Differentiating Instruction in Math: Enough Theory! How do You Really

Do It?

Marian Small

April 2008

How did She get into DI?

What are different developmental stages?o Research study with many thousands

of students

o Creation of developmental maps to describe the stages, or phases, of development for each strand

Using Open Tasks

Start with an Answer

My answer is 15.

What’s my question?

Some Possibilities

o What is 10 + 5?

o What number comes after 14?

o What is 5 less than 20?

o What is a 2-digit factor of 30?

o What is the square root of 225?

o What number has a digital root of 6?

Number Sentences

o What number sentences does this show? Tell as many as you can.

Some Possibilities

o 3 x 5 = 15

o 5 x 3 = 15

o 15 ÷ 3 = 5

o 5 + 5 + 5 = 15

o 10 + 5 = 15

o 3 + 3 + 3 + 3 + 3= 15

Using Percents

o 72 is ___ % of ____.

o Fill in the blanks in different ways.

Some Possibilitieso 100% of 72

o 50% of 144

o 72% of 100

o 200% of 36

o 1% of 7200

o 150% of 48

o 600% of 12

o 0.1% of 72,000

Personal estimates

o About how many meals have you eaten in your life?

o About how many people do you see in a day? Tell how you estimated.

The Calendar

o Pick your favorite day of the week.

o How many months can start on that day in any one year? How do you know?

Alike and Different

o How are the numbers 10 and 45 alike?

o How are they different?

Some possibilities

o They are both 2 digits.

o They are both less than 100.

o They are both greater than 10.

o They are both multiples of 5.

o They are both amounts you can show with nickels.

Some possibilities

o One is more than 30 and one is less.

o One is even and one is odd.

o One is in the forties and one is not.

o One has a 1 as a digit and the other does not.

o One is a multiple of 10 and the other is not.

Alike and Different

o How are the number 3/4 and 5/8 alike and how are they different?

Some possibilities

o They are both fractions.

o They are both less than 1.

o Both have odd numerators and even denominators.

o They can both be written as eighths.

o They can both be written as thousandths.

Some possibilities

o One is more than 7/10 and the other is less.

o One has a denominator of 8 and the other has a denominator of 4.

o One is more than 2/3 and one is less than 2/3.

o One can be written as 12ths and the other can’t. (at least not as a simple fraction)

o The decimal for one starts with 0.6.., but the decimal for the other starts with 0.7…

A Division

Create a division question where each of the digits 2, 4 and 9 appears somewhere in the question.

Some Possibilities

o 94 ÷ 2 = 47

o 249 ÷ 1 = 249

o 216 ÷ 9 = 24

o 99 ÷ 2 = 49.5

Creating a multiplication

o Create an equation involving multiplication of fractions where the numbers 4, 9 and 10 are used somewhere.

Some possibilities

o 4/9 x 10/12= 10/27

o 4/10 x 9/9 = 2/5

o 4/6 x 5/9 = 10/27

Build a sentence

o Use these words and numbers to make a true sentence:

o 10, 50%, twice, difference

Some possibilities

o The difference between 10 and 50% of 80 is twice as much as 15.

o The difference between 50% of 10 and twice as much as 6 is that one is odd and the other is even.

o The difference between twice as much as 50% of 90 and 100 is 10.

Build a sentence

o Use these words and numbers to make a true sentence:

o 4, 2, sum, almost

Some possibilities

o The sum of 4 and 2 is almost 7.

o The sum of 8 groups of 4 and eight groups of 2 is almost 50.

o The sum of the 4 numbers 2, 10, 10, and 10 is almost 35.

A Rectangle within a

Rectangleo Draw a small rectangle.

o Create a bigger rectangle of which the small rectangle is a part. Tell what fractional part it is.

Possible Solutions

Questions for practice

o Replace the boxes with values from 1 to 6 five ways to make this true.

x

Questions for practice

o Replace the boxes with values from 1 to 6 five ways to make this true.

o 234 145 262 BUT 362

o x1 x3 x2 NOT x 3

234 435 523 1086

Toss and Win

• Toss a beanbag 3 times.

• Add the first 2 scores.

Subtract the last one.

! Win a prize with 0.5-1.0

points!

2.8 0.9 1.5

4.2 1.0 0.8

0.7 0.6 2.1

3.1 4.5 1.6

Making Patterns

Use square tiles to create a growing pattern.

Draw it. Tell why it’s a pattern.

Some Possibilities

.

Some Possibilities

Some Possibilities

Triangle sides

o One side of a right triangle is 5 inches long. How long could the other sides be?

Some possibilities

o 3 and 4

o 5 and 5√2

o 12 and 13

You Try!

Open these up:

o How many times as much as 16 is 48?

o How many meters long is your classroom?

o Which shape has a line of symmetry?

Parallel Tasks

Where Does It Go?Draw a line like this:

Choose one of these sets of numbers for the ends of the line:

0 and 20 15 and 16 -8 and -10

What number describes the position of the dot? Why?

Choose your shape

Pick one of these shapes. Represent the shape as many ways as you can. Use pictures, words, numbers and/or objects.

cube square cylinder hexagon

Some possibilities

Cube

o Show a skeleton

o Show a net (or several nets)

o Show one face

o Show all the faces

o Draw an isometric drawing

o Hold up a cubic shaped box

Missing Digits

o Figure out where the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 go.

4 x 2 = [ ] []6 + 49 = 8[]

[ ] x [ ] = 15 7[] + 9[] = []7[]

[] x 7 = 42 OR [][] + []2 = 10[]

[] x 6 = 54

5 x [ ] = [][]

[] x 3 = 2[]

Missing Digits

o Figure out where the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 go.

4 x 2 = 8 36 + 49 = 85

5 x 3 = 15 76 + 94 = 170

6 x 7 = 42 OR 27 + 82 = 109

9 x 6 = 54

5 x 4 = 20

7 x 3 = 21

Make a pattern

Use pattern blocks.

o Create a shape pattern where the 10th shape is a green triangle,

OR

o Create any shape pattern you wish.

Divide the shape

o Pick a shape. Divide it into 4 equal parts.

OR

o Divide this shape into 12 equal parts.

Draw a shape

o Draw a shape where one side is 4 cm long and one angle is 30°.

OR

o Draw a hexagon where one side is 4 cm long, one side is 6 cm long, one angle is 30° and one angle is 150°.

One way to go

Probability Draws

You can put 20 square tiles in a bag- any combo of red, blue and yellow. You will draw one tile.

o A: What tiles would you put in so it is possible, but not likely, to draw a red?

o B: What tiles would you put in so the probability of red is 2/5?

Measurement Hunt

o A: Find 5 items in the room that you think have more area than a recipe card. Check.

o B: Find 5 items in the room that you think have an area between 20 cm2 and 30 cm2. Check.

How many groups

Choose the number of students going to the track event and the number of buses from the choices below. Figure out how many people each bus needs to hold.

o 300 students in 6 buses

OR

o 435 students in 12 buses

Estimating percents

Choose a shape. Estimate the percent that is dark.

OROR

OROR

Cookie prices

Find the price of the larger bag of cookies if you know the price of the smaller one.

6 for $3

6 for $2.50

15 for ?

20 for ?

OROR

In Summary

We need to change our mindset.

Celebrate Differences

They don’t all have to do the same thing at the same time!

Download

You can download this presentation at

www.onetwoinfinity.ca (see quick links)