Unit 8 Putting It All Together — Unit Plan

No. Sample response: The shaded part of the shape is $\frac{1}{2}$. The point on the number line is greater than $\frac{1}{2}$ but less than 1. The shaded part of the diagram is less than $\frac{1}{2}$. 

1. Answers vary.
2. Answers vary.

1. 50 square feet. Sample response: The hallway is 3 feet by 6 feet, so it has an area of 18 square feet. The bedroom is 4 feet by 8 feet, so it has an area of 32 square feet. I added 32 and 18 to get 50.
2. 36 feet. (The perimeter is the same whether students include the sink and stove or not.) Sample responses:
   • I found $2\times10$ and $2\times8$, and then I added 20 and 16 to get 36.
   • I added the lengths of the two sides of the living room and the sides around the sink and stove, and the width of the hallway: $10+8+6+2+2+3+2+3$ and got 36.

$343. Sample response: Tile flooring costs $90, because $18 \times 5$ is $10 \times 5 + 8 \times 5$, which is $50 + 40$ or 90. Adding 253 and 90 together gives 343.

Sample responses:

1. We were able to collect our data quickly and there was no confusion. I think it went well because we showed people the question and the choices instead of just reading them aloud, and we used a recording sheet.
2. We missed some people in the class and couldn't easily tell who we missed. I think it was because we didn't think about a way to make sure everyone had a turn.

24 more students. Sample response: 8 students liked yellow and 10 students liked orange. This is 18 students. 42 students liked blue, which is 24 more students than students who liked yellow and orange together.

Sample response:

• I know a lot more multiplication facts than when I started.
• I can use what I know about fives and tens to find other products quickly.
• Multiplying a number by 8 takes me more time to figure out. I’d like to get faster.

Sample responses:

• Multiplication is how we represent equal groups.
• Multiplication is related to division.
• Multiplication can represent area.
• I can use different strategies to multiply, like using a fact you know.
• There are patterns in the multiplication table.

Sample responses:

• We can think of $24\div4={?}$ as $4\times{?}=24$.
• If I’m dividing, it’s like multiplying, but instead of not knowing the total number of objects, I’m missing the number of equal groups or the number in each group.

• This diagram shows multiplication: the side lengths are known but the area isn’t.

  

  This diagram shows division: the area is known, but a side length is missing.

  

Sample responses:

1. For finding division facts that I didn’t know, it was helpful to think of a related division fact that I did know. It was helpful to think about related multiplication facts.
2. I need to practice dividing large numbers by 7 and by 9.

Sample response: I understand that when equal groups are organized into rows or columns, they are easier to count because we only need to count one row and then multiply by the number of rows.

Sample response: In the Warm-up, I saw 9 groups of 4 and my classmate saw 4 groups of 8 and another group of 4.

Sample response: I explained to my group how I thought about the Estimation Exploration we wrote so that we could think about how other students might respond.

Sample response: When we were designing a Number Talk, I tried to think of how to make the problems similar enough so that we could use the same method for all the problems.