standard_description: Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual model.
Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.
problem_activity: Problem 1
a.   Estimate whether the following sums will be more or less than 1.
i.
$${{3\over4}+{2\over4}}$$
ii.
$${{5\over6}+{3\over6}}$$
b.   Solve for the actual sums in Part (a) above.
Problem 2
Cary computes
$$\frac{9}{10} + \frac4{10}$$
using a different strategy. Here is her reasoning:
[IMG]
“First I broke
$$\frac4{10}$$
into
$$\frac1{10}$$
and
$$\frac3{10}$$
. Then I added
$$\frac9{10}$$
and
$$\frac1{10}$$
to get to 1, then added the other
$$\frac3{10}$$
to get
$$1\frac3{10}$$
.
So
$$\frac{9}{10} + \frac4{10} = 1\frac3{10}$$
."
a.   Is Cary’s calculation correct? Explain.
b.   Will Cary’s strategy always work? If not, give an example of a calculation for which Cary can’t use this strategy.
c.   Use Cary’s strategy to find
$$\frac45+\frac35$$
.
Problem 3
a.   Estimate whether the following differences will be more or less than 1.
i.
$${1{1\over3}-{2\over3}}$$
ii.
$${1{3\over8}-{5\over8}}$$
b.   Solve for the actual differences in Part (a) above.
Problem 4
Corrado computes
$$1\frac15 - \frac25$$
using a different strategy. Here is his reasoning:
[IMG]
“First I broke
$$\frac25$$
into
$$\frac15$$
and
$$\frac15$$
. Then I subtracted
$$\frac15$$
from
$$1\frac15$$
to get to 1, then subtracted the other
$$\frac15$$
to get
$$\frac45$$
.
So
$$1\frac15 - \frac25 = \frac45$$
."
a.   Is Corrado’s calculation correct? Explain.
b.   Will Corrado’s strategy always work? If not, give an example of a calculation for which Corrado can’t use this strategy.
c.   Use Corrado’s strategy to find
$$1\frac2{12}-\frac5{12}$$
.


aligns: no