DIFFERENTIATED INSTRUCTION How, Why and Doing it on the Fly Kelly Zinck HRSB Math Coach.

DIFFERENTIATED INSTRUCTION

How , Why and Doing it on the Fly

Kelly ZinckHRSB Math Coach

My Inspiration

TED Talk – Dan Meyer: Math Class Needs a Makeover

Marian Small – http://www.onetwoinfinity.ca/

http://www.101qs.com – Working on your creative questioning muscles!

Trying it on...

Original Question (as best as I can remember!)

I have 8 coins. Half are quarters, ¼ are dimes and the rest are nickels. How much money do I have in total?

Making it interesting...

I have some coins in my name badge holder. (Shake the coins for dramatic effect!) How much do I have?

You can ask me some questions about my coins.

Talk with a partner about what you might ask me. (engaging the whole class in the process)

Go!

Record and Answer (some) Questions How much money do you have? (nope!) How many coins do you have? (8) What types of coins? (quarters, nickels and

dimes) How many of each? (half are quarters and

1/4 dimes, the rest are nickels) Remember to ask questions of the students.

“How will it help you solve our problem?” “ Why do you want to know that?”

The Most Interesting Question that I Almost Overlooked

What kind of coffee do you drink?

This student figured that I kept my coffee money in my name badge. If he knew the cost of my favourite coffee, he’d have the problem solved. Based on his question, we created a series of extension

questions to keep the problem solving going.

The Challenge in Math Classrooms

Differentiation in math is a relatively new idea

It’s not easy in math to simply provide another book to read.

Perhaps teachers may never have been trained to really understand how students differ mathematically

How Students Might Differ

In one cupboard, you have three shelves with 5 boxes on each shelf. There are three of those cupboards in the room. How many boxes are stored in all three cupboards?

Possible approaches: Liam raises his hand and waits for the teacher to help him. Angela draws a picture of the cupboards, the shelves and the

boxes and counts each box Tara writes 5+5+5+5+5+5+5+5+5 John uses addition and writes 5+5+5=15, then adds again, writing

15+15+15=45 Rebecca uses a combination of multiplication and addition and

writes 3 x 5 = 15, then 15+15+15=45

Principles and Approaches to Differentiating Instruction

There is general agreement that to effectively differentiate instruction, the following elements are needed:

Big Ideas. The focus of instruction must be on the big ideas being taught to ensure they are all addressed, no matter at what level.

Choice. There must be some aspect of choice for the student, whether in content, process or product.

Preassessment. Prior assessment is essential to determine what needs different students have.

The Big Ideas for Number and Operations

There are many ways to represent numbers.

Numbers tell how much or how many.

Number are useful for relating numbers and estimating amounts.

By classifying numbers conclusions can be drawn about them

The Big Ideas for Number and Operations

The patterns in the place value system can make it easier to interpret and operate with numbers.

There are many different ways to add, subtract, multiply and divide numbers. It is important to recognize when each is appropriate to use.

It is important to use and take advantage of the relationships between the operations in computational situations.

Why Open Questions?

Expose student thinking so you know what to do next.

Make students feel like their contributions actually make a difference (ownership of the math)

Enrich and broaden everyone’s learning

Strategies for Creating Open Questions

Give the answer – what is the question?

Choose your own values (“Just Right Numbers”)

Use words like a little, a lot, slightly, just

Create a sentence that includes these words.

Original Question – MMS5 pg.56

Gabi has 4207 pennies.She wants to share them equally among 7 people.How many pennies will each person get?How did you find out?

Opening it up…

Gabi has a lot of pennies.

She wants to share them equally among ___ people.

How many pennies will each person get?

How did you find out?

Gabi has a little more than 4000 pennies.

She wants to share them equally among some people.

How many pennies will each person get?

How did you find out?

More ways...

Create a sentence with the words 4207, equally, and 7.

The answer is 601. What is the question? Gabi has (4207, 210) pennies.

She wants to share them equally among (7, 5) people.How many pennies will each person get?How did you find out?

Original Question: MMS5 pg 263

Helena has 8 doughnuts to share among 5 people. How much will each person get?

Opening it up….

Helena has an even number of doughnuts to share among an odd number of friends.

Can the doughnuts be shared equally without cutting them? Prove your answer.

Helena has about a dozen doughnuts to share among 5 friends?

How much will each person get?

More Ways...

Create a sentence with the words donut, 8, 5 and fraction.

The answer is

Original Question: MMS5 pg 44

A theatre has 16 rows of seats.Each row has 24 seats.How many seats are in the theatre?

Opening it up….

A theatre is made up of rows of seats.

Design your own theatre by choosing the number of rows and the number of seats in each row.

How many seats are in your theatre?

A theatre has ___ rows.

Each row has a little more than 25 seats.

How many seats are in the theatre?

A theatre has ___ rows.

Each row has a little more than 25 seats.

How many seats are in the theatre?

If you added a few more rows, how many seats are in the theatre now?

If you tripled the capacity of the theatre, how many seats would there be?

For every 25 seats, you must include an accessible seat. How many accessible seats would be in the theatre?

If your theatre was full (1/2 full, ¾ full), and each person spent more than $5.00 at the concession stand, how much money was spent on concessions?

Make up some math questions about your theatre.

Original Question: Grade 3 guide

Ask students to give the compatible number for each of the following:

a. 82 b. 49 c. 65 d. 75 e. 60

Opening it up…

Choose a 2-digit number. What is its compatible number?Choose a 2-digit number that has a (5, 9) in the ones place. What is its compatible?Choose another one. What patterns do you notice?

Across the grades…How many more counters to fill up this 10-frame?Compatible numbers to 10?Compatible numbers to 100, 1000, 10 000?Compatible numbers with tenths, hundredths, thousandths?

Try it!

Chose a typical closed form question.

Try opening it up – share your ideas!

Assessment and Management Creating instructional responses for your

learners.

Knowing your purpose. What is the big idea the students need to work on?

Building “grit”

Next Steps

New 4-6 Curriculum PD

Marian Small @ Oak Island

NCTM Annual Conference in New Orleans, LA