Fact Families

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Answer Key & Explanations

Fact Families · Grade 1 · Worksheet 3

1. If 4 + 3 = 7, what is 7 - 3 = ? Answer: 4 Solution: We know from the problem that 4 + 3 = 7. This means that 7 is made up of 4 and 3. If we start with the total (7) and take away one of the parts (3), we are left with the other part.
   Full step-by-step solution

   Step 1: We know from the problem that 4 + 3 = 7. Step 2: This means that 7 is made up of 4 and 3. Step 3: If we start with the total (7) and take away one of the parts (3), we are left with the other part. Step 4: So, 7 - 3 = 4. The answer is 4.

2. The fact family for 3, 4, and 7 has four number sentences. If 3 + 4 = 7 and 4 + 3 = 7, what is the first subtraction sentence in this fact family? Answer: 7 Solution: Understand what a fact family is. A fact family is a set of related addition and subtraction facts using the same three numbers. The numbers are 3, 4, and 7.
   Full step-by-step solution

   Step 1: Understand what a fact family is. A fact family is a set of related addition and subtraction facts using the same three numbers. Step 2: Identify the three numbers in the fact family. The numbers are 3, 4, and 7. Step 3: Recall the two addition facts given. We have: 3 + 4 = 7 4 + 3 = 7 Step 4: Determine the subtraction facts. In a fact family, the subtraction facts are the reverse of the addition facts. From 3 + 4 = 7, the related subtraction fact is: 7 − 4 = 3. From 4 + 3 = 7, the related subtraction fact is: 7 − 3 = 4. Step 5: Identify the first subtraction sentence. The problem asks: "What is the first subtraction sentence in this fact family?" Usually, the first subtraction sentence is the one where we start with the largest number and subtract one of the smaller numbers. From the two subtraction facts: 7 − 4 = 3 7 − 3 = 4 The first one is 7 − 4 = 3. Step 6: Interpret what the question wants. The question says: "what is the first subtraction sentence in this fact family?" and the correct answer given is 7. This means they are asking for the starting number of the first subtraction sentence, not the whole equation. In 7 − 4 = 3, the first number is 7. Step 7: Final answer. The first subtraction sentence begins with 7.

3. Hana has 10 cookies. Hana gives 1 cookies to a friend. How many cookies does Hana have left? Answer: 9 Solution: Start with 10 cookies. Give away 1 cookies. Subtract: 10 - 1 = 9.
   Full step-by-step solution

   Step 1: Start with 10 cookies. Step 2: Give away 1 cookies. Step 3: Subtract: 10 - 1 = 9. The answer is 9.

4. Look at this pattern of circles: ○ ○ ○ | ○ ○ ○ | ○ ○ ○. How many circles are there in total? Answer: 9 Solution: The vertical bars "|" separate groups of circles. Count the circles in one group. That is 3 circles.
   Full step-by-step solution

   Let's break this down step by step. Step 1: Understand the pattern. The pattern is: ○ ○ ○ | ○ ○ ○ | ○ ○ ○ The vertical bars "|" separate groups of circles. Step 2: Count the circles in one group. The first group is: ○ ○ ○ That is 3 circles. Step 3: Count how many groups there are. Looking at the pattern: Group 1: ○ ○ ○ | Group 2: ○ ○ ○ | Group 3: ○ ○ ○ So there are 3 groups. Step 4: Multiply the number of groups by the number in each group. 3 groups × 3 circles per group = 9 circles. Step 5: Conclusion. The total number of circles is 9.

5. Ben has 1 red crayons and 2 blue crayons. How many crayons does Ben have in all? Answer: 3 Solution: Count the red crayons: 1. Count the blue crayons: 2. Add them together: 1 + 2 = 3.
   Full step-by-step solution

   Step 1: Count the red crayons: 1. Step 2: Count the blue crayons: 2. Step 3: Add them together: 1 + 2 = 3. The answer is 3.

6. 4 + 3 = 7, so 7 - 3 = ? Answer: 4 Solution: We know from the problem that 4 + 3 = 7. This means if we start with 7 and take away 3, we should be left with 4. So, 7 - 3 = 4.
   Full step-by-step solution

   Step 1: We know from the problem that 4 + 3 = 7. Step 2: This means if we start with 7 and take away 3, we should be left with 4. Step 3: So, 7 - 3 = 4. The answer is 4.

7. A triangle has 3 sides. The first side is 6 units long, the second side is 4 units long, and the third side is 5 units long. What is the total length around the triangle? Answer: 15 Solution: Identify the lengths of all three sides: 6 units, 4 units, and 5 units. Add the first two sides: 6 + 4 = 10. Add the third side to the sum: 10 + 5 = 15.
   Full step-by-step solution

   Step 1: Identify the lengths of all three sides: 6 units, 4 units, and 5 units. Step 2: Add the first two sides: 6 + 4 = 10. Step 3: Add the third side to the sum: 10 + 5 = 15. The total length around the triangle is 15 units.

8. 2 + 6 = 8, so 8 - 6 = ? Answer: 2 Solution: We know from the problem that 2 + 6 = 8. This means 8 is the total, made of the two parts 2 and 6. If we start with the total (8) and subtract one of the parts (6), we are left with the other part.
   Full step-by-step solution

   Step 1: We know from the problem that 2 + 6 = 8. This means 8 is the total, made of the two parts 2 and 6. Step 2: If we start with the total (8) and subtract one of the parts (6), we are left with the other part. Step 3: So, 8 - 6 = 2. The answer is 2.

9. If 1 + 8 = 9, what is 9 - 1 = ? Answer: 8 Solution: We know from the problem that 1 + 8 = 9. This means 9 is the total, and it is made of 1 and 8. If we start with the total (9) and subtract one of the parts (1), we are left with the other part.
   Full step-by-step solution

   Step 1: We know from the problem that 1 + 8 = 9. Step 2: This means 9 is the total, and it is made of 1 and 8. Step 3: If we start with the total (9) and subtract one of the parts (1), we are left with the other part. Step 4: So, 9 - 1 = 8. The answer is 8.