Embedded Files
Learning Targets
I can use equivalent ratios to describe scaled copies of shapes.
I know that two recipes will taste the same if the ingredients are in equivalent ratios.
Notes
Notes
When two different situations can be described by equivalent ratios, that means they are alike in some important way.
An example is a recipe. If two people make something to eat or drink, the taste will only be the same as long as the ratios of the ingredients are equivalent. For example, all of the mixtures of water and drink mix in this table taste the same, because the ratios of cups of water to scoops of drink mix are all equivalent ratios.
If a mixture were not equivalent to these, for example, if the ratio of cups of water to scoops of drink mix were 6:4, then the mixture would taste different.
Notice that the ratios of pairs of corresponding side lengths are equivalent in figures A, B, and C. For example, the ratios of the length of the top side to the length of the left side for figures A, B, and C are equivalent ratios. Figures A, B, and C are scaled copies of each other; this is the important way in which they are alike.
If a figure has corresponding sides that are not in a ratio equivalent to these, like figure D, then it’s not a scaled copy. In this unit, you will study relationships like these that can be described by a set of equivalent ratios.
Vocabulary
Vocabulary
equivalent ratios: Two ratios a:b and c:d are equivalent ratios if there is a number s that you can multiply both a and b by to get c and d (respectively). For example, 8:6 is equivalent to 4:3 because 8 * ½ = 4 and 6 * ½ = 3. A recipe for lemonade says to use 8 cups of water and 6 lemons. If we use 4 cups of water and 3 lemons, it will make half as much lemonade. Both recipes taste the same, because 8:6 and 4:3 are equivalent ratios.
Activities
Activities
1.1 Remembering Double Number Lines
1.1 Remembering Double Number Lines
If needed, review double number lines first ->
Complete the double number line diagram with the missing numbers.
What could each of the number lines represent? Invent a situation and label the diagram (that's what the empty dashed boxes are for).
Make sure your labels include appropriate units of measure.
1.3 Crescent Moons
1.3 Crescent Moons
Here are four different crescent moon shapes.
What do moons A, B, and C all have in common that the other one doesn’t?
Use numbers to describe how moons A, B, and C are different from moon D.
Use a table and a double number line diagram to represent how moons A, B, and C are different from moon D.
Summary
Summary
Assignment
Assignment
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