UNIT OF STUDY
Title: Unit 6 – Rate, Ratio, Proportion
and Probability
Topic:
Subject/Course: Integrated Algebra A
Grade: 8
UNIT GOALS AND EXPECTATIONS
IMPORTANT CONCEPTS/UNDERSTANDINGS:
• How to find and interpret a unit rate
• How to solve proportions using algebra
• How to solve proportions using the cross products
property
• How to use ratio to find unknown side lengths of
similar figures
• How to find distances using scale and scale
drawings
• How to find probability of an event
• How to determine a sample space
STUDENT LEARNING EXPECTATIONS:
M.13.8.3 – Apply proportional reasoning to solve problems
involving indirect measurements, scale drawings or rates.
G.8.8.3 – Determine appropriate application of geometric
ideas and relationships, such as congruence, similarity and
the Pythagorean theorem, with and without appropriate
technology.
M.12.8.1 – Understand, select and use, with and without
appropriate technology, the appropriate units and tools to
measure angles, perimeter, area, surface area and volume
to solve real world problems.
M.13.8.1 – Draw and apply measurements skills with fluency
to appropriate levels of precision.
DAP.14.8.1 – Design and conduct investigations which
include: adequate number of trials; unbiased sampling;
accurate measurement; record-keeping.
DAP.17.8.1 – Compute, with and without appropriate
technology, probabilities of compound events, using
organized lists, tree diagrams and logic grid.
DAP.17.8.2 – Make predictions based on theoretical
probabilities, design and conduct an experiment to test the
predictions, compare actual results to predict results and
explain differences.
SPECIFIC DECLARATIVE KNOWLEDGE – What I know
• Recognize vocabulary relevant to rates, ratios and
proportions: rate, ratio, proportion, equivalent,
cross product.
• Understand the difference in a ratio and a rate.
• Understand that a proportion is an equation made
up of equivalent ratios.
• Know what a unit rate is and how to find one.
• Understand what a conversion factor is and how to
find an equivalent rate within the same
Length: 2 weeks
Designer: Cox/Nelson
ESSENTIAL QUESTIONS:
• What kinds of questions can be answered using
proportional reasoning?
• How is proportionality of geometric figures used to
solve problems?
• Where do we find probability in everyday life?
• How is probability used to make decisions?
• How are experimental and theoretical probability
related?
• Why does the expected probability not always
match the experimental results?
• How can experimental and theoretical probabilities
be used to make predictions and draw
conclusions?
• How do compound events affect probability?
UNIT VOCABULARY:
• Rate
• Ratio
• Proportion
• Cross product
• Similar figures
• Congruent figures
• Corresponding parts
• Scale
• Scale drawing
• Scale model
• Probability
• Event
• Outcome
• Theoretical probability
• Experimental probability
• Odds
• Odds in favor
• Odds against
• Tree diagram
• Counting Principle (FCP)
SPECIFIC PROCEDURAL KNOWLEDGE – What I need to do
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Create ratios from word problems.
Compare and order ratios.
Find a unit rate.
Write equivalent rates using conversion factors.
Solve a proportion using equivalent ratios.
Solve a proportion using algebra.
Solve a proportion using cross products.
Write and solve proportions from word problems.
Determine if two ratios form a proportion.
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measurement system (linear, weight, capacity,
time) using a conversion factor.
Know that cross products are equal in a proportion.
Know basic geometric concepts (point, line, line
segment, ray, plane, and angle).
Understand the concepts of congruence and
similarity.
Know that corresponding parts in congruent figures
are equal and corresponding parts in similar figures
are proportionate.
Recognize real-world representations of scale
drawings (maps, blueprints) and scale models
(model cars).
Recognize vocabulary relevant to probability:
probability, event, outcome, theoretical,
experimental, tree diagram, sample space,
counting principle and odds.
Identify points, lines, planes, rays, segments and
angles from drawings.
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• Draw a dilation of a right triangle using a scale
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factor of 2 and identify corresponding parts.
• Determine corresponding parts on similar figures.
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• Find the ratio of corresponding side lengths.
• Check figures for similarity by using cross products.
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• Find missing measures in congruent figures by
determining corresponding parts.
• Determine unknown side lengths in similar figures.
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• Use proportions for indirect measurement.
• Create a scale drawing of a rectangular stage using
the scale 1 cm: 3 m.
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• Use scale drawings to find distance.
• Find the scale of a drawing.
• Find a missing dimension of a scale model.
• Find theoretical probability.
• Estimate the likelihood of an event by performing
an experiment.
• Use probability to make a prediction.
• Find the odds an event will occur.
• Make a tree diagram to list all possible outcomes
(sample space) for an event.
• Use the counting principle to find the number of
combinations.
UNIT ASSESSMENTS
(Include tasks related to Dimensions 3 and 4 and Bloom’s Taxonomy)
Open Response #1 – G.8.8.3a, M.12.8.1 – Trapezoid on TLI website (application/analysis level): 1) Copy a trapezoid onto a
grid and draw two line segments to form three congruent triangles. 2) Find area of the trapezoid. 3) Compare area of
trapezoid to area of one of the triangles. Explain the relationship between the two areas.
Open Response #2 – M.13.8.3b – Scale Drawing on TLI website (application level): 1) Using the scale on the drawing, find
the actual length of the longest wall. 2) Draw a different classroom that is 30 by 30 feet using the given scale.
Open Response #3 – DAP.17.8.2 – Coin Toss on TLI website (application/analysis/evaluation level): 1) Based on the table
find probability of heads up/tails up landing. 2) Based on the table, find probability of heads up in 500 trials. 3) Explain why
the theoretical probability could be different than the experimental probability shown in the table.
Traditional Assessments:
Other Evidence of Learning:
• Unit 6 Test
• Jump-Start (warm-up activities)
• Unit 6 Vocabulary Quiz
• In-class activities (individual and group)
• Unit 6 Quizzes
• Journal writing
• TLI Assessment
• Homework assignment
• TLI Open Response
• Responses to teacher questioning
• Student questions and comments
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ACTIVITIES AND LEARNING EXPERIENCES
Ratios and Rates
• APK – Jump-Start: Students will complete problems simplifying ratios to lowest
form.
• Students will write ratios from word problems.
• Students will compare and order ratios by converting to decimal form.
• Students will find a unit rate from a word problem.
• Students will write equivalent rates by multiplying by a conversion factor.
• Students will use equivalent rates to solve word problems.
• Assessment: Students will make a journal entry writing the ratio of girls to total
Resources
M/L Text: Sections 6.1 –
6.8
• M/L text, 6.1
• Skill Check, page
269 TE
• Smart board
• Math journal
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students in the class period, the ratio of boys to total students and the ratio of girls
to boys.
Writing and Solving Proportions
• APK – Jump-Start: Students will work a word problem involving using equivalent
ratios to solve a proportion.
• Students will solve proportions using equivalent ratios.
• Students will solve a proportion using algebra.
• Students will write and solve a proportion from a word problem.
• Students will determine if ratios form a proportion by using cross products.
• Students will solve proportions using cross products.
• Assessment: Students will make a journal entry summarizing the three methods
learned for solving proportions (equivalent ratios, algebraic equation, and
proportion).
Similar and Congruent Figures
• APK – Jump-Start: Students will identify basic geometry concepts (point, line, line
segment, ray, plane and angle).
• Activity: In pairs, students will draw a dilation of a right triangle on a grid using a
scale factor of 2.
• Students will identify corresponding parts on geometric figures.
• Students will find the ratio of corresponding side lengths on geometric figures.
• Students will check for similarity of geometric figures using proportionality of
corresponding side lengths.
• Students will find measures of congruent figures.
• Students will find unknown side lengths in similar figures.
• Students will use proportions to find indirect measurements in real world situations.
• Assessment: Students will make a journal entry finding the height of the school flag
pole if the shadow of the flag pole is 12 feet long and their shadow is 2 feet long.
• Assessment: Students will complete Open Response question #1.
Scale Drawings and Scale Models
• APK – Jump-Start: Students will convert linear measurements using a scale factor.
• Activity: In pairs, students will make a scale drawing to represent a rectangular
stage by using a scale of 1 cm: 3 m.
• Students will find distance using scale drawings.
• Students will find the scale of a drawing by reducing the ratio of corresponding parts
of the actual article to the drawing.
• Students will find a dimension of a scale model by using a proportion with the scale
as one ratio.
• Assessment: Students will complete Open Response question #2.
Probability and Odds
• APK – Jump-Start: In groups of four, students will toss a paper cup and keep a
tally of how many times it lands on its side, rim up or bottom up and answer
questions about the experiment and draw conclusions.
• Students will find theoretical probability.
• Students will conduct experiments to estimate experimental probability.
• Students will use probability to make predictions.
• Students will find odds of an event.
• Students will use a tree diagram to list all the possible outcomes (sample space) for
an event.
• Students will use counting principle to determine the total number of combinations
for two or more events.
• Students will solve word problems involving finding total combinations and the
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M/L Text, 6.2 – 6.3
Mini Quiz
Challenge, page
279, #5
Smart board
Math journal
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M/L Text, 6.4 – 6.5
Activity, page 287
Grid paper
Straight edge
Smart board
Math journal
Open Response
question #1
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M/L text , 6.6
Skill Check, page
300
Activity, page 299
Metric rulers
Smart board
Open Response
question #2
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M/L text, 6.7
Activity, page 305
Small Dixie cups
Foam dice
Pennies
Virtual dice, coin
and spinner on
Smart board
TI-83 calculator –
Prob Sim program
Activity sheets
Group poster
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probability of a specific combination occurring within that total.
Assessment Activity: In groups of four, students will choose a scenario, create a
tree diagram show the different outcome, list the sample space, use counting
principle as a check for total outcomes and find a specific probability using their tree
diagram. Students will create a group poster showing their conclusions and present
to the class.
Assessment: Students will complete Open Response question #3.
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sheets
Markers
Open Response
question #3
Career Connections
Career Link: www.mcdougallittell.com
Marathon runner (Khalid Khannouchi, world record holder 26.2 miles in 2 hr, 5 min, 38 sec)
Glass sculptor (Dale Chihuly)
Archer , decorator, lacrosse player, painter, jeweler, architect, music store manager
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