Grades 6-12/Math Lesson 10 Solving Problems Using Scale
FactorsGrades 6-12 Math Lesson 10 Solving Problems Using Scale
FactorsTime Needed: 60 minutes
Learning Target:Use ratio reasoning to solve problems involving
scale.Vocabulary emphasized:scale factor
Background Vocabulary: RatioEquivalent ratio
Look For:Students will solve problems involving scale in more
than one way, including using pictures, equivalent ratios, rate
tables and graphs.
Materials Needed:Overhead projector & markersRulers (1 for
every 2 students)Copies of 2 worksheets for each studentPrint the
Answer Keys to refer to during the lessonCompass Lesson: 5457 (map
scale); 6797; 6798; M7073 (scale drawing)
PreparationMake copies of student worksheets (2) for every
student.Print out the 2 answer keys so that you can refer to them
during the lesson
Warm-up
Hand out the Warm-Up: Find the Missing Side worksheet. Say, On
this worksheet, the two triangles are scale drawings of each other.
You need to find the measurement of the missing side on the larger
triangle. Give students a few minutes to look at the triangles and
try to find the measurement of the side indicated by the question
mark (?). If your class tends to be shy about sharing, then give
them a minute or two to share with a partner first.Ask, Who would
like to share with the class how they found the measurement of the
missing side? Have students share a couple of different strategies.
If no one shares the strategies on the Answer Key, share these
yourself to give students various methods for solving scaling
problems. You want them to be familiar with using pictures, rate
tables, equivalent ratios and graphs to represent the information
in the problem. Also ask, What is the scale factor from the small
triangle to the large triangle? (4) How did you find it? (You can
find the scale factor by looking at the small sides of both
triangles, one is 3 and the other is 12. Since 3 x 4 = 12, then the
scale factor is 12. This works for the middle side also, 4 x 4 =
16.)
Activity
Say, Now you are going to practice solving some more problems
using scale factors. For each problem, read the information
carefully before you start to solve it. If you get stuck, look back
at the strategies we used to solve the warm-up problem with the two
triangles.Handout the Solving Problems Using Scale Factors
worksheet. If your students struggle with reading, you may want to
read the questions with students before they begin working. Then
give students 5 minutes to work INDEPENDENTLY on the problems. Say,
Now you have 5 minutes to work on your own on these problems.
During the five minutes, you can work on any of the problems. If
you get stuck on one, go on to the next one. You will not get any
help during this first five minutes. If you are not sure how to
start, try one of the strategies we used for the warm-up problem.
After the five minutes are up, I will let you know and then you can
work with a partner if you choose. Does anyone have any questions
about the directions? (Answer any questions students have about
what they are supposed to work on now, but do not give further
instructions about the problems yet. You want to see what students
can do on their own.) You may begin working.After five minutes, say
You may now work with a partner if you choose. If you are working
by yourself and you get stuck, you need to ask another student for
help before asking me. Give students about 10-15 more minutes to
work on the problems. As students are working, walk around to see
what strategies students are using to solve the problems. Below are
some questions you can ask students as they are working: How could
you draw a picture to show the information in this problem? (a good
question to ask a student who is struggling to begin) What is the
scale factor in this problem? Can you solve this problem another
way? (a good question for a student who is only using one method
for all three problems)
Summary
Now bring the class back together for the summary. During the
summary, you are going to have student groups come up to the front
of the class to present their work. Have students share strategies
in the following order (from easiest to hardest):1. Picture2. Rate
Table3. Equivalent Ratios4. GraphIf no one used one of the
strategies, you can choose to share the strategy yourself (refer to
the Answer Key for support), you can ask the students how they
might use the strategy to solve the problem, or you can just focus
on the strategies students are choosing to use. Students may have
developed other strategies for the problem. If so, encourage the
class to apply these strategies to the other two problems to see if
they work consistently to get the correct answer. Below are some
questions to ask after a group has presented: Raise your hand if
you agree with how this group solved this problem. (If anyone
disagrees, ask them to explain why they disagree. If the original
group did the problem incorrectly, then it might be helpful to move
on to other strategies first and then come back to this one after
everyone has agree upon the answer.) Does anyone have questions for
this group about how they solved this problem? (You want to
encourage students to ask questions and to take ownership over
their own learning. If anyone asks a question, praise that student
for asking a question.) Ask the group presenting: Why did you
choose to use this strategy to solve this problem? How do you know
the answer is correct?After you have reviewed each question, say
Which strategies do you think are the easiest to use and which
strategies are the hardest and why? Turn to the person next to you
and share your thoughts about this for 1 minute.After one minute
say, Who would like to share? Give several students the chance to
share their opinions about the strategies. This allows students the
time to analyze the strategies and to hear others opinions about
why some are easier than others. In addition to the discussion, you
could have students raise hands and vote for the easiest and
hardest strategy to get everyones input.After the lesson, post
student work (the ones that are correct) in the classroom or lab so
students can refer to them when solving problems.
ExtensionStudents who are ready to solve a more challenging
scaling problem can work on the Gummi Bear Basketball problem.
Students will need rulers, gummi bears and calculators in order to
complete the problem. NOTE: You may want to suggest to students
that they convert all of the measurements to inches.
Hope Online Learning Academy, 2011Page 4
