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Tonight’s diagnostic test
Try this question:
8 2304 + 39 x 58 =
Now try this one.
Use six different digits, a square root sign and at least two different operations to write a whole number expression.
Calculate the value.
What could a student do?
O x 96 351 = 0
58 x 2 + 36 + 9 = 155
40 ÷ 8 + 961 = 36
Median
The median of a set of five numbers is 15.
What are the numbers?
Some possibilities
14, 14, 15, 16, 16
9, 11, 15, 20, 21
15, 15, 15, 15, 15
15, 15, 15, 15, 16
Think about the difference between
theseA triangular prism has ___ edges.
Or
This is a triangular prism. Tell everything about it that you can.
Using Open Tasks
Start with an Answer
My answer is 8.
What’s my question?
Some Possibilities
o What is 5 + 3?
o What numeral has 2 lines of symmetry?
o What number comes after 7?
o What is the only square root of a number between 40 and 80?
o What digit appears in the decimal representation for 8/9?
Turn it around
One side of a right triangle is 5 cm long. What could the other side lengths be?
Possibilities
3 and 4
5 and 5√2
12 and 13
Using Percents
o 72 is ___ % of ____.
o Fill in the blanks in different ways.
Some Possibilities
o 100% of 72
o 50% of 144
o 200% of 36
o 1% of 7200
o 150% of 48
o 600% of 12
o 0.1% of 72,000
A Special Point
o A graph goes through the point (1,1). What could it be?
Some Possibilities
o y = x
o y = x2
o y = sin (90x)
o y = 2x3 - x
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 possibilitieso 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…
Alike and different
o How is the graph for y = 3x + 2 like the one for y = 3x2 + 2? How is it different?
Some possibilities
o Both go through (0,2)
o Both increase as x increases from 0 to 100.
o Both go through quadrant 1.
Some possibilities
o One has only positive y values and the other doesn’t.
o One is a line and the other isn’t.
o One has an x-intercept and the other doesn’t.
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.
Making Patterns
Use square tiles to make a pattern.
Draw it. Tell why it’s a pattern.
Some Possibilities
Some More Possibilities
A Rectangle within a Rectangle
o 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
An Addition
Create an addition question where each of the digits 4, 9 and 3 appears somewhere in the question (either in an addend or in the sum).
Some Possibilities
o 4 + 9 = 13
o 23 + 94 = 117
o 3 + 4 + 9 = 16
o 94 + 49 = 143
Creating a multiplication
o Create an equation involving division 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
Like a Square
o A certain shape makes me think of a square, but it’s not a square.
o What might the other shape be?
o How is it like a square?
Possible Ideas
You Try!
Open these up:
o How much greater is 20 than 13?
o How many inches long is your pencil?
o What is 1 ÷ 5-3?
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, or √2 and π
What number describes the position of the dot? Why?
Representing 20
Use plastic links to show different combinations of numbers that add to 20.
Use plastic links to show different combinations of numbers that add to 20.
Use plastic links to make it easy to see that 20 has factors.
Representing 20
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 possibilitieso 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
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°.
Probability Draws
You can put 10 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?
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.
OR
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 $2.50
15 for ?
20 for ?
OR
Borrowed with permission from the work of Dr. Marion Small
