A scale is a ratio between the model and the actual representation.
A scale factor is the number used when finding how much a figure was enlarged by or reduced by. The easiest way to find it is to find two corresponding sides and find their simplified ratio.
Similar figures must meet 3 rules in order to be considered similar figures.
1) Must be the same shape and have corresponding sides with the same properties
2) Must have the same/corresponding angles from one shape to the other
3) Must be proportionate (scale factor is the same for all corresponding sides)
Corresponding sides are outlined below by color coding the sides that correspond. Notice that they have the same properties in relation to their respective triangles.
Classwork Similar figures (1-8)
Notes and Practice
1/6 HW: Similar figures (9-16)
In class, we discussed that the constant of proportionality shows the unit rate between units being compared to one another.
The constant of proportionality is determined by how to get from the first unit in a ratio to the second unit.
For example, if there are 30 students in 2 classes, the unit rate would be 15 students per class. This means that the constant of proportionality is 15 since every additional class would get 15 more students.
Tables are another way of viewing ratios. The worksheet here was done in class to show students how to find the constant of proportionality to determine missing values.
1/4 Classwork - Ratios in Tables WS
1/4 Classwork - Ratios in Graphs Video
1/4 Homework - Ratios in Graphs
1/5 Homework - Graphing Unit Rates
Enlarge the slideshow below to review independent and dependent variables as well as how they can be used to interpret and solve a graph, table, or equation.
Unit rate is the amount for 1 item. It is similar to unit price, except unit price asks for how much 1 of something costs.
Ex. Stacy runs 3 miles in 36 minutes. Unit rate would tell how long it takes her to run 1 mile.
Stacy runs 1 mile in 12 minutes.
Ex. 3 gallons of gas cost $6. Unit price would tell how much 1 gallon of gas is.
1 gallon of gas is $2.
Unit Rate WS
To solve a ratio for a missing value, we usually use a proportion to identify the missing number, the variable.
Using the examples from the previous journal entry, we will solve for a missing value under a hypothetical, or "pretend", situation. Set up a proportion for each problem.
1) 5 plates for 2 bowls, how many plates if there are 6 bowls? 15 plates
2) 2 boys: 3 girls, how many girls if there are 12 boys? 18 girls
3) 4 blue blocks to 6 red blocks, how many blue blocks if there are 12 red blocks? 8 blue blocks
Below is an image of different ways to set up the proportion to solve.
Below is a basic ratio word problem as an example of how to solve to find the missing value.
Not all word problems will provide 2 matching units. Sometimes you will be given 3 units that don't seem to match together at all, like the word problem below.
Try some problems like the one from the Sally's test in the video:
1) 5 plates for 2 bowls, how many of each if there are 21 total? 15 plates, 6 bowls
2) 2 boys: 3 girls, how many of each if there are 30 total? 12 boys, 18 girls
3) 4 blue blocks to 6 red blocks, how many of each if there are 60 total? 24 blue blocks, 36 red blocks
4) 3 made shots for every 5 attempts, how many MISSES if there are 20 total attempts? 8 missed shots
Classwork - Ratio word problems
1. A recipe calls for 6 eggs to make 15 pancakes. How many eggs are needed to make 70 pancakes?
2. Sandra drove 126.2 miles in 2 hours at a constant speed. How long would it take her to drive 189.3 miles at the same speed?
3. Carmen earned $144 for 18 hours of work. At this rate, how much will she earn for 36 hours of work?
4. Nine apples cost $2.61. How much will 4 dozen apples cost?
5. In order to determine her pulse rate, Sondra’s nurse count 23 beats in 20 seconds. At this rate, how many beats would she have in 1 minute?
6. Parker uses a cookie recipe that requires ¾ cup of sugar to make 33 cookies. If Parker only wants to make 11 cookies, how much sugar should he use?
Equivalent ratios are very similar to equivalent fractions - ratios just can't be written as mixed numbers because it's comparing two different things instead of showing a part of a whole.
Identify whether the following problems are equivalent ratios or not. Correct the ratio so that it is equivalent if it is not. Explain why they are equivalent.
1) 5 plates for 2 bowls and 10 plates and 6 bowls
2) 2 boys: 3 girls and 6 boys: 9 girls
3) 4 blue blocks to 6 red blocks and 12 blue blocks to 18 red blocks
4) 3 socks to 4 shoes and 12 socks to 9 shoes
A ratio is a way to compare two or more units to one another to show a relationship.
It can be written in 3 different ways, as a fraction, with a colon, or with the word to.
For example, there are 3 dogs for every cat. This would be written as 3/1, 3:1, or 3 to 1. Each of these ways of writing the ratio is read the same way as 3 to 1.
Units are the ways that something is measured. In the example above, the units are dogs and cats. Units do NOT include numbers.
What are the units in the following problems?
1) 5 plates for 2 bowls
2) 2 boys: 3 girls
3) 4 blue blocks to 6 red blocks
Try to write each of the problems (1-3) from above in all the ways that a ratio can be written.
Notes from Class: