Lesson Plan

How Big Should It Be?

Subject Area

Mathematics

Grade(s)

6, 7

Overview

This lesson will allow students to become familiar with the concept of equivalent ratios and similar objects. Through an open investigation, students will develop methods to find equivalent ratios. This is a lesson to be used as part of a unit with Painter Problems and How Far Can You Leap found in ALEX.

This is a College- and Career-Ready Standards showcase lesson plan.

Mathematics (2019) Grade(s): 6

MA19.6.1

Use appropriate notations [a/b, a to b, a:b] to represent a proportional relationship between quantities and use ratio language to describe the relationship between quantities.

Unpacked Content

UP:MA19.6.1

Vocabulary

  • Ratio
  • Ratio Language
  • Part-to-Part
  • Part-to-Whole
  • Attributes
  • Quantity
  • Measures
  • Fraction

Knowledge

Students know:
  • Characteristics of additive situations.
  • Characteristics of multiplicative situations

Skills

Students are able to:
  • Compare and contrast additive vs. multiplicative contextual situations.
  • Identify all ratios and describe them using "For every…, there are…"
  • Identify a ratio as a part-to-part or a part-to whole comparison.
  • Represent multiplicative comparisons in ratio notation and language (e.g., using words such as "out of" or "to" before using the symbolic notation of the colon and then the fraction bar. for example, 3 out of 7, 3 to 5, 6:7 and then 4/5).

Understanding

Students understand that:
  • In a multiplicative comparison situation one quantity changes at a constant rate with respect to a second related quantity. -Each ratio when expressed in forms: ie 10/5, 10:5 and/or 10 to 5 can be simplified to equivalent ratios, -Explain the relationships and differences between fractions and ratios.
Mathematics (2019) Grade(s): 6

MA19.6.3

Use ratio and rate reasoning to solve mathematical and real-world problems (including but not limited to percent, measurement conversion, and equivalent ratios) using a variety of models, including tables of equivalent ratios, tape diagrams, double number lines, and equations.

Unpacked Content

UP:MA19.6.3

Vocabulary

  • Rate
  • Ratio
  • Rate reasoning
  • Ratio reasoning
  • Transform units
  • Quantities
  • Ratio Tables
  • Double Number Line Diagram
  • Percents
  • Coordinate Plane
  • Ordered Pairs
  • Quadrant I
  • Tape Diagrams
  • Unit Rate
  • Constant Speed

Knowledge

Students know:
  • Strategies for representing contexts involving rates and ratios including. tables of equivalent ratios, changing to unit rate, tape diagrams, double number lines, equations, and plots on coordinate planes.
  • Strategies for finding equivalent ratios,
  • Strategies for using ratio reasoning to convert measurement units.
  • Strategies to recognize that a conversion factor is a fraction equal to 1 since the quantity described in the numerator and denominator is the same.
  • Strategies for converting between fractions, decimals and percents.
  • Strategies for finding the whole when given the part and percent in a mathematical and contextual situation.
  • Strategies for finding the part, given the whole and the percent in mathematical and contextual situation.
  • Strategies for finding the percent, given the whole and the part in mathematical and contextual situation.

Skills

Students are able to:
  • Represent ratio and rate situations using a variety of strategies (e.g., tables of equivalent ratios, changing to unit rate, tape diagrams, double number line diagrams, equations, and plots on coordinate planes).
  • Use ratio, rates, and multiplicative reasoning to explain connections among representations and justify solutions in various contexts, including measurement, prices and geometry.
  • Understand the multiplicative relationship between ratio comparisons in a table by writing an equation.
  • Plot ratios as ordered pairs.
  • Solve and justify solutions for rate problems including unit pricing, constant speed, measurement conversions, and situations involving percents.
  • Solve problems and justify solutions when finding the whole given a part and the percent.
  • Model using an equivalent fraction and decimal to percents.
  • Use ratio reasoning, multiplication, and division to transform and interpret measurements.

Understanding

Students understand that:
  • A unit rate is a ratio (a:b) of two measurements in which b is one.
  • A symbolic representation of relevant features of a real-world problem can provide for resolution of the problem and interpretation of the situation.
  • When computing with quantities the transformation and interpretation of the resulting unit is dependent on the particular operation performed.
Mathematics (2019) Grade(s): 7

MA19.7.2

Represent a relationship between two quantities and determine whether the two quantities are related proportionally.

Unpacked Content

UP:MA19.7.2

Vocabulary

  • Equivalent ratios
  • proportional
  • Coordinate plane
  • Ratio table
  • Unit rate
  • Constant of proportionality
  • Equation
  • ordered pair

Knowledge

Students know:
  • (2a) how to explain whether a relationship is proportional.
  • (2b) that the constant of proportionality is the same as a unit rate. Students know:
    • where the constant of proportionality can be found in a table, graph, equation or diagram.
    • (2c) that the constant of proportionality or unit rate can be found on a graph of a proportional relationship where the input value or x-coordinate is 1.

Skills

Students are able to:
  • (2a) determine if a proportional relationship exists when given a table of equivalent ratios or a graph of the relationship in the coordinate plane.
  • (2b) identify the constant of proportionality and express the proportional relationship using a variety of representations including tables, graphs, equations, diagrams, and verbal descriptions.
  • (2c) model a proportional relationship using coordinate graphing.
  • Explain the meaning of the point (1, r), where r is the unit rate or constant of proportionality.

Understanding

Students understand that:
  • (2a) A proportional relationship requires equivalent ratios between quantities. Students understand how to decide whether two quantities are proportional.
  • (2b) The constant of proportionality is the unit rate. Students are able to identify the constant of proportionality for a proportional relationship and explain its meaning in a real-world context. (2c) The context of a problem can help them interpret a point on a graph of a proportional relationship.
Mathematics (2019) Grade(s): 7

MA19.7.17

Solve problems involving scale drawings of geometric figures, including computation of actual lengths and areas from a scale drawing and reproduction of a scale drawing at a different scale.

Unpacked Content

UP:MA19.7.17

Vocabulary

  • Scale drawing
  • Reproduction
  • Scale factor

Knowledge

Students know:
  • how to calculate actual measures such as area and perimeter from a scale drawing.
  • Scale factor impacts the length of line segments, but it does not change the angle measurements.
  • There is a proportional relationship between the corresponding sides of similar figures.
  • A proportion can be set up using the appropriate corresponding side lengths of two similar figures.
  • If a side length is unknown, a proportion can be solved to determine the measure of it.

Skills

Students are able to:
  • find missing lengths on a scale drawing.
  • Use scale factors to compute actual lengths, perimeters, and areas in scale drawings.
  • Use a scale factor to reproduce a scale drawing at a different scale.

Understanding

Students understand that:
  • scale factor can enlarge or reduce the size of a figure.
  • Scale drawings are proportional relationships.
  • Applying a scale factor less than one will shrink a figure.
  • Applying a scale factors greater than one will enlarge a figure.

Primary Learning Objectives

I CAN identify and develop ratios in real world situations.

I CAN identify equivalent ratios.

I CAN compare ratios in real world situations.

Procedures/Activities

  1. Teacher will show the students the video clip of Zoolander (video shows an unintelligent supermodel angered at the reveal of a model of a building, he claims the building is for ants and has to be at least three times as big). The teacher will ask the students, "Why did Zoolander get so upset at Mugato?" Ideal response, "He thought the model of the building was the actual building." The teacher will ask, "What do you think about his statement 'The building has to be at least three times that big'?" Ideal response, "three times as big would still not be big enough for anyone to fit in." 
  2. The teacher will introduce the idea of a scale factor as "a ratio used to enlarge or shrink any shape or object." 
  3. The teacher will present the How Big Should It Be activity. The teacher may have to demonstrate how to measure.
  4. Students will begin the investigative activity. They will be producing a poster with a shape 5 times the original size and 10 times the original size. The teacher will act as a facilitator and coach throughout the investigation. The teacher should address misconceptions and drive inquiry related to ratios. 
  5. Once adequate time (30-45 minutes) is given, the students will share their findings on the document camera. (If a document camera is not available, students may present their work in the front of the class, this is where the students would need chart paper). As the students are sharing, the teacher is acting as the facilitator and coach asking questions that drive ratio understanding. "How did you know to multiply by _____?" "How did you know to do _______?" "Did someone do this differently?" 
  6. Students will complete the Ratio 2 Exit Slip.

 

Assessment Strategies

Formal formative assessment: Ratio 2 Exit Slip

Formal Assessment: Using the Investigative Activity Rubric the teacher will evaluate students' work.

Informal Formative Assessment: As the students are working, the teacher will act as the facilitator and coach. Teacher will ask questions to evaluate students (i.e. How do you know ______? What did you do to get that?) Teacher may pull small groups during investigation on a needs basis.

Acceleration

The investigation has an included extension on the How Big Should It Be Activity Sheet.

Because this is part of a unit, teacher may develop small groups based on the Ratio 2 Exit Slip or informal questioning as part of the investigative activity.

 

Intervention

Struggling students should be grouped with a peer tutor and teacher should pay close attention to those groups to assure complete understanding.

Approximate Duration

Total Duration

61 to 90 Minutes

Background and Preparation

Background/Preparation

  • The teacher must make the appropriate number of copies of the How Big Should It Be activity guide. Copies should be made so that students can work collaboratively. 
  • The teacher must make the appropriate number of copies of the Ratio 2 Exit Slip. Each student should have one.
  • Teacher must prepare the appropriate number of Math Toolboxes.
  • Teacher must download the video: Zoolander Center for Ants.
  • The students must have knowledge of ratios.

 

Materials and Resources

Materials and Resources

Technology Resources Needed

Interactive Whiteboard (Optional) with required software, Document camera, projector, laptop or computer capable of showing videos (TV and DVD player can be used if the DVD is available). 

Approved Date

2013-12-13
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