Unit 9 Putting It All Together — Unit Plan

1. Sample response:
   • $\frac{13}{10} + \frac{9}{10} = \frac{22}{10} = \frac{10}{10} + \frac{10}{10} + \frac{2}{10} = 2\frac{2}{10}$
   • I know $\frac{15}{10}$ is the same as $1\frac{1}{2}$. All the other choices are more than $\frac{1}{2}$ , so I could pick $\frac{15}{10}$ and any of the others.
   • $\frac{15}{10} + \frac{53}{100} = \frac{203}{100} = \frac{100}{100} + \frac{100}{100} + \frac{3}{100} = 2\frac{3}{100}$
2. $\frac{15}{10} + \frac{53}{100} - \frac{9}{10} + \frac{13}{10}$ or $\frac{15}{10}+\frac{9}{10} - \frac{53}{100} - \frac{13}{100}$

16 feet, because $12\frac{4}{6} + 3\frac{2}{6} = 16$.

$4\frac{6}{8}$ or $4\frac{3}{4}$cups. Sample response:

• $7 - 2 = 5$ and $5 - \frac{2}{8} = 4 + \frac{8}{8} - \frac{2}{8}=4\frac{6}{8}$
• I know $\frac{2}{8} = ​ \frac{1}{4}$. So $7 - 2 = 5$ and $5- \frac{1}{4} = 4\frac{3}{4}$

1. 7,837. Sample response:
   • $8,000 - 200 = 7,800$ and $50 - 13 = 37$. Adding 7,800 and 37 gives 7,837.

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2. 58,016. Sample response: $1,984 + 16 = 2,000$ and $2,000 + 58,000 = 60,000$. Adding 58,000 and 16 gives 58,016.

1. 10,468. Sample responses:
   $(2,000 \times 4) + (600 \times 4) + (17 \times 4)$
   = $8,000 + 2,400 + 68$
   = $10,468$

   

2. 728. Sample responses:
   • $52 \times 10 = 520$ and $52 \times 4 = 208$. The sum of 520 and 208 is 728.
   • $14 \times 50 = 700$ and $14 \times 2 = 28$. The sum of 700 and 28 is 728.
   • Using algorithms:

     

     

1. Sample response: A meal at a restaurant in the United States costs about 2 times (or twice) as much as a meal in Ghana.
2. 3 more times. Sample response: In the United States: $4 \times 75 = 300$, which is less than 350. They could eat at a restaurant 4 times. There will be $50 extra. In Ghana: $9 \times 37 = 333$. They could eat out 9 times and have $17 left.

1. D. Sample responses:
   • $1,560 - 4 = 1,560$, ​$1,560 \div 8 =195$​
   • ​$195 \times 8 = 1,560$​,  ​$1,560 + 4 = 1,564$​
2. Sample responses:
   • I know A could not be true because I know $200 \times 8 = 1,600$ and that’s more than the total distance the train traveled.
   • I know C could not be true because the situation says it's just a few more miles to the repair center. 1,500 miles is not a few more miles. $(8 \times 8) + 1,500$ does match the total distance, but it doesn’t match the situation.

Sample response:

• Question: If the band keeps raising $175 each week, how many more weeks before it reaches its goal?
• Answer: 4 weeks. In 6 weeks, the band raises $1,050, so it still needs to raise $650. Three more weeks mean an additional $3 \times 175$ or $525. So one more week would mean $525 + 175$ or $700.

Sample response: After multiplying several numbers multiple times to make estimates, I understand much more that there are different ways to break apart and rearrange the factors to make it easier to find products. Usually I’d just multiply the numbers in the order they were given.

Sample response: In one of the Which Three Go Together? one set showed only numbers. I realized that which group of numbers went together was based on the digits being used. My group helped me see that we also could look at place value, whole numbers versus decimals, and whether the digits are odd or even.

Sample response: Recently, I noticed that one way to find the product of a whole number and a fraction, like $\frac{1}{8}$, is to divide the whole number by the denominator of the fraction. When I multiply 16 by $\frac{1}{8}$, the result is the same as the result of dividing 16 by 8. I have used this observation to check my answers to multiplication problems like this.