standard_description: Interpret multiplication as scaling (resizing), by:
- Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n×a)/(n×b) to the effect of multiplying a/b by 1.
- Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication.
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