# Week 12: Distance, Unit Rate, Integers

Bell Work Week 12 updated

Understanding Special Ratio Word Problems   (Thursday/Friday Advance, and Advanced Virtual)

Unit Rate and Constant Speed Guided Notes  Distance Formula notes:(use with Advanced & Virtual Adv Monday/Tuesday)

Integer Guided Notes (Honors math notes for the week)

Unit Rate Work Practice (use for Regular Math 5th, 7th, Virtual Tuesday)

Proportions guided notes for Reg (Friday: 5th, 7th, Virtual)

Recognizing Proportional Relationships Independent Practice Worksheet

Proportion Solving ( Practice Problems for All Math Advance Students Thurs/Fri)

Rates Practice work ( All Math Advance Students Monday, Wednesday, or Friday)

Adding and Subtracting Rational Numbers (honors Math Monday, Wednesday)

Multiplying & Dividing Negative Numbers (honors Math Thursday)

Finding Ratios and Unit Rate   ( Work for Advanced Students for Wednesday) 2 pages only

Teacher Nancy Morris Math 6th Week 12: Distance, Unit Rate, Integers Distance, Unit Rate, Integers
Standard(s) Taught

Regular Math:

MAFS.6.RP.1.1
Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, “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.”

MAFS.6.RP.1.2: (Links to an external site.)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. For example, “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.”

MAFS.6.RP.1.3: (Links to an external site.) 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.

a. Make tables of equivalent ratios relating quantities with whole-number measurements, finding missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.(to be taught C and P)

b. Solve unit rate problems including those involving unit pricing and constant speed. For 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? (to be taught A)

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. (to be taught P and A).

d. Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.(to be taught C and P)

e. Understand the concept of Pi as a ratio of the circumference of a circle to its diameter. (to be taught C)

Honors:
MAFS.7.RP.1.3 (6H)
MAFS.7.RP.1.3: Use proportional relationships to solve multi-step ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.

Learning Targets and Learning Criteria

Regular Math
Success Criteria:

I know I am successful when I can:

understand that a ratio is a comparison between quantities.
determine when a ratio is describing part-to-part or part-to-whole comparison.
describe ratio relationships between two quantities using ratio language.
use ratio formats interchangeably (4:5,LaTeX: \frac{4}{5}4 5 , 4 to 5).

Success Criteria:

I know I am successful when I can:

understand rate as a ratio that compares two quantities with different units of measure.
understand that unit rates are the ratio of two measurements or quantities in which the second term means “one” such as 60 miles per one hour.
interpret rate language with the @ symbol or with the words per and/or each.
recognize a ratio written as a unit rate, explain a unit rate, and give an example of a unit rate.
convert a given ratio to a unit rate.
given a ratio, identify the unit rate and the rate unit.
recognize that all ratios associated to a given rate are equivalent because they have the same value.

Success Criteria:

I know I am successful when I can:

create and interpret a table of equivalent ratios.
plot pairs of values from a table to a coordinate plane
use a table to compare ratios and find missing values using ratios.
explain the difference between a ratio and a unit rate.
understand that rate problems compare two different units, such as revolutions per minute or miles per hour.
solve real-world problems using ratios and rates.
reason to determine the better buy.
write a percent as a rate over 100, including percents greater than 100 and less than 1.
find the percent of a number using rate methods.
represent the relationship of part to whole to describe percents using models.
convert units by multiplication or division.
understand and explain that Pi is a ratio of the circumference of a circle to its diameter.
determine whether two ratios are equivalent, based on the description of equivalent ratios, using tape diagrams, double number line diagrams, and/or equivalent ratio tables.
create and complete an equivalent ratio table, tape diagram, and/or double number line diagram to solve problems.
calculate the percent of a given number by using visual representations (e.g., strip diagrams, percent bars, one-hundred grids)
find the whole when given both the part and the percent using tape diagrams, double number line diagrams, and tables of equivalent ratios.

Honors:
Success Criteria:

I know I am successful when I can:

use proportional reasoning to solve real-world ratio problems, including those with multiple steps.
use proportional reasoning to solve real-world percent problems, including those with multiple steps, such as markups, markdowns, commissions, and fees
solve percent problems when one quantity is a certain percent more or less than another.
recall conversion of percent from ratio to decimal to percent form.
solve percent of increase/decrease problems.

Classroom Activities

All lessons are subject to change based on teacher need.

Monday:
Virtual Zoom: Advanced 8:00
Students will log into the session and begin working on bell work with problems for unit rate.

As a whole group we will work on guided notes for the interactive notebook on Distance Formula and constant speed. We will complete several examples and work on various types and ways to solve problems using the distance formula. Students will leave the session after notes are finished and work on Edgenuity work (see Assignments Due).

1st Period: Advanced Math
Students will complete the bell work for unit rate.
As a whole group we will work on guided notes for the interactive notebook on Distance Formula and constant speed. We will complete several examples and work on various types and ways to solve problems using the distance formula. Students will practice work for proportions and problems using the distance formula for a formative grade (F2F students)

2nd Period: Regular Math
Bell work will be problems involving unit rate.

I will do a review of unit rate and how to solve problems using unit rate. Students will then work to finish the Unit rate paper that is in the “Not Done Drawer”. Students that finish the assignment will log into IXL and work on work for R- 1-10.

4th Honors Math:
Bell work will be 4 problems proportions with variables.
The lesson will begin with review of integers, absolute value, and additive inverses. Our lesson will continue with adding and subtracting integers guided notes. As a whole group we will complete several practice problems for adding and subtracting using the rules for integers. Students will work on 2 practice pages for adding and subtracting integers.

Tuesday:
Virtual Zoom: 8:00 Regular Math
Bell work will be problems for equivalent ratios and ratio tables.
Students will begin taking guided notes on Equivalent Ratios and Ratio Tables. After completing Ratio Tables we will begin the guided notes on Unit Rate and work on practice problems together. Face to Face: Students will complete practice problems if time permits.
Virtual students will log out of the session and work on Edgenuity work for Ratios.

Face to Face: 5th and 7th
Bell work with equivalent ratio tables.

5th only:

Students will begin taking guided notes on Equivalent Ratios and Ratio Tables. After completing Ratio Tables we will begin the guided notes on Unit Rate and work on practice problems together. Face to Face: Students will complete practice problems if time permits.

7th only: Students will take guided notes on Unit Rate and work as a whole group to complete practice problems. Students will complete Unit Rate work to practice the skills after notes.

Bell work will involve problems for Unit Rate.
As a whole group we will work on guided notes for the interactive notebook on Distance Formula and constant speed. We will complete several examples and work on various types and ways to solve problems using the distance formula. Students will practice work for proportions and problems using the distance formula for a formative grade (F2F students)

Wednesday:

Virtual Students Zoom: Advanced 8:00, Regular 11:40

Bell work will be practice problems for Unit Rate for all classes.

Virtual students will log into their session and participate in the  bell work and then will be excused to work on their Edgenuity work. Students that have any questions or need assistance beyond the session will be encouraged to stay in session and ask questions if it is needed. Students will be encouraged to view the summative study guide to prepare for summative on ratios, unit rates, and proportions test (Advanced Virtual Students Only).

Face to Face Students:

1st: After bell work students will work on practice work that focuses on distance formula and constant speed. Students that require a retake on the previous summative will work to complete this during this class period. Students will also be working to complete any missing assignments they may have in the grade book.

2nd: After  bell work students will be completing guided notes for proportions. Several types will be modeled using different methods to show students there are multiple ways to solve a proportion.

4th: After bell work students will work on guided notes for multiplying and dividing with integers with a few practice problems to help them see the process that should be used to solve these types of problems.

5th: After bell work students will work to complete the guided notes for Unit rate. Students will have practice pages to complete as class work.

7th: After bell work we will work on guided notes for proportions. Students will do practice problems on the skill directly following the lesson.

8th: After bell work students will work on practice problems for ratios, unit rate, and proportions to prepare for summative tomorrow.

Thursday:
Virtual Zoom: Advanced 8:00
Students will log into the session and begin working on bell work with problems for unit rate or proportions.

Students will take a summative on Ratios, Unit Rate, and Proportions on School City. Students will need to remain on camera while testing.
Virtual students that finish the test should make sure they are making adequate progress on their Edgenuity assignments.

Face to Face:
Bell work will be problems for Unit rate.
Student will be taking a summative on Ratios, Unit Rate, and Proportions during the class period. Any student finishing early will work on IXL lessons for Unit Rate.

2nd: Regular Math
Bell work will be problems with ratio tables and equivalent ratios.

I will begin this class with a review of solving proportions in various ways then students will work on independent practice of the skill.

4th Honors Math
Students will complete bell work involving problems for add/subtract integers using rules for each type.
The lesson for today will begin with a review of applying the rules of integers to multiplication and division problems. Students will then work to complete practice problems on using the skill.

Friday:
Virtual Zoom: 8:00 Regular Math

Bell work will be problems with ratio tables and equivalent ratios.

As a whole group we will work on guided notes for solving a proportions with students. We will look at the many different ways that proportions are set up and solved. Together as a whole group lesson we will do several practice problems with the skill. Student will complete practice problems if time permits.

Virtual students will be given a reminder they, should be making sure they are making adequate progress on their Edgenuity assignments.

Face to Face:
5th/7th: Regular Math
Bell work will be problems with ratio tables and equivalent ratios.

As a whole group we will work on guided notes for solving a proportions with students. We will look at the many different ways that proportions are set up and solved. Together as a whole group lesson we will do several practice problems with the skill. Student will complete practice problems if time permits.

I will begin the lesson by reviewing the previous lesson on distance formula and how to apply the formula to various problems. Students will work to complete practice problems as independent practice of the skill.

Assignments Due

Virtual Students:  Due Complete December 4th

Advanced Virtual: Edgenuity Assignments

1. Understanding Unit Rate
2. Comparing Ratios
3. Converting Measurement

Regular Virtual: Edgenuity Assignments

1. Using Ratio Notation
2. Equivalent Ratios
3. Understanding Unit Rate
4. Unit Pricing

All Math Advanced Students: Summative Postponed