Math 647 Unit 1: Early Number and Operations Concepts

Section 4: Strategies for computing basic facts and mental math, and teaching strategies for basic facts.

Goal: The goals this week are for you to

• Overview: Basic facts: what are they, why should we teach them, how can we teach them
• Mental math and basic fact strategies for addition and subtraction
• Array model for multiplication, thecommutative and distributive laws, and why they make sense.
• Mental math and basic fact strategies for multiplication and division.

I want you to start out by reading a couple of papers that have been very influential for the way I think about math facts. Right now, I'm just going to have you read a couple of things, and then answer a few questions about them.

Readings:

Read a lot of the FAQ Basic Facts: Questions, Answers & Comments that Ed Rathmell has written. (Content section of the D2L dropbox). We will be looking at specific addition and subtraction fact strategies in the next few lessons, so if you are looking for something to skip, you can skip some of that. Make sure you read the sections

• "What does it mean to teach basic facts?
• What do we know about teaching basic facts?
• How can we teach thinking strategies?
• When is basic fact drill appropriate?
• How should you assess children on the basic fact

Videos

Make 10 sample lesson ideas

Assignments:

Assn 14: Reflect on your experiences. Write answers to these questions (upload to the drop box)

Mental math and basic fact strategies for addition and subtraction

Addition Facts Strategies:

Overview
Counting On
Use Doubles
Make 10

Assignments

Assn 15: Take the addition facts D2L quiz

You will be allowed to take this quiz twice, and you will get the higher of the two scores (it's OK if you choose to take the quiz only once). I suggest the following strategy as a good one for learning this material:

• watch the lectures and take notes,
• take the quiz,
• go back to your notes and/or the lectures to make sure you understand why any incorrect answers were incorrect (e-mail me if it's unclear after going back to your notes why one answer is correct rather than another--I'd like to know which questions are unclear)
• retake the quiz.

Subtraction Facts Strategies:

• Overview
• Counting Strategies
• Use 10 Derived Facts Strategies
• Use Addition to figure out Subtraction

Read some more details and examples about how to represent and make connections between problem types by using part-whole diagrams.

Assn 16: Practice making and filling in part-whole diagrams for some addition and subtraction word problems.

Readings

• How does the part-part-whole language help students learn subtraction facts?
• Also, the sections in Basic Facts: Questions, Answers & Comments about strategies are is a good source to review the strategies in the videos. (optional)

Assignments

Assn 17: Take the subtraction facts D2L quiz (same structure as addition facts quiz)

Assn 18: Written practice with addition and subtraction facts thinking strategies

Array model for multiplication, the commutative and distributive laws, and why they make sense..

Videos to watch:

Array Model Multiplication: commutative and distributive laws
How to explain the commutative property
How to explain the distributive property

Assignments

 Assn 19: Explaining and understanding with the commutative and distributive laws. You can use the draw tools in Word to make the diagrams, or you can make the diagrams in Smart Notebook, or you can draw the diagrams by hand and use a scanner or camera to insert them into your document.

Mental math and basic fact strategies for multiplication and division.

Videos to watch:

 Part 1: Skip counting, counting up or down from a known fact, commutative law, patterns for 0, 1, 5, 9, 10

If the pattern for multiplying by 9 is new to you, you should watch this longer explanation of the 9's trick

Part 2: Doubling, and counting up or down revisited

Part 3: Distribitive law: breaking apart into known facts

First Edition: On the Children's Strategies CD, on the Multiplication and Division tab, watch the Counting and Derived facts clips

Second Edition: Read clips 4.5, 4.7 and 4.8, and watch the videos: CountMeasDiv and CountPartDiv in D2L->Content->Video clips (these clips come from the first edition CD). Also, review pgs 58-59 on strategies for division.

Reflecting on the division counting/derived facts videos.

Division Facts

Readings:

Read "Dad's" summary and explanation of multiplication fact strategies here: http://www.dadsworksheets.com/v1/Strategies/eight_rules_of_multiplication.html

Assignments:

Assn 20: Multiplication and division facts and fact families (type and dropbox or scan and dropbox)