Open-Ended Questions
Pick up these and run! - Apology, More questions are being migrated from the old site!
NUMBER/ALGEBRA
How can we make 10?
Q: How can we make 10 with counters?
Addition (grade 0/1)
<Concept that may be covered>
Addition, subtraction, friends of 10, Commutative property of addition, adding multiple numbers and concept of 0.
<Possible Students Responses>
1+9, 2+8, 3+7, etc (friends of 10)
4+6 and 6+4 (commutative property)
2+2+6, 3+3+3+1 (multiple numbers)
10+0, 4+6+0 (concept of 0)
<Follow-up questions>
- How did you find these numbers?
- 3+7 and 7+3 both make 10. Can we flip the numbers all the time like this?
- Show me how you find the numbers.
​
Heading 2
Q: Give Naomi and Sam 10 marbles altogether. Who has more?
Add/Subtraction (grade 1)
<Concept that may be covered>
Addition, subtraction, friends of 10, concept of 0, reasoning.
<Possible Students Responses>
Naomi has 3, Sam has 7. Sam has more.
Naomi has 3 and Sam has 3 more.
Naomi has 10 and Sam has 0.
Both have 5 each and no one has more.
etc.
<Follow-up questions>
- How did you find these numbers?
- How can you find Sam has more?
- How many more does Naomi have?
- If Naomi has a lot more than Sam, what do you think Naomi has?
Heading 2
Q: Product of two numbers is 24, what can be the numbers?
Multiplication (Grade 3+)
<Concept that may be covered>
Multiplication, Division, Commutative property of multiplication, Inverse operation, Multiplying by 1, multiplying by 1/2 (upper grades), factors, multiples,
<Possible Students Responses>
3x8, 2x12, 4x6/6x4, 24x1
24 x 1/2
<Follow-up questions>
- Are they ALL combinations?
- How can you tell that you have ALL?
- What about 30?
- If i give you a bigger number, will there be more factors? Why? Why not?
​
How can we make 10?
Q: A positive number and a negative number make 5 when you add them.
What can they be?
Addition (grade 6+)
<Concept that may be covered>
Integers, negative numbers, adding negative number to positive, commutative property of addition (with negative numbers) etc
<Possible Students Responses>
7 and -2, -3 and 8 etc
4+(-9) and (-9) +4 (commutative)
<Follow-up questions>
- Does commutative property work with negative numbers? Why? Why not?
- What can be the largest number that you can use? Why?
- What is the smallest number can be used? Why?
- What happens if we change the number from 5 to 3. Can we form a conjecture?
Heading 2
Q: How can you (evenly) share 24 marbles?
Mul/Divison (grade 3+)
<Concept that may be covered>
Multiplication, division, factors, multiples, grouping, sharing, reasoning
<Possible Students Responses>
Two people 12 each.
Three friends 8 marbles each.
3,3,3,3,3,3,3,3
​
<Follow-up questions>
- How many ways can we share 24 marbles?
- How can we find ALL different ways?
- If we have more marbles, can we share with more people? Why? Why not?
- What number is a good number (of marbles) to be able to share the marble with more people?
- What is a bad number?
Heading 2
Q: My number has 6 factors. What can it be?
Number/Algebra (Grade 5+)
<Concept that may be covered>
Multiplication, division, factors, multiples, reasoning etc
<Possible Students Responses>
12, 18, 20 etc
<Follow-up questions>
- Are there any more?
- How many numbers have exactly six factors? Reason?
- Are there any GOOD ways to find the amount of factors?
- What makes a number to have more factors?
- What makes the number have only few factors?
​
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MONEY (Number/Measurement)
How can we make 10?
Q: How can you make $5?
Add/Sub/Pattern (grade 2+)
<Concept that may be covered>
Addition, subtraction, pattern, fractions, measurement, conversion
<Possible Students Responses>
$2, $2, $1
$2, $1, $1, $1
10 x 50c
etc
<Follow-up questions>
- Can you make $5 with 5 coins? How?
- Least amount of coins? Most?
​
Heading 2
Q: My father gave us some money and each sibling received $4.50.
How many siblings and how much altogether?
Mul/Divison (grade 3+)
<Concept that may be covered>
Multiplication, division, fractions, multiples, grouping, sharing, reasoning
<Possible Students Responses>
Two siblings and $9 altogether​
Seven siblings and $31.50
<Follow-up questions>
- What is the largest amount of money as an answer? (no limit)
​
​
Heading 2
Q: I have coins of various types, but only one of each kind. What amount of money can you make? What types of coins do you have?
PATTERN (Grade 5+)
<Concept that may be covered>
Fraction, addition, subtraction, ,
<Possible Students Responses>
3x8, 2x12, 4x6/6x4, 24x1
24 x 1/2
<Follow-up questions>
- Are they ALL combinations?
- How can you tell that you have ALL?
- What about 30?
- If i give you a bigger number, will there be more factors? Why? Why not?
​
PATTERNS
How can we make 10?
Q: A number pattern starts with 1, 2, ....
Continue the pattern and show me the rule.
(grade 2+)
<Concept that may be covered>
Addition, subtraction, pattern, reasoning, etc
<Possible Students Responses>
1, 2, 3, 4, 5, ... (+1)
1, 2, 4, 8, 16, ... (x2)
1, 2, 1, 2, 1, 2, ... (repeat)
​
etc
<Follow-up questions>
- What is a pattern?
- What about the patter starts with 1, 3?
- Can you make a decreasing pattern?
- Can you make an increasing pattern?
​
Heading 2
Q: What do you think 'Triangular Numbers' look like?
Patterns (grade 4+)
<Concept that may be covered>
Addition, multiplication, subtraction, factors, multiples, patterns, sharing, reasoning
<Possible Students Responses>
3, 6, 9, 12, 15 ....
1, 3, 6, 10, 15 (triangular numbers)
3, 9, 27, 81, ...
<Follow-up questions>
- How did you make the numbers?
- What rule does your pattern have?
- Whose pattern do you like? Why?
- Whose numbers represent 'TRIANGLE' best? Why?
- What about 'Square Numbers'?
- 'Pentagonal Numbers'?
Heading 2
Q: How many students would form the best class in order to make even groups to play games?
Number/Pattern(Grade 3+)
<Concept that may be covered>
Multiplication, Division, factors, multiples, reasoning
<Possible Students Responses>
20,
24,
30,
36?
<Follow-up questions>
- What numbers are good? Bad? Why?
- What number has most factors under 30? Is it the only number?
- What number is the best if over 30?
- If we can include a teacher to play games, what number can be good?
​
GEOMETRY
How can we make 10?
Q: Draw rectangles with an area of 12 square cm.
Area (grade 3+)
<Concept that may be covered>
Multiplication, division, area, factors, fractions, multiples, pattern, definition of rectangle, definition of square, area model of multiplication, length and width, commutative property of multiplication, arrays, reasoning
<Possible Students Responses>
(drawing) 2x12, 3x8, 4x6
(listing) 1x12, 2x6, 3x4
<Follow-up questions>
- How can you tell that you drew ALL rectangles?
- Tall rectangles and wide ones. Are they the same? Why? Why not?
Heading 2
Q: Draw a triangle with an area of 6 square cm.
Area (grade 5+)
<Concept that may be covered>
Multiplication, division, area, factors, fractions, multiples, pattern, definition of rectangle/triangle, area model of multiplication, length and width, commutative property of multiplication, arrays, reasoning
<Possible Students Responses>
(drawing: base x height) 2x12, 3x8, 4x6
(listing) 1x12, 2x6, 3x4
<Follow-up questions>
- Are there any more?
- Do they need to be right-angled triangles? (if no variety)
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Q:
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<Follow-up questions>
MEASUREMENT
How can we make 10?
Q: .
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DATA
How can we make 10?
Q: .
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CHANCE
How can we make 10?
Q: .
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