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? oResearch study with many thousands of students oCreation 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 oWhat is ? oWhat number comes after 14? oWhat is 5 less than 20? oWhat is a 2-digit factor of 30? oWhat is the square root of 225? oWhat number has a digital root of 6?

Number Sentences oWhat number sentences does this show? Tell as many as you can.

Some Possibilities o3 x 5 = 15 o5 x 3 = 15 o15 ÷ 3 = 5 o = 15 o = 15 o = 15

Using Percents o72 is ___ % of ____. oFill in the blanks in different ways.

Some Possibilities o100% of 72 o50% of 144 o72% of 100 o200% of 36 o1% of 7200 o150% of 48 o600% of 12 o0.1% of 72,000

Personal estimates oAbout how many meals have you eaten in your life? oAbout how many people do you see in a day? Tell how you estimated.

The Calendar oPick your favorite day of the week. oHow many months can start on that day in any one year? How do you know?

Alike and Different oHow are the numbers 10 and 45 alike? oHow are they different?

Some possibilities oThey are both 2 digits. oThey are both less than 100. oThey are both greater than 10. oThey are both multiples of 5. oThey are both amounts you can show with nickels.

Some possibilities oOne is more than 30 and one is less. oOne is even and one is odd. oOne is in the forties and one is not. oOne has a 1 as a digit and the other does not. oOne is a multiple of 10 and the other is not.

Alike and Different oHow are the number 3/4 and 5/8 alike and how are they different?

Some possibilities oThey are both fractions. oThey are both less than 1. oBoth have odd numerators and even denominators. oThey can both be written as eighths. oThey can both be written as thousandths.

Some possibilities oOne is more than 7/10 and the other is less. oOne has a denominator of 8 and the other has a denominator of 4. oOne is more than 2/3 and one is less than 2/3. oOne can be written as 12ths and the other can’t. (at least not as a simple fraction) oThe 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 o94 ÷ 2 = 47 o249 ÷ 1 = 249 o216 ÷ 9 = 24 o99 ÷ 2 = 49.5

Creating a multiplication oCreate an equation involving multiplication of fractions where the numbers 4, 9 and 10 are used somewhere.

Some possibilities o4/9 x 10/12= 10/27 o4/10 x 9/9 = 2/5 o4/6 x 5/9 = 10/27

Build a sentence oUse these words and numbers to make a true sentence: o10, 50%, twice, difference

Some possibilities oThe difference between 10 and 50% of 80 is twice as much as 15. oThe difference between 50% of 10 and twice as much as 6 is that one is odd and the other is even. oThe difference between twice as much as 50% of 90 and 100 is 10.

Build a sentence oUse these words and numbers to make a true sentence: o4, 2, sum, almost

Some possibilities oThe sum of 4 and 2 is almost 7. oThe sum of 8 groups of 4 and eight groups of 2 is almost 50. oThe sum of the 4 numbers 2, 10, 10, and 10 is almost 35.

A Rectangle within a Rectangle oDraw a small rectangle. oCreate a bigger rectangle of which the small rectangle is a part. Tell what fractional part it is.

Possible Solutions

Questions for practice oReplace the boxes with values from 1 to 6 five ways to make this true. x

Questions for practice oReplace the boxes with values from 1 to 6 five ways to make this true. o BUT 362 o x1 x3 x2 NOT x

Toss and Win Toss a beanbag 3 times. Add the first 2 scores. Subtract the last one. ! Win a prize with points!

Making Patterns Use square tiles to create a growing pattern. Draw it. Tell why it’s a pattern.

Some Possibilities.

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

Some possibilities o3 and 4 o5 and 5√2 o12 and 13

You Try! Open these up: oHow many times as much as 16 is 48? oHow many meters long is your classroom? oWhich 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 2015 and 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 oShow a skeleton oShow a net (or several nets) oShow one face oShow all the faces oDraw an isometric drawing oHold up a cubic shaped box

Missing Digits oFigure out where the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 go. 4 x 2 = [ ] [] = 8[] [ ] x [ ] = 15 7[] + 9[] = []7[] [] x 7 = 42 OR [][] + []2 = 10[] [] x 6 = 54 5 x [ ] = [][] [] x 3 = 2[]

Missing Digits oFigure out where the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 go. 4 x 2 = = 85 5 x 3 = = x 7 = 42 OR = x 6 = 54 5 x 4 = 20 7 x 3 = 21

Make a pattern Use pattern blocks. oCreate a shape pattern where the 10 th shape is a green triangle, OR oCreate any shape pattern you wish.

Divide the shape oPick a shape. Divide it into 4 equal parts. OR oDivide this shape into 12 equal parts.

Draw a shape oDraw a shape where one side is 4 cm long and one angle is 30°. OR oDraw 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. oA: What tiles would you put in so it is possible, but not likely, to draw a red? oB: What tiles would you put in so the probability of red is 2/5?

Measurement Hunt oA: Find 5 items in the room that you think have more area than a recipe card. Check. oB: Find 5 items in the room that you think have an area between 20 cm 2 and 30 cm 2. 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. o300 students in 6 buses OR o435 students in 12 buses

Estimating percents Choose a shape. Estimate the percent that is dark. OR

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 $ for ? 20 for ? OR

In Summary We need to change our mindset.

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

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