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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
PPS Math Curriculum Grade 6 Unit 1
Copyright 2011, The Leadership and Learning Center. 866.399.6019. All rights reserved.
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
PPS Math Curriculum Grade 6 Unit 1
Copyright 2011, The Leadership and Learning Center. 866.399.6019. All rights reserved.
PPS Math Curriculum Grade 6 Unit 1
Copyright 2011, The Leadership and Learning Center. 866.399.6019. All rights reserved.
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
21st Century Learning Skills
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
❑ Initiative and Leadership
❑ Curiosity and Imagination
❑ Innovation and Creativity
❑ Critical thinking and Problem Solving
❑ Flexibility and Adaptability
❑ Effective Oral and Written
Communication
❑ Accessing and Analyzing Information
❑ Other
PPS Math Curriculum Grade 6 Unit 1
Copyright 2011, The Leadership and Learning Center. 866.399.6019. All rights reserved.
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
PPS Math Curriculum Grade 6 Unit 1
Copyright 2011, The Leadership and Learning Center. 866.399.6019. All rights reserved.
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
PPS Math Curriculum Grade 6 Unit 1
Copyright 2011, The Leadership and Learning Center. 866.399.6019. All rights reserved.
Interdisciplinary Connections and Related
Focus Standards
Specific to Task #2
21st Century Learning Skills
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.
❑ Teamwork and Collaboration
❑ Initiative and Leadership
x Curiosity and Imagination
❑ Innovation and Creativity
x Critical thinking and Problem Solving
x Flexibility and Adaptability
❑ Effective Oral and Written Communication
x Accessing and Analyzing Information
❑ Other
PPS Math Curriculum Grade 6 Unit 1
Copyright 2011, The Leadership and Learning Center. 866.399.6019. All rights reserved.
Performance Task # 2 Scoring Guide
PPS Math Curriculum Grade 6 Unit 1
Copyright 2011, The Leadership and Learning Center. 866.399.6019. All rights reserved.
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 .
PPS Math Curriculum Grade 6 Unit 1
Copyright 2011, The Leadership and Learning Center. 866.399.6019. All rights reserved.
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
21st Century Learning Skills
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.
❑ Teamwork and Collaboration
❑ Initiative and Leadership
x Curiosity and Imagination
❑ Innovation and Creativity
x Critical thinking and Problem Solving
x Flexibility and Adaptability
❑ Effective Oral and Written Communication
x Accessing and Analyzing Information
❑ Other
PPS Math Curriculum Grade 6 Unit 1
Copyright 2011, The Leadership and Learning Center. 866.399.6019. All rights reserved.
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
Surveyed and recorded
responses as less than 10 as
expected
4
Surveyed and recorded
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
PPS Math Curriculum Grade 6 Unit 1
Copyright 2011, The Leadership and Learning Center. 866.399.6019. All rights reserved.
Research-Based Effective Teaching Strategies
21st Century Learning Skills
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
❑ Initiative and Leadership
❑ Curiosity and Imagination
❑ Innovation and Creativity
❑ Critical thinking and Problem Solving
❑ Flexibility and Adaptability
❑ Effective Oral and Written
Communication
❑ Accessing and Analyzing Information
❑ Other