Directions: Using each of the digits from 0-9 only once, fill in the boxes to make the equation true.

Do all fractions have smaller numerators than denominators?

The answer is: 9/3 +8/4 + 5/6 = 70/12

Source: Denise White

]]>Directions: Arrange the digits 1-6 into two 3-digit whole numbers. Make the sum as close to 1000 as possible.

How should the hundreds values align to make the solution as close to 1,000 as possible?

993 (multiple ways to create the solution)

Source: Ian Kerr

]]>Directions: Using the digits 0-9 at most once, fill in the boxes to make the largest possible greatest common factor.

How can we tell if your three numbers have any relationship with each other?

How can we use our knowledge of multiples?

97 would be the largest possible GCF (using the numbers 97 and 485 or 97 and 582)

Source: Howie Hua

]]>Directions: Using the digits 0-9 at most once, fill in the boxes to make the smallest possible least common multiple.

How can we tell if your three numbers have any relationship with each other?

How can we use our knowledge of multiples?

07 14 28 will get us an LCM of 28.

Source: Howie Hua

]]>Directions: Using the digits 0-9 at most once, fill in the boxes to make the largest possible greatest common factor.

Do your numbers have any relationship with each other?

Using 48 and 96, we can obtain the GCF of 48.

Source: Howie Hua

]]>Directions: Given the point (3,5), use digits 1-9, at most one time, to find a point (__, __) that minimizes the slope of the line that passes through the two points. The slope cannot be undefined.

How is the steepness of a line determined?

How do we calculate slope between two points? Explain which of the two slopes are steeper 1/9 or 9/1?

What does minimize mean?

Can you draw a picture that would help you find another point? Can you find another point?

Because of the vagueness of “minimize the slope”, here are two possible answers.

Points that minimize the slope: (9,6) or (9,4) if we think about the shallowest slope.

If we think about minimizing as the most left on the number line, then the here are the points that minimize the slope: (2,9) and (3,1)

Source: Nanette Johnson (Problem Based on Andrew Constantinescu’s Problem) and Andrew Constantinescu

]]>Directions: Given the point (3,5), use digits 1-9, at most one time, to find a point (__, __) that maximizes the slope of the line that passes through the two points. The slope cannot be undefined.

How is the steepness of a line determined? How do we calculate slope between two points? Explain which of the two slopes are steeper 1/9 or 9/1?

Can you find another point?

Can you find another point?

Points that maximize the slope: (4,9) and (2,1)

Source: Andrew Constantinescu

]]>Directions: Using the digits 0 through 9, without repeating any digits, find the quotient closest to 1.

What can you explain about the quotient of any number and itself?

If we are looking for a quotient of 1, explain what that tells us about the relationship between the dividend and divisor?

If we are looking for a quotient of 1, explain what that tells us about the relationship between the dividend and divisor?

7.01/6.98 and 6.98/7.01

Source: Michael Dennis

]]>Directions: Using the digits 1 to 9 at most one time each, fill in the boxes to make a true statement.

How can thinking about the two numbers being multiplied together help you figure out the product?

Number of Unique Solutions: 58

1: 3 x (7 – 2) = 15

2: 3 x (8 – 4) = 12

3: 3 x (9 – 1) = 24

4: 3 x (9 – 4) = 15

5: 3 x (9 – 5) = 12

6: 4 x (6 – 3) = 12

7: 4 x (7 – 3) = 16

8: 4 x (8 – 5) = 12

9: 4 x (9 – 1) = 32

10: 4 x (9 – 5) = 16

11: 4 x (9 – 6) = 12

12: 6 x (5 – 1) = 24

13: 6 x (5 – 2) = 18

14: 6 x (5 – 3) = 12

15: 6 x (7 – 3) = 24

16: 6 x (7 – 4) = 18

17: 6 x (7 – 5) = 12

18: 6 x (8 – 1) = 42

19: 6 x (9 – 1) = 48

20: 6 x (9 – 5) = 24

21: 6 x (9 – 7) = 12

22: 7 x (5 – 1) = 28

23: 7 x (5 – 3) = 14

24: 7 x (6 – 1) = 35

25: 7 x (6 – 3) = 21

26: 7 x (8 – 1) = 49

27: 7 x (8 – 5) = 21

28: 7 x (8 – 6) = 14

29: 7 x (9 – 1) = 56

30: 7 x (9 – 3) = 42

31: 7 x (9 – 4) = 35

32: 7 x (9 – 5) = 28

33: 7 x (9 – 6) = 21

34: 8 x (4 – 2) = 16

35: 8 x (5 – 1) = 32

36: 8 x (5 – 3) = 16

37: 8 x (6 – 3) = 24

38: 8 x (7 – 5) = 16

39: 8 x (9 – 1) = 64

40: 8 x (9 – 2) = 56

41: 8 x (9 – 5) = 32

42: 8 x (9 – 6) = 24

43: 8 x (9 – 7) = 16

44: 9 x (4 – 1) = 27

45: 9 x (4 – 2) = 18

46: 9 x (5 – 1) = 36

47: 9 x (5 – 3) = 18

48: 9 x (6 – 1) = 45

49: 9 x (6 – 3) = 27

50: 9 x (6 – 4) = 18

51: 9 x (7 – 1) = 54

52: 9 x (7 – 2) = 45

53: 9 x (7 – 5) = 18

54: 9 x (8 – 1) = 63

55: 9 x (8 – 2) = 54

56: 9 x (8 – 3) = 45

57: 9 x (8 – 4) = 36

58: 9 x (8 – 5) = 27

Source: Owen Kaplinsky

]]>Directions: Using the digits 1 to 9, at most one time each, fill in the boxes to make a true statement.

How can thinking about the two numbers being multiplied together help you figure out the product?

What two numbers have a product that is very close to 50?

How can you make those two numbers?

What two numbers have a product that is very close to 50?

How can you make those two numbers?

There two closest products are:

7 x (8 – 1) = 49

7 x (9 – 2) = 49

7 x (8 – 1) = 49

7 x (9 – 2) = 49

Source: Owen Kaplinsky

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