These two powerpoints contain ideas about decimals. The first one is not as organized as the second. the first one contains my notes about introducing the strips in class and the ideas I am keeping in mind as I work with a unit on decimals. Class Monday October 29

This second power point is focused on introducing the area model for decimals. The challenge is to help students see the links between number lines and area models. Decimal Update 2018

The decimal folder master:Decimal expander

**BEGINNING DOT COLLECTIONS**

Here are some assorted pages. They are just focused on number under 7 for the current Grade ones. Dot Collections Student Pages pdf

Here are some dot collection PPTs:

**WHAT’S COVERED IS THE WAY I INTRODUCE INVERSES. GRADE 2 AND 3 DEFINITELY NEED TO GET HERE. **

#### WC set up PPT

#### What’s covered using cards PPT

**IF STUDENTS ARE COUNTING THE DOTS, **

**THEY ARE NOT READY FOR THE NUMBER YOU CHOSE**

## I use two ten frames to develop number from 10 to 20. Grade 3 definitely need this kind of practice.

## Place value is much more than naming a position in a number. DO NOT LET OR TEACH STUDENTS TO IGNORE THE ZEROES. RIGHT FROM THE START THE ZEROES IN THE NUMBERS ARE IMPORTANT.

Rolling a 6 and saying it is 600 is not the same experience as seeing and saying 600.

Reading a number is not enough, we need to see that students can record it in words, expanded notations and with multiplicative units. Keeping and explaining the zeroes makes all the difference. When we short cut by ignoring the expanded notation, students fall behind and stay behind.

The number expander alone is not enough. After students read to the position, they should record the number.

## IMAGERY FOR 2 DIGIT NUMBER: Grade 2 and 3

I encourage use of the 100 GRID to build imagery for 2 digit number. Students must **trust** ten as a unit so they** BUILD** tens and place them in the grid, make expander cards and show how 30 + 3 fit together to make 33. Describe 33 as:

**3 tens, 3 ones 2 tens, 13 ones**

**3 (10) + 3(1) 2 (10) + 13 (1)**

**30 + 3 20 + 13**

Here are 2 powerpoints that help you think about how to work with this grid idea in Grades 2 and 3.

Strategies for mental fluency with addition and subtraction come from this work.

The number expander folder: Place Value Folder to millions

THE FOCUS IS to build a sense of size and relationships, to express numbers multiple ways. This builds flexible thinking and reasoning skills. The grid is a tool for thinking that students will use to explain a range of concepts across a range of grades. A 100 grid should not be mixed with or replaced by what teachers call “the hundred chart”. This chart is often used in ways that reduce flexible thinking and focuses students on rote counting and trying to remember rules. As my teaching has evolved I have found it does not promote the kind of flexible thinking I want my students to develop so I do not use it.

**Three digit numbers is the first time I introduce the number folder. FOLDING is critical. Then write the number showing the zeroes. **

Now can you explain where the 30 tens are in the image and how 30 tens is the same as 300. 30 (10) = 300.

## The imagery gives way to expanded notation. Expanding the numbers is critical to all students being successful. DO NOT “DROP” the Zeroes.

## Important Reads:

This brief is from the Chicago group. Excellent food for thought

Research and Practice review-math

What is number sense and how do we approach it with our teaching:

Do not agree with it all but a good read:

Developing the big ideas of number

Nora Newcombe: Spatial Reasoning and Curriculum Seeing Relationships Newcombe

Another Newcombe article on the importance of spatial reasoning: Picture This

This document was on the EDEL 316 site so you may already have it. Ontario Document on Spatial Reasoning Ontario Spatial Reasoning

**This book highlights current research with many contributors from Canada involved. Brent Davis is at U of Calgary. I am willing to lend out my copy. I will order for library.**

The Cover above is this document: Spatial ability handbook copy of introduction

Despite its age this publication is quite insightful and a reminder that these are not new understandings. It takes us forever in education to pay attention to what we are learning in research about learning.

An article about Order of Operations order-of-operations-the-myth-and-the-math

Spatial Reasoning with Appendix 2

Great tasks, problems and thinking. Anything and everything on the NRich website. https://nrich.maths.org

Susan Lamon writes everything you need to know and understand about Fractions. If you plan to teach Junior high I highly recommend because it is filled with examples and tasks. Again I am willing to lend out mine. Very practical and hands on.

Despite its age this article by JJ Greenwood is still so highly relevant. Again it was on the EDEL 316 site so you may have read it . Read it again. He really helps to make sense of process as a part of the learning and how you might include students in the assessment of their own understanding. JJ Greenwood

This article is written by a colleague and friend in Australia. Chris is from the Torres Islands and the only person in his culture to obtain a PhD in mathematics. His life’s passion is to make mathematics accessible to his culture. Timely and relevant, a first nation’s perspective on learning mathematics. Maths as storytelling

George Gadanadis is a friend and colleague at Western University. He has a number of passions one of which involves the Arts, poetry and story in math. The math is deep and rich and for young children. His materials and website are quite phenomenal. http://researchideas.ca/mathperformance.html

George’s work continues to evolve and he is now interested in computational thinking a hot topic that many are reducing to the trendy word “coding” and boxing up for more surface level trite. If you are curious take a look and listen http://imaginethis.ca/