Phases of Basic Fact Mastery
Students can go through the three phases below for fact mastery.
Phase 1: Counting (Count with objects or mentally).
Phase 2: Deriving (Use reasoning strategies based on known facts).
Phase 3: Mastery (Efficient production of answers).
Too often students are not given experiences in phase 2 and the emphasis is on memorization to go from phase 1 to phase 3. Phase 2 is crucial for developing mathematical thinking and mastery based on understanding.
Addition Fact Strategies
The problems presented in the book align with the strategies below. The strategies are listed in the order they can be used in the book. Problems can be solved in more than one way. The use of base 10 blocks and 10 frames can aid students’ thinking. There are a number of websites that have base 10 blocks and 10 frames.
1 more/2 more
In this strategy, students solve problems that require adding 1 or 2 to a number. Students can do this by counting on from the given number or adding two.
4 + 2 = 6
The counting on strategy for this problem would be to start at 4 and count two more to get the answer 5, 6.
Combinations that make 10
These facts involve numbers that add up to 10. These are important facts for students to know.
7 + 3 = 10
In this strategy, students would decompose one number in order to make a 10 and then add the remaining part of the number.
8 + 6
8 + 2 + 4
10 + 4
Students can work with problems that involve adding the same number.
4 + 4 = 8
If students know their doubles, they can then use those facts to be able to solve near doubles problems.
6 + 7
6 + 6 + 1
12 + 1
In this strategy, students decompose numbers to work with fives and then add the remaining numbers.
7 + 8
5 + 2 + 3 + 5
5 + 5 + 2 + 3
10 + 5
The commutative property of addition states that you can add numbers in any order. Students can double the number of facts that they know when they use this property. This property is not true for subtraction.
3 + 4 = 7
4 + 3 = 7
Questions to ask children while reading the book or while they play the games in the back of the book
-How did you figure it out?
-Can you say out loud how you thought about it in your head?
-Is there another way you could figure it out?
-Can you think of another fact that strategy would work well with?
-If someone didn’t know the answer to ____, how would you tell them to figure it out?
Stohlmann, M. (2019). Go knights go! Seattle, WA: KDP.
Christian, author, and professor of mathematics education.