Strategies + ADDITION + Count All Count each number's amount and then count all starting back at 1.  Count On Count one number's amount and then continue counting... without going back to 1.  Think about doubles that can make up your number(s) or are close.  Working with Fives Decompose numbers to identify fives within numbers and add.  Making Tens Identify tens within numbers and add.  Using Compensation Compensate by shifting quantities from one addend to the other.  Using Known Facts Think about the numbers and how they are related to facts that you know.  Decomposing Use place value to decompose numbers - e.g., tens and ones. Add the numbers together by using place value.  Splitting Split the numbers into other addition facts and add using addition facts.  Jumps of 10 One number is kept whole and multiples of 10 are added.  Next Friendly Number Shift quantities to reach a 'friendly' number and adjust the other addend or the sum accordingly.  - SUBTRACTION - Using CountersCount out the number of chips for the first number and remove the second number of chips.  Counting Up Start with the second number and count up to the first number, keeping track of the whole number spaces between the two numbers.  Counting Back Start at 1 number and count backwards by the number being subtracted.  Making a 10 Addition facts for 10 can be used to find differences from 10.  Jumps of 10 Using a pattern of jumps of 10 may be used to reinforce close facts.  Using Doubles Uses addition doubles for subtraction halves (half doubles). May be used for facts close to the halves.  Related Addition Facts Uses reasoning to draw from known addition facts and relates them to subtraction. Seeing relationships between operations is vital for fluency and flexibility!  | Strategies x MULTIPLICATION x Representing Each Item Counting by Ones Count each group separately, then count the whole.  Repeated Addition Skip Counting Count by saying 4 + 4 = 8 and 8 + 4 = 12 or by saying, 4, 8, 12.  Unitizing Counting By Counting each group as one unit and realizing that each group must have the same number of objects. Groups may be regrouped into other equivalent groups before calculating.  Doubling Recognize that multiplying by 2 doubles a number.  Halving and Doubling Split one factor in half and double another factor.  Using the Distributive Property Partial Products A number in a multiplication expression can be decomposed into 2 or more numbers using addition or subtraction.  Using the Distributive Property of Tens Partial Products A Number in a multiplication expression is decomposed into 2 or more numbers with one (or more) of the numbers being a multiple of 10.  Using the Commutative Property Numbers can be multiplied in any order without effecting the product.  Associative Property The numbers being multiplied can be regrouped without changing the product.  ÷ DIVISION ÷ Representing Each Group and Counting All Make a representation for a group and put a tally mark for each object in the group. Repeat this until the number of tallies is the total count. Then count the number of groups to answer 'How many groups?'  Repeated Addition Skip Counting Counting On Make a representation for a group and record the number of objects in the group. Repeat, skip counting by the number of objects in each group until the total required is reached. The number of groups is the number of skip counts.  Using the Distributive Property of Multiplication Use simpler multiplication facts to determine how many groups there are.  Using the Commutative Property of Multiplication This strategy relies on knowledge of fair shares and equal groups. Count out all the items one by one into groups until all items are distributed.  |