MATH - Grade 1
Math Challenges with single problems
Source: https://www.openmiddle.com/category/grade-1/
Activity 1
Using the digits 0 to 9 at most one time each, place a digit in each box to create a true statement.
Hint: Can you show two numbers you could add together using your fingers?
There are many answers. Here are some possibilities:
1 + 2 = 3 and 4 + 5 = 9; 2 + 4 = 6 and 5 + 3 = 8.
Activity 2
Use the digits 1-9, at most once, to complete the equation.
What is the greatest result you can make?
What is the least result you can make?
Hint:
What numbers work (or won’t work) for the tens digits?
Could the result have a zero in the one’s place?
Could the least result be less than 10?
Could the greatest result be greater than 100?
Answer:
27 – 8 = 14 + 5
25 – 8 = 13 + 4 (or 14 + 3) ~ least result of 17 = 17
95 – 2 = 87 + 6 (or 86 + 7) ~ greatest result of 93 = 93
Activity 3
Directions: Use four of these dominoes to form a square with the same number of dots on each side. Source: Joshua Nelson
Hint:
What is the largest sum you can make?
What is the smallest sum you can make?
Answer: See below
Activity 4
Directions: Use four of these dominoes to form a square with the same number of dots on each side.
Hint:
What is the largest sum you can make?
What is the smallest sum you can make?
Answer: See below
Activity 5
Directions: Using the digits 1 to 9 at most one time each, place a digit in each box to create a true statement.
Hint:
Are there numbers that are helpful to use first or save for last?
What would a drawing/model look like to match this equation?
Answer: See below
Number of Unique Solutions: 48 (allowing for permutations)
1: 8 = 2+6 = 1+3+4
2: 8 = 2+6 = 1+4+3
3: 8 = 2+6 = 3+1+4
4: 8 = 2+6 = 3+4+1
5: 8 = 2+6 = 4+1+3
6: 8 = 2+6 = 4+3+1
7: 8 = 6+2 = 1+3+4
8: 8 = 6+2 = 1+4+3
9: 8 = 6+2 = 3+1+4
10: 8 = 6+2 = 3+4+1
11: 8 = 6+2 = 4+1+3
12: 8 = 6+2 = 4+3+1
13: 9 = 1+8 = 2+3+4
14: 9 = 1+8 = 2+4+3
15: 9 = 1+8 = 3+2+4
16: 9 = 1+8 = 3+4+2
17: 9 = 1+8 = 4+2+3
18: 9 = 1+8 = 4+3+2
19: 9 = 2+7 = 1+3+5
20: 9 = 2+7 = 1+5+3
21: 9 = 2+7 = 3+1+5
22: 9 = 2+7 = 3+5+1
23: 9 = 2+7 = 5+1+3
24: 9 = 2+7 = 5+3+1
25: 9 = 4+5 = 1+2+6
26: 9 = 4+5 = 1+6+2
27: 9 = 4+5 = 2+1+6
28: 9 = 4+5 = 2+6+1
29: 9 = 4+5 = 6+1+2
30: 9 = 4+5 = 6+2+1
31: 9 = 5+4 = 1+2+6
32: 9 = 5+4 = 1+6+2
33: 9 = 5+4 = 2+1+6
34: 9 = 5+4 = 2+6+1
35: 9 = 5+4 = 6+1+2
36: 9 = 5+4 = 6+2+1
37: 9 = 7+2 = 1+3+5
38: 9 = 7+2 = 1+5+3
39: 9 = 7+2 = 3+1+5
40: 9 = 7+2 = 3+5+1
41: 9 = 7+2 = 5+1+3
42: 9 = 7+2 = 5+3+1
43: 9 = 8+1 = 2+3+4
44: 9 = 8+1 = 2+4+3
45: 9 = 8+1 = 3+2+4
46: 9 = 8+1 = 3+4+2
47: 9 = 8+1 = 4+2+3
48: 9 = 8+1 = 4+3+2
Activity 6
Directions: Using the digits 1 to 9, at most one time each, fill in the boxes to create a true number sentence with the greatest possible value.
Hint:
What does the equal sign tell you?
How do we know if both sides of the equal sign have the same value?
What is the greatest possible value each side of the equal sign can have?
Answer: See below
The greatest value that the side with the subtraction sign can have is 8 (from 9 – 1). So, possible answers include:
2 + 6 = 9 – 1
6 + 2 = 9 – 1
3 + 5 = 9 – 1
5 + 3 = 9 – 1
4 + 4 = 9 – 1 is not an answer because the 4 is used twice.
There might also be conversations about whether 2 + 6 = 1 – 9 is an answer. This may lead into conversations about how addition is commutative (1 + 4 equals 4 + 1) but subtraction is not (1 – 4 does not equal 4 – 1).
What students MIGHT think is correct, but is NOT correct is something like:
4 + 5 = 9 – (any number other than 0)
This would be because 4 + 5 = 9. However, both sides of the equal sign must have the same value, and they do not when you subtract another number other than zero.
Activity 7
Directions: Using the digits 1 to 9 at most one time each, place a digit in each box to create two true number sentences. You may reuse all the digits for each number sentence.
Hint:
What does the equal sign tell you?
How do we know if both sides of the equal sign have the same value?
Answer: See below
There are many answers to this problem including:
1 + 6 = 9 – 2
2 + 3 = 6 – 1
What students MIGHT think is correct, but is NOT correct is:
1 + 6 = 7 – (any number other than 0)
2 + 3 = 5 – (any number other than 0)
This would be because 1 + 6 = 7 and 2 + 3 = 5. However, both sides of the equal sign must have the same value, and they do not when you subtract another number other than zero.
Activity 8
Directions: Complete the story problem and answer statement.
Version 1 (Difficult)
Lucy has _____ apples. She has nine _____ (more/less) than Marcus. How many apples does _____ (Lucy/Marcus) have?
_____ (Lucy/Marcus) has _____ apples.
Version 2 (Medium Difficulty)
Lucy has _____ apples. She has nine less than Marcus. How many apples does _____ (Lucy/Marcus) have?
_____ (Lucy/Marcus) has _____ apples.
Version 3 (Easy)
Lucy has _____ apples. She has nine more than Marcus. How many apples does Marcus have?
Marcus has _____ apples.
Hint:
Who has more in your problem, Lucy or Marcus?
Should you adjust how many apples Lucy has in the beginning?
How many apples does it make sense for Lucy to have in a “more” problem?
How many apples does it make sense for Lucy to have in a “less” problem?
Challenge: Complete the statement using only numbers within 20.
Answer: Multiple Correct Answers:
Lucy has 11 apples. She has nine more (more/less) than Marcus. How many apples does Marcus (Lucy/Marcus) have?
Marcus (Lucy/Marcus) has 2 apples.
Lucy has 12 apples. She has nine less (more/less) than Marcus. How many apples does Marcus (Lucy/Marcus) have?
Marcus (Lucy/Marcus) has 21 apples.
Activity 9
Directions: Using the digits 0-9 at most one time each, fill in the boxes below to make a true statement.
Hint: How can we pair up the numbers so that all the pairs are equivalent?
Answer: Each pair should add up to 9, for example 4 + 5 = 1 + 8…and so on
Activity 10
Directions: How can we figure out how many dots there are below?
Hint: What is another strategy for figuring out the number of dots?
Answer:
Strategies will vary for counting the 11 dots. Some will see a column of 5 down the middle and 2 sets of 3 dots on either side. Some will see 3 rows of 3 dots and 2 extra dots between them.
