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Overview
Overview
In this addition and subtraction strategy students use a known fact that is closely related to the unknown fact to help them solve an equation.
In the example from the video, 6+5 is unknown. The student thinks about a closely-linked known fact, 6+4=10, then adjusts the initial equation by one, and therefore the answer by one which would make 11.
Commonly used known facts may include doubles, such as 6+6 or 5+5, to solve a problem and adjust their solution accordingly, or combinations of 10 (6+4, 7+3 etc.) to arrive at the answer.
Examples of what students might do:
equivalence
Marcus also constructs the key idea of equivalence by adjusting both sides of the equation. He knows that, for addition, if he adds to or subtracts from an addend, then the same amount must be added to or subtracted from the sum to maintain equivalence.
Adapted from Alex Lawson What to Look For Resource (pg. 62-66)
Marcus adjusts the calculation by taking 1 from the 7 and adding it to the 5 to make 6 + 6, a double he knows.
Marcus knows a nearby fact, such as 5 + 6 = 11 , and adjusts; in this case, by adding 2 to the 6 and 2 to the sum.
Marcus knows a nearby fact, such as 15 - 8 = 7 and adjusts; in this case, since the start number (13) is less than 15, then the difference is 2 less than 7.
A powerful strategy for children to possess is using facts that they know to assist them in determining the answer to facts that they do not yet know.
Note #1
Common known facts may include making 10 facts and doubles facts.
Note #2
Students may use these known facts as a starting point to solve unknown equations.
For example, a student who has become comfortable making 10 may using the following strategy to solve 6 + 3.
They may recall that 6 + 4 = 10 and start with that. Knowing 3 is 1 less than 4, they may subtract 1 from their final answer to get 9.
Note #3
Students may also use known double facts to help solve an unknown equation. For example, 15 + 16 may be looked at as 15 + 15 = 30. The student knows that 16 is one more than 15 and add one to the final answer.
Note #4
Students may also use known double facts to help solve an unknown equation. For example, 15 + 16 may be looked at as 15 + 15 = 30. The student knows that 16 is one more than 15 and add one to the final answer.
Supporting Students with Using a Known Fact
Supporting Students with Using a Known Fact
Use tools like the rekenrek to model student thinking when one fact is derived from another.
Modelling 'using known fact' strategy using a rekenrek when solving word problems.
Question: You have 14 gummi bears. You eat 5. How many do you have left?
As students begin to reason with the numbers mentally, their thinking can be shown in written form.
Example:
Student: I know 5+7 is 12 because it is the same as 5+6, which is 11, and 1 more
Teacher: 5+7=5+6+1
(Lawson pg. 39)
Next Steps!
As students build on their strategies for working with numbers in more and more flexible ways, they can begin to develop other strategies such as decomposing one or both addends to find anchors of five, for example 6+7 =(5+1) +(5+2)and then onto up and over 10, for example 7+5=(7+3) +2.
Games to Promote Using a Known Fact
Games to Promote Using a Known Fact
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).
I Spy
I Spy
In this game, students challenge each other to find different ways of making the same sum.
In this variation of the classic "concentration" or "memory" game, students make a match by finding 2 cards that add to 10 (Lawson; pg. 172).
This game supports known facts for combinations of ten.
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