Unit 3 Extending Operations To Fractions — Unit Plan

1. B
2. $\frac{9}{4}$ sandwiches or $2\frac{1}{4}$ sandwiches. Sample responses:
   • A diagram showing 9 groups of $\frac{1}{4}$.
   • I counted by $\frac{1}{4}$ nine times.
   • I know 4 groups of $\frac{1}{4}$ sandwiches is 1 whole sandwich, so 8 groups of $\frac{1}{4}$ sandwiches make 2 whole sandwiches. Adding $\frac{1}{4}$ sandwich makes $2\frac{1}{4}$.

$6 \times \frac{1}{12}$. Its value is $\frac{6}{12}$. Sample response:

• There are 6 equal groups of $\frac{1}{12}$.
• I counted by $\frac{1}{12}$ six times.
• If all the shaded parts are moved to a single rectangle that represents 1 whole, they would take up 6 parts, which represent $\frac{6}{12}$.

1. 1. $5 \times \frac{1}{8} = \frac{5}{8}$, five groups of 1 eighth make 5 eighths.
   2. $7 \times \frac{1}{3} = \frac{7}{3}$, because I drew a diagram showing 7 groups of $\frac{1}{3}$.
2. 1. $8 \times \frac{1}{9}$
   2. $6 \times \frac{1}{5}$

1. $\frac{12}{5}$. Sample response: 6 groups of 2 fifths make& 12 fifths.

2. $\frac{15}{10}$. Sample response: 5 groups of $\frac{3}{10}$ make $\frac{15}{10}$.

1. Agree. Sample response: $2 \times \frac{6}{8}$ is $\frac{12}{8}$ or 12 groups of $\frac{1}{8}$, and $3 \times 4 \times \frac{1}{8}$ is $12 \times \frac{1}{8}$, which is also 12 groups of $\frac{1}{8}$.
2. Sample responses: $4 \times \frac{3}{9}$, $6 \times \frac{2}{9}$, $2 \times 3 \times \frac{2}{9}$

1. $\frac{15}{4}$ liters. Sample response: $5 \times \frac{3}{4} = \frac{15}{4}$
2. No, Han bought less milk than Tyler did. Sample response: $3 \times \frac{5}{8} = \frac{15}{8}$, and $\frac{15}{8}$ is less than $\frac{15}{4}$ because an eighth is less than a fourth.

• $\frac{1}{4} + \frac{2}{4} + \frac{4}{4} = \frac{7}{4}$
• $\frac{6}{4} + \frac{1}{4} = \frac{7}{4}$
• $\frac{5}{4} + \frac{2}{4} = \frac{7}{4}$

1. Sample response:

   1. $\frac{10}{10} + \frac{3}{10} = \frac{13}{10}$ and $\frac{5}{10} + \frac{8}{10} = \frac{13}{10}$
   2. $1 + \frac{3}{10} = \frac{13}{10}$

   

   Number line. 21 evenly spaced tick marks. First tick mark, 0. Eleventh, 1. Twenty first, 2. Arrow, labeled ten tenths, from first tick mark to eleventh tick mark. Arrow, labeled three tenths, from eleventh tick mark to point at fourteenth tick mark, labeled thirteen tenths. 

   

   Number line. 21 evenly spaced tick marks. First tick mark, 0. Eleventh, 1. Twenty first, 2. Arrow, labeled five tenths, from first tick mark to sixth tick mark. Arrow, labeled eight tenths, from sixth tick mark to point at fourteenth tick mark, labeled thirteen tenths.   

2. $\frac{14}{5}$ or $2\frac{4}{5}$

   

1. $\frac{12}{5} - \frac{4}{5} = \frac{8}{5}$ or $\frac{12}{5} - \frac{4}{5} = 1\frac{3}{5}$. Sample responses:

   

   

2. $2\frac{1}{5} - \frac{7}{5} = \frac{4}{5}$. Sample responses:

   

   

1. $\frac{7}{6}$ or $1\frac{1}{6}$. Sample response:
   • $2 - \frac{5}{6} = \frac{12}{6} - \frac{5}{6} = \frac{7}{6}$
   • $2 - \frac{5}{6} = \left(1 + \frac{6}{6}\right) - \frac{5}{6} = 1 + \left(\frac{6}{6} - \frac{5}{6}\right) = 1 + \frac{1}{6} = 1\frac{1}{6}$
2. $\frac{13}{6}$ or $2\frac{1}{6}$. Sample response:
   • $4 - \frac{11}{6} = \frac{24}{6} - \frac{11}{6} = \frac{13}{6}$
   • $4 - \frac{11}{6} = \left(2 + \frac{12}{6}\right) - \frac{11}{6} = 2 + \left(\frac{12}{6} - \frac{11}{6} \right) = 2 + \frac{1}{6} = 2\frac{1}{6}$
   • $\frac{11}{6}$ is $\frac{1}{6}$ away from 2. I subtracted 2 from 4, and then add $\frac{1}{6}$ back to get $2 \frac{1}{6}$

$4\frac{2}{4}$ inches. Sample reasoning:

• $7\frac{1}{4}$ is $6 + 1 + \frac{1}{4}$, which is $6 + \frac{4}{4} + \frac{1}{4}$ or $6 + \frac{5}{4}$. I subtracted 2 wholes from 6 wholes, which gives 4 wholes, and then subtracted $\frac{3}{4}$ from $\frac{5}{4}$, which gives $\frac{2}{4}$.
• I know 3 is $\frac{1}{4}$ more than $2\frac{3}{4}$. I subtracted 3 from $7 \frac{1}{4}$ to get $4\frac{1}{4}$, and the I added $\frac{1}{4}$ back because I subtracted $\frac{1}{4}$ more than needed earlier.

1. Sample responses:
   • I would decompose $\frac{13}{5}$ into a whole number and a fraction and write it as a mixed number.
   • I would write $1\frac{2}{5}$ as a fraction without a whole number.
2. $1\frac{1}{5}$ or $\frac{6}{5}$. Sample response:
   • $\frac{13}{5} = \frac{10}{5} + \frac{3}{5} = 2+\frac{3}{5} = 2\frac{3}{5}$ and $2\frac{3}{5} - 1\frac{2}{5} = 1\frac{1}{5}$
   • $1\frac{2}{5} = \frac{5}{5} + \frac{2}{5} = \frac{7}{5}$ and $\frac{13}{5}-\frac{7}{5} = \frac{6}{5}$

1.  

   

2. $3\frac{7}{8}$ inches. Sample response: $5\frac{6}{8} - 1\frac{7}{8} = 4 \frac{14}{8} -1\frac{7}{8} = 3\frac{7}{8}$

1. Nine students grew more than $1\frac{3}{8}$ inches. Sample response: $1\frac{3}{8}$ is located between $1\frac{1}{4}$ and $1\frac{2}{4}$, and there are 9 points to the right of $1\frac{3}{8}$.
2. $2\frac{2}{8}$ inches. Sample response: $3\frac{1}{8} - \frac{7}{8} = 2\frac {9}{8} - \frac{7}{8} =2\frac{2}{8}$.

1. $\frac{6}{10}$ or $\frac{60}{100}$
2. $\frac{6}{10}$ or $\frac{60}{100}$
3. $\frac{63}{100}$
4. $\frac{88}{100}$

1. $\frac{106}{100}$ or $1\frac{6}{100}$
2. $\frac{22}{100}$
3. $\frac{12}{10}$ or $\frac{120}{100}$
4. $\frac{132}{100}$ or $1\frac{32}{100}$

1. $\frac{53}{100}$cm. Sample response: $\frac{15}{100} + \frac{2}{10} + \frac{18}{100} = \frac{33}{100} + \frac{20}{100} = \frac{53}{100}$
2. $\frac{74}{100}$cm. Sample response: $\frac{2}{10} + \frac{22}{100} + \frac{18}{100} + \frac{14}{100} = \frac{20}{100} + \frac{54}{100} = \frac{74}{100}$

Yes. Sample response: The H shape is $5 \times \frac{11}{8}$ or $\frac{55}{8}$ inches tall. The notebook is $9 \times \frac{8}{8}$ or $\frac{72}{8}$ inches tall.