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Building Blocks towards Fluency with Multiplication
Task
As we were reminded in the video, one of the building blocks for computational fluency is the ability to understand and trust the base-ten, multiplicative structure of our number system. Students come to understand that the 3 in 328 represents 3 hundreds and that this can also be thought of as 30 tens or as one-tenth of 3000. They are flexible in how they think about numbers based on what they know about place value.
Below are two calculator games designed to help students come to understand this concept. Take a moment to try these games with a partner. As you play them, think about the ways in which they might help reinforce place value.
MIX AND MATCH TASK: Print Instructions
PLACE VALUE WIPE OUT GAME: Print Instructions
Discuss
What place value concepts did you bump into as you played these games? In what ways do you see these concepts contribute to a student's procedural fluency? What other tasks, games or activities have you found helpful to build this important idea?
Record your ideas in Section 4.1a of your digital handout.
Task
Another important building block are the properties of multiplication. Below is a chart of some selected properties.
Review the chart to prepare for the task.
Analyze the three work samples below.
Discuss
For each sample, talk about what you notice.
a) Name the property the student might be using and explain why you believe this to be so.
b) Write a question you might ask each student about the strategy used to help him/her verbalize this idea.
c) Record your thinking in Section 4.1b of your digital handout.
Optional: Feeling Creative?
The names "Commutative Property", "Associative Property" and "Distributive Property" can feel a bit intimidating and unwieldy. And it's probably true that the technical terms are not as important to know as the principle behind the term.
So put on your creative hats and see what alternative, kid-friendly names you can come up with! For example, the students in one teacher's class calls the Commutative Property "The Old Switcheroo".
Write your suggestions in Section 4.1c of your digital handout and see what you can come up with!
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Task
PART A: Brainstorming Strategies
Suppose you didn't know 6 x 8. How could you find the answer?
a) Model your strategy with an array like the one below. Show how you partitioned the array into smaller pieces or rearranged parts or added rows and compensated to leverage familiar facts and derive your answer.
b) Write the symbolic representation -- the number sentence -- that models your array.
c) Name the property of multiplication that you implicitly drew on for your strategy.
d) Now think about how a student might describe your strategy. Record the "student's words" in Section 4.1d of your digital handout, along with the matching number sentence you would use to represent the thinking. A sample response for 6 x 7 is provided.
e) As time and interest allows, consider how a student could think about other "basic facts" and add your thinking to the same 4.1d section as well.
PART B: Strengthening Recall of Basic Facts
For many students the prospect of memorizing 100 disconnected multiplication facts(!) seems too daunting a task to even consider. But by looking for patterns and uncovering strategies for deriving facts, this task becomes much more manageable. In fact, it becomes logical and reasonable.
Read pp 30-34 from the Guide to Effective Instruction, Volume 5: Teaching Basic Facts and Multidigit Computation (selected pages 27-34). As you come across strategies that support the recall of facts, cross them off of the Mathies Interactive Multiplication Chart (Check out a list of all Mathies Learning Tools).
What facts do you have left? If any, how might students deal with these facts?
Discuss
PART A: Resources
Below is a game that could be used to reinforce basic facts in a problem solving context and emphasize the connection between multiplication and division. Take a moment to play this game with a partner and talk about the learning students would encounter. For materials you will need one game board, two paper clips and some two-colour counters.
MULTIPLICATION TIC TAC TOE: Print Instructions
What other tasks and activities have you come across to help strengthen your students' automaticity with basic facts? Share your resources with your group.
PART B: The Question of Timed Tests
Mad Minutes, "round the World, and other speed races have been a hallmark schools for decades in the quest to increase fluency with basic facts. What are your thoughts on the topic? What do you see as advantages and disadvantages? What does "automatic retrieval" mean to you and how does this happen?
Read the quote below from Marilyn Burns and bring her thoughts into your conversation.
What do you think?
Express your thoughts on the subject of timed tests in Section 4.1e of your digital handout.
And if not timed tests, what alternatives might you suggest to help students practise their basic facts and develop automaticity?
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