creating mathematical conversations using open questions marian small sydney august, 2015 #llcaus...
TRANSCRIPT
![Page 1: Creating Mathematical Conversations using Open Questions Marian Small Sydney August, 2015 #LLCAus #LoveLearning @LLConference](https://reader030.vdocuments.us/reader030/viewer/2022032709/56649eb65503460f94bbf1db/html5/thumbnails/1.jpg)
Creating Mathematical Conversations using Open Questions
Marian SmallSydney
August, 2015
#LLCAus#LoveLearning@LLConference
![Page 2: Creating Mathematical Conversations using Open Questions Marian Small Sydney August, 2015 #LLCAus #LoveLearning @LLConference](https://reader030.vdocuments.us/reader030/viewer/2022032709/56649eb65503460f94bbf1db/html5/thumbnails/2.jpg)
Let’s warm up
• The answer to a question is 100.• What might the question have been?
![Page 3: Creating Mathematical Conversations using Open Questions Marian Small Sydney August, 2015 #LLCAus #LoveLearning @LLConference](https://reader030.vdocuments.us/reader030/viewer/2022032709/56649eb65503460f94bbf1db/html5/thumbnails/3.jpg)
Maybe
• What is 10 x 10?• What comes after 99?• How old are you when you are REALLY old?• What is a number in the pattern 10, 20, 30,…?• What is a number you can represent with
one base ten block?
![Page 4: Creating Mathematical Conversations using Open Questions Marian Small Sydney August, 2015 #LLCAus #LoveLearning @LLConference](https://reader030.vdocuments.us/reader030/viewer/2022032709/56649eb65503460f94bbf1db/html5/thumbnails/4.jpg)
Agenda
• Why open-ended?• We will look at lots of examples• We will look at strategies to create them.• We will create them.
![Page 5: Creating Mathematical Conversations using Open Questions Marian Small Sydney August, 2015 #LLCAus #LoveLearning @LLConference](https://reader030.vdocuments.us/reader030/viewer/2022032709/56649eb65503460f94bbf1db/html5/thumbnails/5.jpg)
Why open-ended?
• To be accessible• To challenge• To evoke rich conversations
![Page 6: Creating Mathematical Conversations using Open Questions Marian Small Sydney August, 2015 #LLCAus #LoveLearning @LLConference](https://reader030.vdocuments.us/reader030/viewer/2022032709/56649eb65503460f94bbf1db/html5/thumbnails/6.jpg)
Balance
• You put yellow cubes on one side of a pan balance.
• You put blue cubes on the other side.• What would make the balance look like this?
![Page 7: Creating Mathematical Conversations using Open Questions Marian Small Sydney August, 2015 #LLCAus #LoveLearning @LLConference](https://reader030.vdocuments.us/reader030/viewer/2022032709/56649eb65503460f94bbf1db/html5/thumbnails/7.jpg)
We might discuss
Which might work?• 1 and 2?• 5 and 3?• 9 and 1?• What sort of relationship are we looking for?
![Page 8: Creating Mathematical Conversations using Open Questions Marian Small Sydney August, 2015 #LLCAus #LoveLearning @LLConference](https://reader030.vdocuments.us/reader030/viewer/2022032709/56649eb65503460f94bbf1db/html5/thumbnails/8.jpg)
Patterns
• The 10th shape in a pattern is .• What could the pattern be?
![Page 9: Creating Mathematical Conversations using Open Questions Marian Small Sydney August, 2015 #LLCAus #LoveLearning @LLConference](https://reader030.vdocuments.us/reader030/viewer/2022032709/56649eb65503460f94bbf1db/html5/thumbnails/9.jpg)
We might discuss
• Is it repeating?• If it is, how long could the core be?• If the core is 3, where would the triangles in
the core be?• Could it be a growing pattern?
![Page 10: Creating Mathematical Conversations using Open Questions Marian Small Sydney August, 2015 #LLCAus #LoveLearning @LLConference](https://reader030.vdocuments.us/reader030/viewer/2022032709/56649eb65503460f94bbf1db/html5/thumbnails/10.jpg)
Representing numbers
• A two-digit number is represented with twice as many one blocks as ten blocks.
• What number could it be?
![Page 11: Creating Mathematical Conversations using Open Questions Marian Small Sydney August, 2015 #LLCAus #LoveLearning @LLConference](https://reader030.vdocuments.us/reader030/viewer/2022032709/56649eb65503460f94bbf1db/html5/thumbnails/11.jpg)
We might discuss
• Are you allowed to have 5 ten rods and 10 ones?
• What do you notice about the possible numbers: 12, 24, 36, 48, 60,….
![Page 12: Creating Mathematical Conversations using Open Questions Marian Small Sydney August, 2015 #LLCAus #LoveLearning @LLConference](https://reader030.vdocuments.us/reader030/viewer/2022032709/56649eb65503460f94bbf1db/html5/thumbnails/12.jpg)
Adding mentally
• Two numbers are really easy to add in your head. What might they be?
![Page 13: Creating Mathematical Conversations using Open Questions Marian Small Sydney August, 2015 #LLCAus #LoveLearning @LLConference](https://reader030.vdocuments.us/reader030/viewer/2022032709/56649eb65503460f94bbf1db/html5/thumbnails/13.jpg)
We might discuss
• Why is it easy to add 0?• 1?• 10?• 100?• What else is easy?
![Page 14: Creating Mathematical Conversations using Open Questions Marian Small Sydney August, 2015 #LLCAus #LoveLearning @LLConference](https://reader030.vdocuments.us/reader030/viewer/2022032709/56649eb65503460f94bbf1db/html5/thumbnails/14.jpg)
Words
• A sentence has 40 letters in it.• What number of words do you think it has?
Why?
![Page 15: Creating Mathematical Conversations using Open Questions Marian Small Sydney August, 2015 #LLCAus #LoveLearning @LLConference](https://reader030.vdocuments.us/reader030/viewer/2022032709/56649eb65503460f94bbf1db/html5/thumbnails/15.jpg)
We might discuss
• What assumptions we make• How valid those are• The fact that we can’t know
![Page 16: Creating Mathematical Conversations using Open Questions Marian Small Sydney August, 2015 #LLCAus #LoveLearning @LLConference](https://reader030.vdocuments.us/reader030/viewer/2022032709/56649eb65503460f94bbf1db/html5/thumbnails/16.jpg)
Fill in the blanks
• 5 of ______ is less than 2 of ______.• What amounts could go in the blanks?
![Page 17: Creating Mathematical Conversations using Open Questions Marian Small Sydney August, 2015 #LLCAus #LoveLearning @LLConference](https://reader030.vdocuments.us/reader030/viewer/2022032709/56649eb65503460f94bbf1db/html5/thumbnails/17.jpg)
We might discuss
• Is the first number more or less than the second? Why?
• Is it more than half or less than half? Why?
![Page 18: Creating Mathematical Conversations using Open Questions Marian Small Sydney August, 2015 #LLCAus #LoveLearning @LLConference](https://reader030.vdocuments.us/reader030/viewer/2022032709/56649eb65503460f94bbf1db/html5/thumbnails/18.jpg)
Addition puzzle
• You add two numbers.• The answer is twice as much as if you
subtract them.• What might the numbers be?
![Page 19: Creating Mathematical Conversations using Open Questions Marian Small Sydney August, 2015 #LLCAus #LoveLearning @LLConference](https://reader030.vdocuments.us/reader030/viewer/2022032709/56649eb65503460f94bbf1db/html5/thumbnails/19.jpg)
We might discuss
• Why it works for so many numbers.• What visual might show us why it is true• What algebra might show us why it is true
![Page 20: Creating Mathematical Conversations using Open Questions Marian Small Sydney August, 2015 #LLCAus #LoveLearning @LLConference](https://reader030.vdocuments.us/reader030/viewer/2022032709/56649eb65503460f94bbf1db/html5/thumbnails/20.jpg)
Visual
10 10 10
10
![Page 21: Creating Mathematical Conversations using Open Questions Marian Small Sydney August, 2015 #LLCAus #LoveLearning @LLConference](https://reader030.vdocuments.us/reader030/viewer/2022032709/56649eb65503460f94bbf1db/html5/thumbnails/21.jpg)
Visual
5 5 5
5
![Page 22: Creating Mathematical Conversations using Open Questions Marian Small Sydney August, 2015 #LLCAus #LoveLearning @LLConference](https://reader030.vdocuments.us/reader030/viewer/2022032709/56649eb65503460f94bbf1db/html5/thumbnails/22.jpg)
Visual
8 8 8
8
![Page 23: Creating Mathematical Conversations using Open Questions Marian Small Sydney August, 2015 #LLCAus #LoveLearning @LLConference](https://reader030.vdocuments.us/reader030/viewer/2022032709/56649eb65503460f94bbf1db/html5/thumbnails/23.jpg)
Algebra
• x + y = 2y – 2x, so• 3x = y
• x + 3x = 4x• 3x – x = 2x
![Page 24: Creating Mathematical Conversations using Open Questions Marian Small Sydney August, 2015 #LLCAus #LoveLearning @LLConference](https://reader030.vdocuments.us/reader030/viewer/2022032709/56649eb65503460f94bbf1db/html5/thumbnails/24.jpg)
Square tiles
• Use the squares.• Make a design that is ALMOST half red.
![Page 25: Creating Mathematical Conversations using Open Questions Marian Small Sydney August, 2015 #LLCAus #LoveLearning @LLConference](https://reader030.vdocuments.us/reader030/viewer/2022032709/56649eb65503460f94bbf1db/html5/thumbnails/25.jpg)
We might discuss
• How to start with half and half and add either one more of another colour or subtract one red.
![Page 26: Creating Mathematical Conversations using Open Questions Marian Small Sydney August, 2015 #LLCAus #LoveLearning @LLConference](https://reader030.vdocuments.us/reader030/viewer/2022032709/56649eb65503460f94bbf1db/html5/thumbnails/26.jpg)
Multiplication
• You multiply two numbers and the product is ALMOST 400. What could the numbers have been?
![Page 27: Creating Mathematical Conversations using Open Questions Marian Small Sydney August, 2015 #LLCAus #LoveLearning @LLConference](https://reader030.vdocuments.us/reader030/viewer/2022032709/56649eb65503460f94bbf1db/html5/thumbnails/27.jpg)
We might discuss
• Why we can’t be sure what almost means• How if you start with, e.g. 2 x 200, you are
more likely to change the 200 than the 2• How you change• Whether you go up or down
![Page 28: Creating Mathematical Conversations using Open Questions Marian Small Sydney August, 2015 #LLCAus #LoveLearning @LLConference](https://reader030.vdocuments.us/reader030/viewer/2022032709/56649eb65503460f94bbf1db/html5/thumbnails/28.jpg)
Rectangles
• A length is four times the width of a rectangle.
• What do you notice about the relationship between perimeter and width?
![Page 29: Creating Mathematical Conversations using Open Questions Marian Small Sydney August, 2015 #LLCAus #LoveLearning @LLConference](https://reader030.vdocuments.us/reader030/viewer/2022032709/56649eb65503460f94bbf1db/html5/thumbnails/29.jpg)
We might discuss
• Why the perimeter is always 2 ½ of the length.
![Page 30: Creating Mathematical Conversations using Open Questions Marian Small Sydney August, 2015 #LLCAus #LoveLearning @LLConference](https://reader030.vdocuments.us/reader030/viewer/2022032709/56649eb65503460f94bbf1db/html5/thumbnails/30.jpg)
I can see that
![Page 31: Creating Mathematical Conversations using Open Questions Marian Small Sydney August, 2015 #LLCAus #LoveLearning @LLConference](https://reader030.vdocuments.us/reader030/viewer/2022032709/56649eb65503460f94bbf1db/html5/thumbnails/31.jpg)
I can see that
![Page 32: Creating Mathematical Conversations using Open Questions Marian Small Sydney August, 2015 #LLCAus #LoveLearning @LLConference](https://reader030.vdocuments.us/reader030/viewer/2022032709/56649eb65503460f94bbf1db/html5/thumbnails/32.jpg)
I might ask….
• You add 2 fractions.• The sum is []/15.• What fractions might you have added?
![Page 33: Creating Mathematical Conversations using Open Questions Marian Small Sydney August, 2015 #LLCAus #LoveLearning @LLConference](https://reader030.vdocuments.us/reader030/viewer/2022032709/56649eb65503460f94bbf1db/html5/thumbnails/33.jpg)
Someone might say
• 3/15 + 6/15 OR• 1/3 + 2/5 OR• 2/3 + 1/15 OR• 3/5 + 2/15 OR• 2/4 + 16/32 (if the answer is 15/15)
![Page 34: Creating Mathematical Conversations using Open Questions Marian Small Sydney August, 2015 #LLCAus #LoveLearning @LLConference](https://reader030.vdocuments.us/reader030/viewer/2022032709/56649eb65503460f94bbf1db/html5/thumbnails/34.jpg)
We would discuss
• That we usually use a common multiple as the denominator when we add two fractions, but not necessarily.
![Page 35: Creating Mathematical Conversations using Open Questions Marian Small Sydney August, 2015 #LLCAus #LoveLearning @LLConference](https://reader030.vdocuments.us/reader030/viewer/2022032709/56649eb65503460f94bbf1db/html5/thumbnails/35.jpg)
A problem I tried in Grade 4
![Page 36: Creating Mathematical Conversations using Open Questions Marian Small Sydney August, 2015 #LLCAus #LoveLearning @LLConference](https://reader030.vdocuments.us/reader030/viewer/2022032709/56649eb65503460f94bbf1db/html5/thumbnails/36.jpg)
We would discuss
• Some properties were easier to use than others (e.g. a very small angle OR angle bigger than a right angle OR symmetry) to make the problem accessible.
• Could talk about what combos didn’t work• Could talk about what automatically
happened when certain combos were chosen
![Page 37: Creating Mathematical Conversations using Open Questions Marian Small Sydney August, 2015 #LLCAus #LoveLearning @LLConference](https://reader030.vdocuments.us/reader030/viewer/2022032709/56649eb65503460f94bbf1db/html5/thumbnails/37.jpg)
Or
• Certain properties don’t mix (e.g. some, but not all, equal side lengths AND four equal side lengths).
• Some properties automatically come together (e.g. 4 equal side lengths and some parallel sides)
![Page 38: Creating Mathematical Conversations using Open Questions Marian Small Sydney August, 2015 #LLCAus #LoveLearning @LLConference](https://reader030.vdocuments.us/reader030/viewer/2022032709/56649eb65503460f94bbf1db/html5/thumbnails/38.jpg)
Adding fractions
• You add two fractions less than 1.• The answer is a little less than 5/4.• What might the fractions have been?
![Page 39: Creating Mathematical Conversations using Open Questions Marian Small Sydney August, 2015 #LLCAus #LoveLearning @LLConference](https://reader030.vdocuments.us/reader030/viewer/2022032709/56649eb65503460f94bbf1db/html5/thumbnails/39.jpg)
We could discuss
• Why 9/10 + 1/4 (or something like that works)
• Why at least one fraction has to be more than ½
• Why both fractions can be more than half, but not if one is too close to 1
![Page 40: Creating Mathematical Conversations using Open Questions Marian Small Sydney August, 2015 #LLCAus #LoveLearning @LLConference](https://reader030.vdocuments.us/reader030/viewer/2022032709/56649eb65503460f94bbf1db/html5/thumbnails/40.jpg)
Consider this problem
• A sweater was on sale, 40% off.• A pair of pants was on sale, 20% off.• The sale prices were the same.• How did the original prices compare?
![Page 41: Creating Mathematical Conversations using Open Questions Marian Small Sydney August, 2015 #LLCAus #LoveLearning @LLConference](https://reader030.vdocuments.us/reader030/viewer/2022032709/56649eb65503460f94bbf1db/html5/thumbnails/41.jpg)
Could be solved numerically
• If the original sweater price was $100, the sale price is $60.
• If $60 is 80% of the pants price, 20% is $15, so 100% is $75.
![Page 42: Creating Mathematical Conversations using Open Questions Marian Small Sydney August, 2015 #LLCAus #LoveLearning @LLConference](https://reader030.vdocuments.us/reader030/viewer/2022032709/56649eb65503460f94bbf1db/html5/thumbnails/42.jpg)
Could be solved numerically
• If the original sweater price was $50, the sale price is $30.
• If $30 is 80% of the pants price, 40% is $15, so 100% is $15 + 15 + 7.50 = $37.50.
• The pants price is 3/4 of the sweater price.
![Page 43: Creating Mathematical Conversations using Open Questions Marian Small Sydney August, 2015 #LLCAus #LoveLearning @LLConference](https://reader030.vdocuments.us/reader030/viewer/2022032709/56649eb65503460f94bbf1db/html5/thumbnails/43.jpg)
Could be solved algebraically
• 6/10 s = 8/10 p• 6s = 8p• 3s = 4p• So p/s = 3/4 , so the pants cost 3/4 of the
sweater.
![Page 44: Creating Mathematical Conversations using Open Questions Marian Small Sydney August, 2015 #LLCAus #LoveLearning @LLConference](https://reader030.vdocuments.us/reader030/viewer/2022032709/56649eb65503460f94bbf1db/html5/thumbnails/44.jpg)
Could be solved visually
![Page 45: Creating Mathematical Conversations using Open Questions Marian Small Sydney August, 2015 #LLCAus #LoveLearning @LLConference](https://reader030.vdocuments.us/reader030/viewer/2022032709/56649eb65503460f94bbf1db/html5/thumbnails/45.jpg)
We could discuss
• When you know a relationship between percents, you can’t know the absolute values, only relative values.
![Page 46: Creating Mathematical Conversations using Open Questions Marian Small Sydney August, 2015 #LLCAus #LoveLearning @LLConference](https://reader030.vdocuments.us/reader030/viewer/2022032709/56649eb65503460f94bbf1db/html5/thumbnails/46.jpg)
Right triangles
• One side of a right triangle is 10 cm long. What might be the lengths of the other two sides?
![Page 47: Creating Mathematical Conversations using Open Questions Marian Small Sydney August, 2015 #LLCAus #LoveLearning @LLConference](https://reader030.vdocuments.us/reader030/viewer/2022032709/56649eb65503460f94bbf1db/html5/thumbnails/47.jpg)
We might discuss
• Whether or not the triangle could be isosceles
• The idea that the 10 could be a leg or a hypotenuse
![Page 48: Creating Mathematical Conversations using Open Questions Marian Small Sydney August, 2015 #LLCAus #LoveLearning @LLConference](https://reader030.vdocuments.us/reader030/viewer/2022032709/56649eb65503460f94bbf1db/html5/thumbnails/48.jpg)
Multiplying integers
• You multiply two integers. The result is about 50 less than one of them.
• What might they be?
![Page 49: Creating Mathematical Conversations using Open Questions Marian Small Sydney August, 2015 #LLCAus #LoveLearning @LLConference](https://reader030.vdocuments.us/reader030/viewer/2022032709/56649eb65503460f94bbf1db/html5/thumbnails/49.jpg)
We could discuss
• Why it is likely one is positive and one is negative, but
• Why it could be 0 and 50 or 0 and 49, etc.• Why there can’t be a really big positive
integer
![Page 50: Creating Mathematical Conversations using Open Questions Marian Small Sydney August, 2015 #LLCAus #LoveLearning @LLConference](https://reader030.vdocuments.us/reader030/viewer/2022032709/56649eb65503460f94bbf1db/html5/thumbnails/50.jpg)
Algebra
• Create a story that you would represent with the equation 3x + 5y = 60.
![Page 51: Creating Mathematical Conversations using Open Questions Marian Small Sydney August, 2015 #LLCAus #LoveLearning @LLConference](https://reader030.vdocuments.us/reader030/viewer/2022032709/56649eb65503460f94bbf1db/html5/thumbnails/51.jpg)
Maybe
• I build triangles and pentagons with toothpicks. I used 60 toothpicks. How many of each?
• Some kids were in groups of 3 and some in groups of 5. There were 60 kids. How many of each size group?
• I bought a bunch of notebooks that each cost $3 and a bunch of packs of paper that each cost $5. I spent $60. How many notebooks and how many packs of paper?
![Page 52: Creating Mathematical Conversations using Open Questions Marian Small Sydney August, 2015 #LLCAus #LoveLearning @LLConference](https://reader030.vdocuments.us/reader030/viewer/2022032709/56649eb65503460f94bbf1db/html5/thumbnails/52.jpg)
Maybe
• I bought 3 identical pairs of shorts and 5 identical t-shirts and spent $60. How much did each cost?
• There were 3 identical groups of girls and 5 identical groups of boys. There were 60 kids. How many girls were in a group? How many boys in a group?
![Page 53: Creating Mathematical Conversations using Open Questions Marian Small Sydney August, 2015 #LLCAus #LoveLearning @LLConference](https://reader030.vdocuments.us/reader030/viewer/2022032709/56649eb65503460f94bbf1db/html5/thumbnails/53.jpg)
We could discuss
• that 3x can either mean a lot of 3s (x of them) or 3 of the same thing.
![Page 54: Creating Mathematical Conversations using Open Questions Marian Small Sydney August, 2015 #LLCAus #LoveLearning @LLConference](https://reader030.vdocuments.us/reader030/viewer/2022032709/56649eb65503460f94bbf1db/html5/thumbnails/54.jpg)
Volume
• A cone and cylinder have the same volume.• The cylinder is taller.• Create possible dimensions.
![Page 55: Creating Mathematical Conversations using Open Questions Marian Small Sydney August, 2015 #LLCAus #LoveLearning @LLConference](https://reader030.vdocuments.us/reader030/viewer/2022032709/56649eb65503460f94bbf1db/html5/thumbnails/55.jpg)
We could discuss
• The relationship forced by the formulas between the radii if the heights are the same
• The relationship forced by the formulas between the heights if the radii are the same
![Page 56: Creating Mathematical Conversations using Open Questions Marian Small Sydney August, 2015 #LLCAus #LoveLearning @LLConference](https://reader030.vdocuments.us/reader030/viewer/2022032709/56649eb65503460f94bbf1db/html5/thumbnails/56.jpg)
Powers
• Write 88 as the sum of powers in different ways.
![Page 57: Creating Mathematical Conversations using Open Questions Marian Small Sydney August, 2015 #LLCAus #LoveLearning @LLConference](https://reader030.vdocuments.us/reader030/viewer/2022032709/56649eb65503460f94bbf1db/html5/thumbnails/57.jpg)
We could discuss
• How using the exponent 1 can be very helpful
![Page 58: Creating Mathematical Conversations using Open Questions Marian Small Sydney August, 2015 #LLCAus #LoveLearning @LLConference](https://reader030.vdocuments.us/reader030/viewer/2022032709/56649eb65503460f94bbf1db/html5/thumbnails/58.jpg)
Linear Relations
• A system of equations is graphed. The solution is a point in Quadrant II.
• What might the equations be?
![Page 59: Creating Mathematical Conversations using Open Questions Marian Small Sydney August, 2015 #LLCAus #LoveLearning @LLConference](https://reader030.vdocuments.us/reader030/viewer/2022032709/56649eb65503460f94bbf1db/html5/thumbnails/59.jpg)
We might discuss
• Why if you know the solution is, e.g. (–3,1), it is easy to come up with equations numerically.
• e.g. since –3 = 3 x (–1), one equation is x = 3y.• Since 2 x (–3) + 4 x (1) = –2, another equation
is 2x + 4y = –2, etc.
![Page 60: Creating Mathematical Conversations using Open Questions Marian Small Sydney August, 2015 #LLCAus #LoveLearning @LLConference](https://reader030.vdocuments.us/reader030/viewer/2022032709/56649eb65503460f94bbf1db/html5/thumbnails/60.jpg)
Mathletics tasks
![Page 61: Creating Mathematical Conversations using Open Questions Marian Small Sydney August, 2015 #LLCAus #LoveLearning @LLConference](https://reader030.vdocuments.us/reader030/viewer/2022032709/56649eb65503460f94bbf1db/html5/thumbnails/61.jpg)
Task
![Page 62: Creating Mathematical Conversations using Open Questions Marian Small Sydney August, 2015 #LLCAus #LoveLearning @LLConference](https://reader030.vdocuments.us/reader030/viewer/2022032709/56649eb65503460f94bbf1db/html5/thumbnails/62.jpg)
Video and interactive
• Let’s check them out
![Page 63: Creating Mathematical Conversations using Open Questions Marian Small Sydney August, 2015 #LLCAus #LoveLearning @LLConference](https://reader030.vdocuments.us/reader030/viewer/2022032709/56649eb65503460f94bbf1db/html5/thumbnails/63.jpg)
Opening up Questions
• Start with the answer. Ask for the question.• The answer is “a square”.• The answer is “2/3”.• The answer is √10.• The answer is 4x – 2.
![Page 64: Creating Mathematical Conversations using Open Questions Marian Small Sydney August, 2015 #LLCAus #LoveLearning @LLConference](https://reader030.vdocuments.us/reader030/viewer/2022032709/56649eb65503460f94bbf1db/html5/thumbnails/64.jpg)
Opening up Questions
Similarities and differences• How are 7 and 10 alike and different?• 350 and 550?• 3x and 2x• Adding and subtracting
![Page 65: Creating Mathematical Conversations using Open Questions Marian Small Sydney August, 2015 #LLCAus #LoveLearning @LLConference](https://reader030.vdocuments.us/reader030/viewer/2022032709/56649eb65503460f94bbf1db/html5/thumbnails/65.jpg)
Opening up Questions
Choose your own values for the blanks.• Add 5[] + []9• [][] is a little less than 4[]. What can go in the
blanks?• [] is about 25 less than []. What values can go
in the blanks?
![Page 66: Creating Mathematical Conversations using Open Questions Marian Small Sydney August, 2015 #LLCAus #LoveLearning @LLConference](https://reader030.vdocuments.us/reader030/viewer/2022032709/56649eb65503460f94bbf1db/html5/thumbnails/66.jpg)
Opening up Questions
Use “soft” words.• The square root of a number is ABOUT 30.
What could it be?• The quotient of two numbers is a LITTLE LESS
than 20. What could they be?• A line is VERY steep. It goes through (4,2).
What could the equation be?
![Page 67: Creating Mathematical Conversations using Open Questions Marian Small Sydney August, 2015 #LLCAus #LoveLearning @LLConference](https://reader030.vdocuments.us/reader030/viewer/2022032709/56649eb65503460f94bbf1db/html5/thumbnails/67.jpg)
Your turn
• Choose three curriculum topics.• Create different sorts of rich open questions
you could use.
• We will share!