Unit 5 Place Value Patterns And Decimal Operations — Unit Plan

Sample responses: One thousandth can be represented on a grid. It can be written as 0.001. It's really small. It is one tenth of one hundredth. I wonder if there is something smaller than 1 thousandth.

1. Sample response:

   
2. Sample responses:
   • One tenth, four hundredths, and nine thousandths
   • One hundred forty-nine thousandths
   • $\frac{149}{1,000}$

1. 0.579
2. $\frac{579}{1,000}$
3. $\left(5 \times 0.1\right) + \left(7 \times 0.01\right) + \left(9 \times 0.001\right)$
4. five hundred seventy-nine thousandths

1. 0.026 ounces
2. Sample response: One hundredth ounce and 16 thousandth ounce weights, because a hundredth is the same as 10 thousandths.

Andre. Sample response: They each threw it 5 meters but then 1 tenth is 10 hundredths and that's more than 9 hundredths.

1. 

2. 0.359 is greater. Sample response: It's farther to the right.

1. 1.7 grams
2. 1.67 grams

1. 17.6
2. 17.64

556.040, 565.004, 565.4

• Nearest tenth: 49.3 seconds
• Nearest hundredth: 49.26 seconds

1.33. Sample responses: $1.20 + 0.10 = 1.30$ , $1.30 + 0.03 = 1.33$

25.05. Sample responses:

• $21+3=24$, $0.40+0.60=1.00$, $24+1=25$, $25+0.05=25.05$
•  

  

1. Sample response: The decimal places are not lined up so the 30 in 38.7 is treated like it's only 3.
2. 48.16. Sample response: 

   

2.17. Sample response: $3-1=2$, $0.57-0.40=0.17$, $2.00+0.17=2.17$

301.47. Sample responses:

• $321 - 20 = 301$, $0.8 - 0.4 = 0.4$, $0.07 - 0 = 0.07$, $301+0.4+0.07=301.47$
•  

  

1. 70.83. Sample response:
   

   

2. 242.02. Sample response: $236.87+0.13=237$, $237+5.02=242.02$

1. 0.8. Sample response: 0.4 is 4 tenths and double that is 8 tenths or 0.8.
2. 0.12. Sample response: 0.03 is 3 hundredths and 4 groups of 3 hundredths is 12 hundredths or 0.12.

1. 0.1
2. 3
3. 0.15
    

1. A, B, and D
2. Sample response: $15 \times 0.2$ is 30 tenths or 3 and $15 \times 0.01$ is 15 hundredths or 0.15. Then $3 - 0.15 = 2.85$.

1. 0.18 (or equivalent)
2. 0.78 (or equivalent)

1.  Sample response: $2.5 = 25 \times 0.1$ and $6.4 = 64 \times 0.1$ so $2.5 \times 6.4 = (25 \times 64) \times 0.01$
2. 16. Sample response: $25 \times 64 = 1,600$ so $2.5 \times 6.4 = 16.00$

1. 70. Sample response: $1 \div 0.1 = 10$ and $7 \times 10 = 70$
2. 700. Sample response: There are 100 hundredths in 1, so there are 700 hundredths in 7.

1. 24. Sample response: There are 2 groups of 0.5 in 1 whole and $12 \times 2=24$.
2. 650. Sample responses:
   • There are 50 groups of 0.02 in 1. Since there are 13 wholes, that means there will be 13 times as many 0.02s which is the same as 13 groups of 50.
   • $50 \times 0.02=1$, $500 \times 0.02 = 10$, $100\times 0.02=2$ and $50 \times 0.02 = 1$ so $(500 + 100 + 50) \times 0.02 = 10 + 2 + 1 = 13$

1. 0.3. Sample response: There are 9 tenths so that’s 3 groups of 3 tenths.
2. 0.03. Sample response: There are 9 hundredths so that’s 3 groups of 3 hundredths.
3. 0.16. Sample response: There are 80 hundredths so that’s 5 groups of 16 hundredths.

• 160. Sample responses: 
  • $1.6 \div 0.01 = 160 \div 1$
  • There are one hundred 0.01s in 1, sixty 0.01s in 0.6, and one hundred sixty 0.01s in 1.6.
• 287. Sample responses:
  • $2.87 \div 0.01 = 287 \div 1$
  • There are two hundred 0.01s in 2, eighty 0.01s in 0.8, seven 0.01s in 0.07, and two hundred eighty-seven 0.01s in 2.87.