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.

Technology tool
Help files
Equation Editor (use for assn 21)
These are the same videos as you will find in the link to assn 21. 
Using Equation Editor part 1; part 2
If you find that you do not have Equation Editor in your copy of Word (it did come free with Word, but it may not have been installed) an easy fix is to download and install the 30 day free trial version of MathType.  After  30 days, it turns into Math Type lite which is very similar to Equation Editor..

About Assignments:
  • Everything called an assignment (with an assignment number) will be graded. 
  • Unless it is a D2L quiz, you should be turning something in for each assignment to the appropriate D2L Dropbox
  • After assignment 21, you will have had experience with each of the programs/file types you will be using in this class.  For each assignment it is your responsibility to:
    • Format the problems and answers so that you have sufficient space to answer each problem appropriately.  This may sometimes involve changing my formatting to include more white-space.
    • Choose an appropriate program/file type to submit your work.  Except for the occasional assignment where I specify a file type (such as videos) you may choose whichever of the following is most conventient for you.  Please submit work in one of these forms:
      • A Microsoft Word document
      • A SMART Notebook file
      • A handwritten, scanned in, picture which has been inserted into a Microsoft Word document
      • A link to a video on the web, where the link has been pasted into a Word document.
      • A video uploaded in .swf format (other formats may also be acceptable--check with me first)
    • If for some reason you can't use one of these file formats (for example, if you can't insert your scanned documents into Word), you need to contact me and work something out individually.

Goal: The goals this week are for you to

Basic facts: what are they, why should we teach them, how can we teach them.

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.


Read a lot of the FAQ Basic Facts: Questions, Answers & Comments that Ed Rathmell has written. 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?" and "How should you assess children on the basic facts?"


Make 10 sample lesson ideas


Assn 19: Write responses to these questions (upload to the drop box) June 18

Mental math and basic fact strategies for addition and subtraction

Videos to watch

Addition Counting Strategies

Addition Derived Facts Strategies

Subtraction Counting Strategies

Subtraction Derived Facts Strategies

And using Addition to figure out Subtraction


(optional) The sections in Basic Facts: Questions, Answers & Comments about strategies are is a good source to review the strategies in the videos.


Assn 20: Write some word problems for teaching addition and subtraction facts strategies (dropbox) June 18

Assn 21: Write a speed sheet for addition facts practice (dropbox) June 18

Assn 22: Watch the lesson Dino Math which is # 12 in the Teaching Math Video Library K-4 at, and then write me an answer to these two questions (dropbox) June 21

Array model for multiplication, thecommutative 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

To read:

 Let me know if you need me to write something for here. 


 Assn 23: Explaining and understanding with the commutative and distributive laws (dropbox) June 21

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

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

Division Facts


From the Math Trailblazers: Teachers site, read the TIMS Tutor on Math Facts pages 258-260 (Multiplication and Division facts Strategies)

Read the article Learning to Think in the Content->Readings section of D2L


Assn 24: Multiplication Fact Strategies (dropbox or scan and dropbox) June 23

Assn 25: Watching Division Strategies (dropbox) June 23

Assn 26: Fact Families  (dropbox) June 23

[you should work on the exam review, and then arrange to take the exam on or before June 26.]