Building Speed and Fluency
Mental Math Strategy 
Resources to Practice this Skill 

Strategy, Explanation, Example 
Dice or Card Game 
Online activity Please note: Most of these games require Flash which is not accessible on the iPad 
Compensation Strategy Addition You can round the numbers up or down when adding, and then adjust the answer to compensate for the rounding. Eg. To add 28 and 36, I think 30+36=66, and 2 to get 64.
Round one or more of the numbers to numbers that are easier to work with, then compensate. Eg. 256+687 Round 687 to 700, an easier number to work with, by adding 13. Which give you 256+700=956. Subtract 13 by decomposition: 95610=946, then 9463=943.

Draw 4 cards to create a 2digit by 2digit addition problem. Use rounding up and down on one or both numbers to solve the problem. 
http://www.onlinemathlearning.com/additiongrade3.html Addition tips including compensation: https://www.mathsisfun.com/numbers/additiontipstricks.html 
Compensation Strategy Multiplication When multiplying larger numbers, we can also use the compensation strategy. Eg. 3x19 = ? 19 is close to 20, so we can multiply by the next multiple of ten which is 20. Then we build down because we have an extra group of 3. 3x19 becomes 3x20 = 60 – 3. So 3x19 = 57. Multiplying, rounding numbers up or down them build down 
Draw 3 cards to create a 2digit by 1digit multiplication problem. Use rounding up and down on one or both numbers to solve the problem. 
Use the compensation strategy to help you quickly solve problems in these games: http://www.kidsmathtv.com/free/multiply2by2digitnumbersgamefor4thgrademonsterboardgame/ 
Transformation
Strategy Eg. 46+28=? Adding 2 to 28 makes it 30, an easy number to work with but if 2 is added into this equation, then 2 must be subtracted from the 46. 28+2=30 and 462=44 so 30+44=74. Eg. 256+687=? Add 13 to 687 to make it 700, subtract 13 from 256 to make it 243 so 700+243=943. 
Start with the number 19. Draw 2 cards to create another 2digit number, for example 45. Use the transformation strategy to take 1 from your second number, add 1 to 19. 44+20=64. Other numbers to try as starters include 17, 21, 38 and 49. 

Multiplication using
the Split Strategy Automatic calculation of multiplications beyond 10x10 by multiplying numbers in 2 parts. Eg. 18x6=? This can be thought of as 10x6 + 8x6 = 60+48=108 
Finger Tables Each partner holds up ? out of 10 fingers, times the two sets of fingers together. Take turns to call out answer. Split the Dice Roll 3 dice. Create one 2digit number and one 1digit number. Multiply the two numbers together using the split strategy to find the answer. 
http://www.mathplayground.com/multiplication_blocks/index.html 
Doubling and Halving Strategy The factors of a multiplication question can be changed by halving the largest factor and doubling the smaller factor. Eg. 16x3 = ? We can halve 16 and double 3 to become: 8x6 = 48. Halve the larger factor, double the smaller factor i.e. 16x3=8x6 
Halving Square Numbers Flip over card, square the number then divide by 2. 

Multiplication by 1000 Automatically multiply any number by 1000. When we multiply by 1000 we move the number three place values to the left. Eg. 45x1000 = 45000 
Each finger is worth 1000. Partner holds up ? fingers, other player answers 1000 x ?, ie 2 fingers equals 2000 Draw two playing cards to create a 2 or 3 digit number, multiply by 1000 
http://kids.britannica.com/lm/games/GM_5_5/GM_5_5.htm https://www.mathgames.com/skill/5.19multiplicationupto1000 
Factors Recognise and articulate the association between multiplication and division. Explain that factors are the numbers we can multiply together to get another number and automatically recall some factors using multiplication tables knowledge. Eg. 2x3=6. Two and three are factors of 6. 
Factors Draw two cards to create a 2 digit number.List the factors of that number 
http://www.mathplay.com/FactorsandMultiplesJeopardy/FactorsandMultiplesJeopardy.html 
Multiples Explain that a multiple is the result of multiplying a number by an integer (not a fraction) and automatically recall multiples of a given number. Eg. 12 is a multiple of 3 as 3x4=12 
Using Human Reaction Cards, students are timed to see how fast they can go through the multiples on the card in ascending or descending order. 
http://www.mathplay.com/FactorsandMultiplesJeopardy/FactorsandMultiplesJeopardy.html 
Dividing by 100 
In pairs, students use the cards horizontally across the grid saying the division fact for each multiple. Their partner times their speed.ision facts of each multiple 

Equivalence of Decimals, Fractions and Percentages Develop an understanding of the equivalence of proper fractions and their relationship to decimal fractions. A proper fraction is one where the numerator is smaller than the denominator. Eg. 1⁄4 is a proper fraction which is equivalent to 25/100 = 25% 
Equivalent fractions Player 1 holds up number of fingers on one hand, for the numerator, then fingers on their second hand for the denominator. For eg. 3 and 6 create 3/6 

Rounding for Checking Use rounding as a way of identifying calculation errors resulting in unreasonable results. Eg. 417x8 = ? I know that 417x10 = 4710 and 400x8 = 3200 so a reasonable answer will be between these two. 
Using cards/dice, create a number with a number of digits as specified teacher. Round to the nearest place value identified by the teacher Ie Draw 4 cards for 1234, round to nearest tens equals 1230 
https://mirshahi.wikispaces.com/Rounding+Numbers+Game%2C+Practice+and+Test http://www.primaryresources.co.uk/maths/pdfs/IM_check1.pdf http://www.bbc.co.uk/skillswise/worksheet/ma06roune3westimatinganswerstocalculations 
Division Facts Relate all multiplication facts to division. For instance, I know that 9x3=27, so 27÷3=9 and 27÷9=3 
In pairs, students use the cards horizontally across the grid saying the division fact for each multiple. Their partner times their speed.ision facts of each multiple 

Counting in Fractions and Decimals Count by fractions up to tenths, both 1/10 and decimals, 0.1 
Adult chooses a fraction (start with simple fractions and progress to improper fractions then mixed numbers), student counts on in fractions Draw 2 playing cards to form a fraction. Count on and back I.e. You draw 4 and 5 to create ⅘. Count on with improper fractions with 5/5 (one whole), 6/5, 7/5… or Mixed numbers with 1 whole, 1 and ⅕, 1 and ⅖... Roll a dice, this number becomes the digit in the tenths place of the decimal. Count on and back. I.e. If you roll a 5 you create 0.5. Count on with 0.6, 0.7, 0.8… Count back with 0.4, 0.3, 0.2... 
https://www.studyladder.com.au/games/activity/countingonfractions21304?lc_set= 
Fractions Automatically add and subtract fractions with the same denominator. Eg. 4/10 + 3/10 = ? and 4/10 – 3/10 = ? 
Creating One Randomly draw two playing cards each to create a fraction. What will you have to add or subtract to reach one whole? 
http://www.mathsgames.org/fractiongames.html http://www.mathplayground.com/Decention/Decention_Secure.swf 