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PPS Math Curriculum Grade 6 Unit 1

Copyright 2011, The Leadership and Learning Center. 866.399.6019. All rights reserved.

Performance Task # 1

Task 1: Cooking with Fractions

Goal: Convert a recipe to make exactly enough food for a class of 13 people.

Role: You are a professional chef catering our class party.

Audience: Mrs. Page who has hired you to prepare food and the class who will eat your food at the

party.

Situation: You have been “hired” by Mrs. Page to prepare a dish for our class party. Your recipe

needs to be modified to make exactly enough food to serve each person in our class one serving.

Product: Converted recipe to show how much of each ingredient you will need to make your

recipe.

Focus Standards: 6.NS.1 Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. Supporting Standards: 6.NS.3 Fluently add, subtract, multiply, and divide multi-digit decimals using the standards algorithm for each operation. What essential Question(s) and corresponding Big Idea(s) will this task target?

How do you divide a fraction?

How can you use a model to show division by a fraction?

There are multiple models and/or procedures for comparing and computing with fractions, just as there are with whole numbers. Operations with fractions have the same meanings as operations with whole numbers, even though the algorithms differ. How will the students apply the concepts and skills? What will they do and/or

produce?

Students will add, multiply, and divide fractions convert a recipe to make exactly enough

food for a specified amount of people. Students will produce a sample cook page of their

converted recipe to show how much of each ingredient you will need to make your recipe.

What resources, instruction, and information will students need in order to

complete the task?

Step 1: Choose a Recipe



Step 2: Set up a Table to display all ingredients, recipe, and serving amounts (Fractions) Step 3 Take the original recipe and divide the amount needed for each ingredient by the number of servings that your recipe makes Step 4: Perform calculation to determine the amount of ingredients needs for the converted recipe. step 5: Create a table to show all recipe/ingredient conversions Recipe table template

What evidence of learning will I look for to show that I know all of my students have

conceptually learned the concepts and skills – the standard(s)

Student level of understanding shall be based on the accuracy of their recipe conversion

chart, and computations.

How can I differentiate the application and/or evidence to meet the varying needs of my

students?

The activity can be modified by teachers as needed to meet the skills levels and

needs by:

Give a personal cue to begin work Give work in smaller units Provide immediate reinforces and feedback Make sure the appropriate books and materials are available Introduce the assignment in sequential steps Check for student understanding of instructions Check on progress often in the first few minutes of work Provide time suggestions for each task Provide a checklist for long detailed tasks Use technological resources



Interdisciplinary Connections and Related Focus

Standards

Specific to Task #1

21st Century Learning Skills

Specific to Task #1

CCSS.ELA-Literacy.W.6.8 Gather relevant information

from multiple print and digital sources; assess the

credibility of each source; and quote or paraphrase the

data and conclusions of others while avoiding plagiarism

and providing basic bibliographic information for sources.

CCSS.ELA-Literacy.W.6.6 Use technology, including the

Internet, to produce and publish writing as well as to

interact and collaborate with others; demonstrate

sufficient command of keyboarding skills to type a

minimum of three pages in a single sitting.

NJCC 5.1.8.A.2 Use mathematical, physical, and

computational tools to build conceptual-based models and

to pose theories.

x Teamwork and Collaboration

❑ Initiative and Leadership

❑ Curiosity and Imagination

❑ Innovation and Creativity

x Critical thinking and Problem Solving

❑ Flexibility and Adaptability

x Effective Oral and Written Communication

❑ Accessing and Analyzing Information

❑ Other

Research-Based Effective Teaching Strategies


Task /Activities that solidifies mathematical concepts

Use questioning techniques to facilitate learning

Reinforcing Effort, Providing Recognition

Practice , reinforce and connect to other ideas within mathematics

Promotes linguistic and nonlinguistic representations

Cooperative Learning

Setting Objectives, Providing Feedback

Varied opportunities for students to communicate mathematically

Use technological and /or physical tools

those that apply to the unit:

❑ Teamwork and Collaboration




❑ Critical thinking and Problem Solving


❑ Effective Oral and Written

Communication


❑ Other

http://www.corestandards.org/ELA-Literacy/W/6/8/




Performance Task # 2 Goal: Keep track of expenses and income over a 4-week period.

Role: You are yourself.

Audience: Mrs. Page who has hired you to prepare food and the class who will eat your food at the

party.

Situation: You have a job and an allowance. You will keep track of how you use/ spend your money

over a 4-week period.

Product: Expense account form.

Focus Standards: 6.NS.5: Understand that positive and negative numbers are used together to describe

quantities having opposite directions or values. Use positive and negative numbers to

represent quantities in real-world contexts explaining the meaning of 0 in each situation

Supporting Standards: 6.NS.3: Fluently add, subtract, multiply, and divide multi-digit decimals using the standards algorithm for each operation. Which standard(s) (priority/supporting) will the task address?

6. NS.5:Understand that positive and negative numbers are used together to describe

quantities having opposite directions or values. Use positive and negative numbers to

represent quantities in real-world contexts explaining the meaning of 0 in each situation.

What essential Question(s) and corresponding Big Idea(s) will this task target?

How are integers useful in life?

How do we add and subtract integers?

How does a numbers relationship to zero affect its' value?

Negative numbers are used to represent quantities that are less than zero. Understand numbers values, and relationships among numbers and number systems. Which “unwrapped specific concepts and skills will this task target?

Understand positive and negative numbers, Use and negative numbers to represent quantities How will the students apply the concepts and skills? What will they do and/or

produce?

Students will apply their understanding of positive and negative numbers to design and



develop a working budget for one month. Within that budget, students will utilize integers to

maintain an accurate account of monies saved and spent.

What resources, instruction, and information will students need in order to complete

the task?

Computer/internet access

Budget template

Check books

Play Money

Number lines What evidence of learning will I look for to show that I know all of my students have

conceptually learned the concepts and skills – the standard(s)?

Students present their original budgets demonstrating all transactions and calculations over

that period as well as a copy of any revised budgets, if needed. In addition, a summary of

specific activities will be evaluated to determine student understanding of integers.

How can I differentiate the application and/or evidence to meet the varying needs of

my students?

To differentiate the application, small groups of students with learning needs will be given a number line to work with and the ELL students will pair with an English/Spanish speaking student to complete task. Give a personal cue to begin work Give work in smaller units Provide immediate reinforces and feedback Make sure the appropriate books and materials are available Introduce the assignment in sequential steps Check for student understanding of instructions Check on progress often in the first few minutes of work Provide time suggestions for each task Provide a checklist for long detailed tasks Use technological resources



Interdisciplinary Connections and Related

Focus Standards

Specific to Task #2


Specific to Task #2

CCSS.ELA-Literacy.W.6.6 Use technology,

including the Internet, to produce and publish

writing as well as to interact and collaborate

with others; demonstrate sufficient command

of keyboarding skills to type a minimum of

three pages in a single sitting.



x Curiosity and Imagination



x Flexibility and Adaptability

❑ Effective Oral and Written Communication

x Accessing and Analyzing Information

❑ Other




Performance Task # 2 Scoring Guide



Performance Task # 3

Students will calculate the mean, median, and mode from survey data they collect. From this data, they determine

which measures of central tendency best represent the average.

Students will create three survey questions for your peers to answer, survey your classmates and record their

responses on a data collection sheet. Students will ask 15 peers question one, 20 peers question two, and 25 peers

question three. Students will then create a plot graph and calculate mean, median, mode and interquartile range .

Then students explain how measures of central tendency and variability in each data set is affected by data

Focus Standards:

6.SP.1; 6.SP.2; 6.SP.3; 6.SP.5c,d

Calculate, compare, and interpret measures of center and variability in a data set to answer a

statistical question. (Including median, mean, interquartile range, mean absolute deviation and overall pattern).

Supporting Standard

Which standard(s) (priority/supporting) will the task address?

6.SP.1; 6.SP.2; 6.SP.3; 6.SP.5c,d

Calculate, compare, and interpret measures of center and variability in a data set to answer a

statistical question. (Including median, mean, interquartile range, mean absolute deviation and overall pattern).

What essential Question(s) and corresponding Big Idea(s) will this task target?

What are mean, median, mode, and range?

How do we find mean, median mode, and range in a given set of data?

How do they help us better understand the data? Which “unwrapped specific concepts and skills will this task target?

Recognize statistical questions Understand a set of data Recognize that a measure of center for a numerical data set summarizes all of its values Summarize numerical data sets How will the students apply the concepts and skills? What will they do and/or produce?

Students will create three survey questions for your peers to answer, survey your classmates and record

their responses on a data collection sheet. Students will ask 15 peers question one, 20 peers question

two, and 25 peers question three. Students will then create a plot graph and calculate mean, median,

mode and interquartile range . Then students explain how measures of central tendency and variability

in each data set is affected by data .



What resources, instruction, and information will students need in order to complete the task?

Grade 6 Unit 1 Performing Task 3

What evidence of learning will I look for to show that I know all of my students have conceptually

learned the concepts and skills – the standard(s)?

Teachers shall assess students based on their ability to calculate the mean, median, and mode from survey data they

collect. Teachers will also be able to evaluate evidence of learning based on students data display, and their written

assessment

How can I differentiate the application and/or evidence to meet the varying needs of my

students?

Give a personal cue to begin work Give work in smaller units

Provide immediate reinforces and feedback Make sure the appropriate books and materials are available Introduce the assignment in sequential steps Check for student understanding of instructions Check on progress often in the first few minutes of work Provide time suggestions for each task Provide a checklist for long detailed tasks Use technological resources

Interdisciplinary Connections and Related Focus

Standards

Specific to Task #3


Specific to Task #3

CCSS.ELA-Literacy.W.6.2a Introduce a topic;

organize ideas, concepts, and information, using

strategies such as definition, classification,

comparison/contrast, and cause/effect; include

formatting (e.g., headings), graphics (e.g., charts,

tables), and multimedia when useful to aiding

comprehension.

CCSS.ELA-Literacy.W.6.1b Support claim(s) with

clear reasons and relevant evidence, using credible

sources and demonstrating an understanding of the

topic or text.



x Curiosity and Imagination



x Flexibility and Adaptability

❑ Effective Oral and Written Communication

x Accessing and Analyzing Information

❑ Other



Performance Task # 3 Scoring Guide

Survey and Graphing Rubric

1 pts

2 pts

3 pts

4 pts

Data Collected 1

Student did not meet the

expected number of

responses

2

Surveyed and recorded

responses of less than 20 as

expected

3


responses as less than 10 as

expected

4


responses as expected

Calculation Data 1

Calculations are missing or

incorrect

2

Correctly calculated 2 out of 4 of

the mean, median, mode, and

interquartile range.

3

Correctly calculated 3 out of

4 of the mean, median,

mode and interquartile

range.

4

Correctly calculated the mean,

median, mode and interquartile

range.

Displays of Data 1

Few have appropriate labels

on the x-axis.

Few have appropriate labels

on the y-axis.

Data is somewhat plotted

correctly.

2

Some have appropriate labels on

the x-axis.

Some have appropriate labels on

the y-axis.

Data is somewhat plotted

correctly.

3

Most have appropriate

labels on the x-axis.

Most have appropriate

labels on the y-axis.

Data mostly plotted

correctly.

4

.

Appropriate labels on the x-

axis included.

Appropriate labels on the y-

axis included.

Data plotted correctly.

Reflection Explanation is missing, or

unrelated to problem.

There is an incomplete

explanation. Student does not or

limit elements of the data set to

support reasoning

There is an explanation.

Student uses data set to

support reasoning

There is a clear, effective and

strong explanation. Student effectively uses data set to

support reasoning



Research-Based Effective Teaching Strategies


Task /Activities that solidifies mathematical concepts

Use questioning techniques to facilitate learning

Reinforcing Effort, Providing Recognition

Practice , reinforce and connect to other ideas within mathematics

Promotes linguistic and nonlinguistic representations

Cooperative Learning

Setting Objectives, Providing Feedback

Varied opportunities for students to communicate mathematically

Use technological and /or physical tools

those that apply to the unit:





❑ Critical thinking and Problem Solving


❑ Effective Oral and Written

Communication


❑ Other

performance task # 1 task 1: cooking with fractionsplainfieldnjk12.org/departments/math/docs/unit...

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