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

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

How can we tell if it is even possible to make a whole number product?

What digits would be better or worse choices for making a whole number product?

What digits would be better or worse choices for making a whole number product?

There are many answers. For example:

9.6 x 8.75 = 84

9.6 x 1.25 = 12

1.6 x 3.75 = 6

4.8 x 3.75 = 18

4.8 x 6.25 = 30

4.8 x 1.25 = 6

6.4 x 1.25 = 8

Note what they all have in common!

9.6 x 8.75 = 84

9.6 x 1.25 = 12

1.6 x 3.75 = 6

4.8 x 3.75 = 18

4.8 x 6.25 = 30

4.8 x 1.25 = 6

6.4 x 1.25 = 8

Note what they all have in common!

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 you represent your equation using pictures?

What does the equals sign mean?

What does the equals sign mean?

There are multiple answers including:

3 + 5 = 9 – 1

1 + 2 = 6 – 3

4 + 1 = 7 – 2

3 + 5 = 9 – 1

1 + 2 = 6 – 3

4 + 1 = 7 – 2

Source: Owen Kaplinsky

]]>Directions: Using the digits 0 to 9, at most one time each, fill in the boxes to make a true statement.

How can you choose digits for your addends so that the sum is a double digit number?

There are multiple answers including:

(6 x 4) + (3 x 9) = 51

(8 x 1) + (4 x 3) = 20

(6 x 4) + (3 x 9) = 51

(8 x 1) + (4 x 3) = 20

Source: Owen Kaplinsky

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

How does choosing the digits for the denominator affect the decimal value?

How might choosing the digit for the decimal make finding the digits for the fraction easier?

How might choosing the digit for the decimal make finding the digits for the fraction easier?

There are many possible answers including:

9/18 = 0.5

7/14 = 0.5

7/35 = 0.2

9/18 = 0.5

7/14 = 0.5

7/35 = 0.2

Source: Owen Kaplinsky

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

How does choosing the divisor and dividend affect the quotient?

What digits would be bad choices for the divisor?

What digits would be bad choices for the dividend?

What digits would be bad choices for the divisor?

What digits would be bad choices for the dividend?

There are many possible answers including:

9 ÷ 2 = 4.5

6 ÷ 4 = 1.5

8 ÷ 5 = 1.6

9 ÷ 2 = 4.5

6 ÷ 4 = 1.5

8 ÷ 5 = 1.6

Source: Owen Kaplinsky

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

What possible values can the single digit have?

The only possible answer is 8 ÷ 4 = 6 ÷ 3 = 2

Source: Owen Kaplinsky

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

What has to be true about the pairs of numbers inside the parenthesis?

There are many answers including:

8 = (6+2) = (7+1) = (5+3)

9 = (8+1) = (7+2) = (6+3)

7 = (6+1) = (3+4) = (5+2)

8 = (6+2) = (7+1) = (5+3)

9 = (8+1) = (7+2) = (6+3)

7 = (6+1) = (3+4) = (5+2)

Source: Owen Kaplinsky

]]>