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Overview
Overview
Knowing basic math facts in all the operations is key for students to be proficient in multi-digit calculations. However, students should not be encouraged or expected to simply memorize these basic facts.
“Over time, and with much experience and focused practice, children’s addition and subtraction calculations will become automatic. A child who is proficient has come to know his or her calculations to 20, not as isolated facts to be memorized, but as the result of working with different strategies and the construction of key ideas that can be applied across many calculations” (What To Look For, pp. 21-22).
In order to access the reasoning strategies referenced in this document, students need to know certain basic facts. For example, to use the "Up over 10" strategy, students need to know what pairs of numbers make 10, and be able to decompose the second number in the problem:
8 + 5
= 8 + 2 + 3
= 13
This knowledge of math facts to 20 is the foundation for the reasoning strategies needed to learn multiplication and division facts, as well as mathematical reasoning used in many areas of math.
Much research supports the idea that students need to learn math facts through using reasoning strategies.
"As students come to know basic facts in any operation, they progress through three phases (Baroody, 2006):
Phase 1: Counting (counts with objects or mentally)
Phase 2: Deriving (uses reasoning strategies based on known facts)
Phase 3: Mastery (efficiently produces answers)"
(From Math Fact Fluency : 60+ Games and Assessment Tools to Support Learning and Retention by Jennifer Bay-Williams and Gina Kling, p.4)
Students should learn addition (and subtraction) math facts in a certain order.
Source: Math Fact Fluency: 60+ Games and Assessment Tools to Support Learning and Retention by Jennifer Bay-Williams and Gina Kling, p. 6
Foundational strategy
One more than and 2 more than, one less than, 2 less than facts
Where does this go?
Counting on: solving 5 + 7 - “5,6,7,8,9,10, 11, 12”
and counting back:
solving 11 - 4 - "11, 10, 9, 8, 7"
Doubles (4 + 4, 8 + 8)
Reasoning strategies for multiplication (double your 2’s to get 4’s double 4’s to get 8’s)
Pairs of numbers that add to 10
Decomposing numbers to 10
Up and over 10, down and over 10
"8 + 5 = 8 + 2 + 3
= 13"
or "14 - 6 = 14 - 4 - 2
= 8"
Efficient counting on “I know 5 x 7 = 35, 6 x 7 is one more group of 7 .
35 + 7 = 35 + 5 + 2
= 42”
Facts involving removing a group
“I know 9 x 10 = 90.
To find 9 x 9, I need to remove a group of 9.
90 - 9 = 81”
Supporting Students with Automatic Retrieval
Supporting Students with Automatic Retrieval
How should students learn basic facts?
Experts have a number of suggestions:
Explicitly teach reasoning strategies
Inventory the known and unknown facts for each student
Build in success by beginning with easier and more useful strategies like combinations of 10
Provide engaging activities
From Elementary and Middle School Mathematics: Thinking Developmentally by John A Van de Walle et al, 2018, pp. 173-174
Games to Promote Automatic Retrieval
Games to Promote Automatic Retrieval
A modified version of the traditional "war" card game. This game provides a wider range of 'known facts' to be used to determine the sum of the two cards flipped. (Lawson; pg. 176).
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