ALEX Lesson Plan

     

How Big Should it Be?

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  This lesson provided by:  
Author:Tim McKenzie
Organization:UAB/UABTeach
The event this resource created for:CCRS
  General Lesson Information  
Lesson Plan ID: 33091

Title:

How Big Should it Be?

Overview/Annotation:

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.

 Associated Standards and Objectives 
Content Standard(s):
Mathematics
MA2015 (2016)
Grade: 6
1 ) Understand the concept of a ratio, and use ratio language to describe a ratio relationship between two quantities. [6-RP1]

Examples: "The ratio of wings to beaks in the bird house at the zoo was 2:1 because for every 2 wings there was 1 beak." "For every vote candidate A received, candidate C received nearly three votes."


NAEP Framework
NAEP Statement::
4NPO4a: Use simple ratios to describe problem situations.

NAEP Statement::
8NPO3a: Perform computations with rational numbers.

NAEP Statement::
8NPO4a: Use ratios to describe problem situations.

NAEP Statement::
8NPO4b: Use fractions to represent and express ratios and proportions.

NAEP Statement::
8NPO4d: Solve problems involving percentages (including percent increase and decrease, interest rates, tax, discount, tips, or part/whole relationships).



Alabama Alternate Achievement Standards
AAS Standard:
M.AAS.6.1- Select a ratio to match a given statement and representation.


Mathematics
MA2015 (2016)
Grade: 6
3 ) Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. [6-RP3]

a. Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios. [6-RP3a]

b. Solve unit rate problems including those involving unit pricing and constant speed. [6-RP3b]

Example: If it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours' At what rate were lawns being mowed'

c. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent. [6-RP3c]

d. Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. [6-RP3d]


NAEP Framework
NAEP Statement::
8M2b: Solve problems involving conversions within the same measurement system such as conversions involving square inches and square feet.

NAEP Statement::
8M2c: Estimate the measure of an object in one system given the measure of that object in another system and the approximate conversion factor. For example:
  • Distance conversion: 1 kilometer is approximately 5/8 of a mile.
  • Money conversion: U.S. dollars to Canadian dollars.
  • Temperature conversion: Fahrenheit to Celsius.


NAEP Statement::
8NPO3a: Perform computations with rational numbers.

NAEP Statement::
8NPO4a: Use ratios to describe problem situations.

NAEP Statement::
8NPO4b: Use fractions to represent and express ratios and proportions.

NAEP Statement::
8NPO4d: Solve problems involving percentages (including percent increase and decrease, interest rates, tax, discount, tips, or part/whole relationships).



Alabama Alternate Achievement Standards
AAS Standard:
M.AAS.6.3- Solve simple real-world problems using ratio/rate reasoning.
M.AAS.6.3a- Answer simple questions about a table of equivalent ratios with whole-number measurements.
M.AAS.6.3b- Calculate unit-rate problems, including those involving unit pricing.
M.AAS.6.3c- Identify a percentage equivalent to a fraction (e.g., 1/2, 1/4, 1).
M.AAS.6.3d- Identify the decimal equivalent of a percentage (limited to 10%, 20%, 25%, 40%, and 50%).


Mathematics
MA2015 (2016)
Grade: 7
2 ) Recognize and represent proportional relationships between quantities. [7-RP2]

a. Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin. [7-RP2a]

b. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. [7-RP2b]

c. Represent proportional relationships by equations. [7-RP2c]

Example: If total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn.

d. Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate. [7-RP2d]


NAEP Framework
NAEP Statement::
4A1e: Recognize or describe a relationship in which quantities change proportionally.

NAEP Statement::
8A2c: Graph or interpret points represented by ordered pairs of numbers on a rectangular coordinate system.

NAEP Statement::
8M1i: Solve problems involving rates such as speed or population density.

NAEP Statement::
8NPO1b: Model or describe rational numbers or numerical relationships using number lines and diagrams.

NAEP Statement::
8NPO1d: Write or rename rational numbers.

NAEP Statement::
8NPO1e: Recognize, translate or apply multiple representations of rational numbers (fractions, decimals, and percents) in meaningful contexts.

NAEP Statement::
8NPO3a: Perform computations with rational numbers.

NAEP Statement::
8NPO3f: Solve application problems involving rational numbers and operations using exact answers or estimates as appropriate.

NAEP Statement::
8NPO4a: Use ratios to describe problem situations.

NAEP Statement::
8NPO4b: Use fractions to represent and express ratios and proportions.

NAEP Statement::
8NPO4c: Use proportional reasoning to model and solve problems (including rates and scaling).



Alabama Alternate Achievement Standards
AAS Standard:
M.AAS.7.2- Use a ratio to model or describe a real-world relationship (ratio or rate).


Mathematics
MA2015 (2016)
Grade: 7
11 ) Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale. [7-G1]


NAEP Framework
NAEP Statement::
8G1d: Draw or sketch from a written description polygons, circles, or semicircles.

NAEP Statement::
8G1f: Demonstrate an understanding about the two-and three-dimensional shapes in our world through identifying, drawing, modeling, building, or taking apart.

NAEP Statement::
8G3b: Apply geometric properties and relationships in solving simple problems in two and three dimensions.

NAEP Statement::
8G3c: Represent problem situations with simple geometric models to solve mathematical or real-world problems.

NAEP Statement::
8G3f: Describe or analyze simple properties of, or relationships between, triangles, quadrilaterals, and other polygonal plane figures.

NAEP Statement::
8M3a: Solve problems involving indirect measurement such as finding the height of a building by comparing its shadow with the height and shadow of a known object.



Alabama Alternate Achievement Standards
AAS Standard:
M.AAS.7.11- Given a geometric figure, recognize a similar scaled figure with the same orientation.


Local/National Standards:

Math Practice Standards:

  • Make sense of problems and persevere in solving them.
  • Reason abstractly and quantitatively.
  • Construct viable arguments and critique the reasoning of others.
  • Model with mathematics.
  • Use appropriate tools strategically.
  • Attend to precision.
  • Look for and make use of structure.
  • Look for and express regularity in repeated reasoning.

Primary Learning Objective(s):

I CAN identify and develop ratios in real world situations.

I CAN identify equivalent ratios.

I CAN compare ratios in real world situations.

Additional Learning Objective(s):

 
 Preparation Information 

Total Duration:

61 to 90 Minutes

Materials and Resources:

  • How Big Should It Be Activity Guide (found in attachments)
  • Investigative Activity Rubric (found in attachments)
  • Ratio 2 Exit Slip (found in attachments)
  • Chart paper
  • Yard stick
  • Math Toolbox which includes the following: pencil, paper, graph paper, markers, scissors, glue, calculator, and sticky notes

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). 

Background/Preparation:

  • The teacher must make the appropriate number of copies of the How Big Should It Be activity guide (found in attachments). 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 (found in attachments). Each student should have one.
  • Teacher must prepare the appropriate number of Math Toolboxes.
  • Teacher must download the video at the link below.  Zoolander Center for Ants (If YouTube is not available through your school system, you may download the video using www.keepvid.com)
  • The students must have knowledge of ratios.

 

  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 (found in attachments). 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.


Attachments:
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  Assessment  

Assessment Strategies

Formal formative assessment: Ratio 2 Exit Slip

Formal Assessment: Using the Investigative Activity Rubric (found in attachments) 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 (found in attachment)

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.


View the Special Education resources for instructional guidance in providing modifications and adaptations for students with significant cognitive disabilities who qualify for the Alabama Alternate Assessment.