is 6 + 1  so  9 + 1 + 6 =   10 + 6 = 16

  • Addition facts for 10 can be used to find differences from 10

6 + 4 = 10  can be helpful in finding   10 – 4 = 6    and   10 – 6 = 4

 

Doubles Plus or Minus (addition)

  • Think about doubles that can make up you numbers or are close to your number

Doubles are easier facts to recall and can be very useful

6 + 7 = ?     7 is 6+1  so you have 6+6+1=13  or 7+7-1=13

Using Doubles (subtraction)

  • Uses addition doubles for subtraction halves (half doubles):

Knowing 8 + 8 = 16  and  6 + 6 = 12 uses the idea of half doubles 16 – 8 = 8    and   12 - 6 = 6   may be used to reinforce close facts:  15 – 8 = 7  and  13 – 6 = 7

 

Working with fives (addition)

  • Decompose numbers to identify fives within numbers and add

6 +  7 =  ?     6 is 5 +1  and   7 is  5 + 2    so you have    5 + 1 + 5 + 2 = 10 + 3 = 13

 

Using Known Facts (addition)

  • Think about the numbers and how they are related to facts you know

7 + 8 = ?   I know that 8 + 8  is 16 and  7 + 8 is one less than that so  7 + 8 = 15

 

Decomposing  (addition)

  • Use place value to decompose numbers – e.g., tens and ones. Add the numbers together by using place value

27 + 44 =   27  is 20 + 7  and 44 is 40 + 4  so you have 20 + 40 = 60  and  7 + 4 = 11

then 60 + 11 = 71

 

Splitting (addition)

  • Split the numbers into other addition facts and add using addition facts

65 + 25 =    60 is 50 + 15  so you have 50 + 15 + 25 =  75 + 15 = 90

 

Jumps of 10 (addition)

One number is kept whole and multiples of 10 are added.

44 + 27 =    44 + 10 + 10 + 7 = 71

Examples were adapted from: Minton, L. (2007).  What if your ABCs were your 123s?  Building connections between literacy and numeracy.  Thousand Oaks, CA: Corwin Press, A Sage Publication.

 

Here are some activities to reinforce number relationships and practice using mental math strategies:

  • Tell math/number stories using real life situations. Say: “There are 9 spoons in the drawer.  I take out 4 spoons.  How many spoons are left in the drawer?”, “ We need 8 cans of chicken broth.  We only have 4 in the cupboard.  How many more do we need to buy?” More challenging situations might involve adding or subtracting larger numbers, or situations where your child might have to add or subtract more than once to solve the problem.

 

  • Use 10 beads or buttons to play a hiding game. Hide 4 in your hand, leaving 6 visible.  Ask: “How many are missing?”  Repeat, taking turns.

 

  • Place 3 pennies in a line. Add another line of 3 pennies.  Say: “I have 3 pennies.  I add 3 more.  Now I have 6 pennies.”  Have your child arrange the 6 pennies another way.

 

  • Play the broken calculator game with your child. Ask your child to pretend that the number 8 key on the calculator is broken.  Ask how he or she can make the number 18 appear on the screen without the 8 key (eg. 20-2, 15+3).  Ask other questions of the same type by using different “broken” keys.  Make this task easier or more challenging by varying the number your child must show on the calculator.

 

  • Play number games with your child using cards to add and subtract. Shuffle the cards and then leave them face down in a pile. Each player takes two cards and adds the numbers.  The player with the higher sum gets the other player’s cards.  Continue to take and add up two cards at a time until no cards are left.  The player with more cards is the winner.  The game can also be played with subtraction.  The player with the lower difference gives his or her cards to the other player.  The person with the fewest cards at the end is the winner.