The session, Math Continuum: Multiplication and Division - Session 3, was presented online on Thursday, November 14th. This online session was presented by Heather Wark (Lakehead University), Denise Ladd, and Tien Ngo (LKDSB Instructional Coaches).
Children should learn their number facts. However, they would benefit from learning these facts by using an increasingly sophisticated series of strategies rather than by jumping directly to memorization. - (Lawson, 2016, p. 4)
Strategies help students find an answer even if they forget what was memorized. Discussing math fact strategies focuses attention on number sense, operations, patterns, properties, and other critical number concepts. - (O’Connell & SanGiovanni, 2011, p. 5)
Strategies Include: - Array Model - Decomposing a Factor - Starting from a known fact - Distributive Property Join us for the next sessions that will dig into the strategies:
The session, Math Continuum: Addition and Subtraction - Session 2, was presented online on Tuesday, November 5th. This online session was presented by Heather Wark (Lakehead University), Janna Vlasschaert, and Pam Gallant (LKDSB).
Children should learn their number facts. However, they would benefit from learning these facts by using an increasingly sophisticated series of strategies rather than by jumping directly to memorization. - (Lawson, 2016, p. 4)
Strategies help students find an answer even if they forget what was memorized. Discussing math fact strategies focuses attention on number sense, operations, patterns, properties, and other critical number concepts. - (O’Connell & SanGiovanni, 2011, p. 5)
Strategies include:
- Doubles
- 5 anchor
- Known fact
- Up over 10
Join us for the next sessions that will dig into the strategies:
Strand: Number Sense and Numeration, Addition & Multiplication Math Strategy: Using Familiar Facts
Materials: • Triplets deck addition (BLM16 and BLM17) • Triplets deck multiplication (BLM19 and BLM20) (These are located in the Guides to Effective Instruction, Vol. 5) Overview:
Using the addition or multiplication cards provided in the GEIM Volume 5, students can play independently, in groups, or with the whole class. Students will have to match their answer card with the matching fact cards for each set. An example of a triplet would be the three cards: 3+5, 5+3, and 8; or 3 x 6, 6 x 3, and 18. In addition to sorting and matching the cards, you can also play a variation called « Go Fish », where students need 3 cards to make the set.
How this Supports Student Learning:
This game provides students an opportunity to strengthen their understanding of « commutative » property, which stems from the idea of moving stuff around. Addition and multiplication have the property of commutativity. When numbers are added or multiplied, the operation can occur with the values in any order and the same answer will be obtained: 3 + 2 = 5, 2 + 3 = 5; 4 x 6 = 24, 6 x 4 = 24. Subtraction and division are not commutative. Where to next?
Some students immediately see the connection between the commutative property of addition and multiplication. For others, this is something that has to be seen, felt and experienced many times before they believe it. That's okay! This activity provides an opportunity for the learners who need to see the connections to have that time. This property allows students to work with numbers flexibly, as they adjust numbers to make them easier to work with. One option to support students in grasping this concept would be to build arrays for multiplication and represent amounts with manipulatives when adding. Placing the values in the part-whole model would also support students to grasp this property.
Addition: Ten Frame activities in the Guide to Effective Instruction: Number Sense and Numeration K-3 support this thinking (i.e., Ten in the Nest, Ten Frame Cards, etc).
Multiplication: The game Boxed Out could support this thinking.
Materials: • 1 deck of cards with 10, J, Q and K removed • A math tool to help solve the problem (rekenrek, counters or square tiles) • 3 players
Overview:
In this game students work to find the “missing part” or value of the card on their head. Students take turns being the “sum finder”, adding up the value of the two cards and shouting out the sum. Each student needs to use the part they see (the value of the card on the other players forehead) and the whole to determine the value of the card on their forehead. After each turn the players rotate their roles by one so that each player has a chance to be the sum finder or to find the missing part.
How this Supports Student Learning:
Students are able to practice a variety of math strategies through this game. Students can find the missing part by counting on, making ten, using doubles or familiar facts. In this game, each player could be practising a different strategy. Having a math tool nearby will support students in solving the problem.
Where to next?
For students that are developing their ability to join numbers, removing all cards greater than 5 may be helpful. As students become comfortable finding the missing part you can increase the complexity of the game by adding higher value cards, eventually including 10 - K, and assigning a value to each card. Alternately you can refer to each card as a decimal tenths. For example if player 1 draws a 7 and player 2 draws a 4 the sum finder would call out “1 and 1 tenth”. In order for the “part finders” to win the round they must refer to their card as a tenth (I.e.7/10 or 2/10 in this case).
Math strategy: Using a Known Fact
Math strand: Number sense and numeration
Overview:
Using this addition and subtraction strategy students use a known fact that is closely related to the unknown fact to help them solve the equation. In the example from the video, 6+5 is unknown. The student thinks about a closely linked known fact, 6+4 = 10, then adjust the initial equation by one, and therefore the answer by one which would make 11.
Students may also commonly use a nearby double fact such as 6+6 or 5+5 to solve the problem, and adjust their solution accordingly.
How This Supports Student Learning:
Students who are using the known fact strategy are developing relational reasoning. They are beginning to work with numbers in more efficient and flexible ways, relying less on counting. They are continuing to build on part-whole relationships, recognizing that a first number (or part), plus a count of the second number (part), will give them the total amount (whole).
Where to Next:
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 such as Go fish 10, make 10 concentration, and handful of dice, from page 168- 171 from the ‘what to look for’ book by Alex Lawson can help children understand and see that smaller numbers make up larger numbers.
For more information about games other strategies please visit us on Instagram and Twitter at @LKelempro #EngageLK!
