ALEX Lesson Plan

     

How Far Can You Leap?

You may save this lesson plan to your hard drive as an html file by selecting "File", then "Save As" from your browser's pull down menu. The file name extension must be .html.

  This lesson provided by:  
Author:Tim McKenzie
Organization:UAB/UABTeach
The event this resource created for:CCRS
  General Lesson Information  
Lesson Plan ID: 33080

Title:

How Far Can You Leap?

Overview/Annotation:

This lesson will allow students to become familiar with the concept of unit rate. Through an open investigation students will develop methods to find unit rate with a table, equivalent ratios, or an equation. This is a lesson to be used as part of a unit with "Painter Problems" and "How Big Should It Be?"

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
2 ) Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0, and use rate language in the context of a ratio relationship. [6-RP2]

Examples: "This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar." "We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger." (Expectations for unit rates in this grade are limited to non-complex fractions.)


NAEP Framework
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.6.2- Recognize rate vocabulary in a real-world situation (e.g., miles per hour, dollars per pound).


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
1 ) Compute unit rates associated with ratios of fractions, including ratios of lengths, areas, and other quantities measured in like or different units. [7-RP1]



NAEP Framework
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.7.1- Calculate a unit rate (numbers limited to whole numbers under 100).


Local/National Standards:

Math Practice Standards: 

1. Make sense of problems and persevere in solving them.

2. Reason abstractly and quantitatively.

3. Construct viable arguments and critique the reasoning of others. 

4. Model with mathematics.

5. Use appropriate tools strategically.

6. Attend to precision.

7. Look for and make use of structure.

8. 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.

I CAN use equivalent ratios to find the unit rate.

Additional Learning Objective(s):

 
 Preparation Information 

Total Duration:

61 to 90 Minutes

Materials and Resources:

How Far Can You Leap? Activity Guide (found in attachments), Investigative Activity Rubric (found in attachments), Rate Exit Slip (found in attachments), Chart paper, painter's tape, Math Toolbox which includes the following: pencil, paper, graph paper, markers, scissors, glue, calculator, sticky notes

Technology Resources Needed:

Interactive whiteboard (Optional) with required software, document camera, projector, access to search engine (individually or whole group)

Background/Preparation:

The teacher must make the appropriate number of copies of the How Far Can You Leap? 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 Rate Exit Slip (found in attachments). Each student should have one.

Teacher must prepare the appropriate number of Math Toolboxes. 

Teacher must mark off a starting point for the leap. In a long hallway with square tiles works best, but this can easily be modified to do an outdoor lesson. Instead of floor tiles, the teacher can mark off feet.

The students must have knowledge of ratios. 

  Procedures/Activities: 

1. The teacher will instruct the students to search for "fastest car in the world" (if available, students can use individual devices or this can be done in small or whole group). The teacher will ask "How do we know it is the fastest car in the world?" Students will give responses, an ideal response is "because it tells us the speed." The teacher will ask the students, "How is speed displayed?" Ideal student response "Miles per hour." The teacher will introduce speed as a rate and explain that in 1 hour that car can go n miles. The teacher will introduce rate as a ratio where a unit equals 1. 

2. The teacher will ask students for other rates we use every day. Ideal student response "dollars per hour". The teacher will show the students a rate/ratio of $40 for five hours. The teacher will ask, "Is this a rate?" Ideal response, "No, because the hours is not equal to one." The teacher will pose an open-ended question "How can we get our hours down to one?" Allow students to give suggestions and strategies. Teacher will drive students to set up a table or use equivalent ratios. 

3. The teacher will introduce the activity How far can you leap? The teacher will demonstrate (or have a student demonstrate a leap), start with both feet together and jump with one foot. If needed, teacher will demonstrate the leap progression in the activity (the directions are on the activity guide). Students will begin investigation. As students are working, teacher will act as a facilitator or coach asking questions that drive understanding. 

4. Once adequate time (30-45 minutes) is given, the students will share their finding 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 do you know that ratio is equivalent to the first ratio?" "How did you know to do _______?" "Did someone do this differently?" Teacher will spawn debate on who has the best rate at jumping tiles. 

5. Toward the end of the class students will complete the Rate Exit Slip (found in attachments). 



Attachments:
**Some files will display in a new window. Others will prompt you to download.
  Assessment  

Assessment Strategies

Formal Formative Assessment: Rate 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 Far Can You Leap? Activity Sheet (found in attachments).

Intervention:

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


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.