M/J Grade 6 Mathematics
Advanced / Unit : 17Modules 17
/ Dates:
Oct 3 – Oct 7
Florida Standard(s):
Benchmarks, descriptions, DOK levels, standards unpacked (know/do) highlighted / MAFS.7.NS.1.1: (DOK 2) Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.
c. Understand subtraction of rational numbers as adding the additive inverse, p – q = p + (–q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts. [conceptual, application]
d. Apply properties of operations as strategies to add and subtract rational numbers. [conceptual, procedural]
¨ Identify subtraction of rational numbers as adding the additive inverse property to subtract rational numbers, p - q = p + (-q).
¨ Apply and extend previous understanding to represent addition and subtraction problems of rational numbers with a horizontal or vertical number line.
¨ Represent the distance between two rational numbers on a number line is the absolute value of their difference and apply this principle in real-world contexts.
¨ Apply the principle of subtracting rational numbers in real-world contexts.
MAFS.7.NS.1.3: (DOK 2) Solve real-world and mathematical problems involving the four operations with rational numbers.
Add, subtract, multiply, and divide rational numbers.
Solve real-world mathematical problems by adding, subtracting, multiplying, and dividing rational numbers, including complex fractions.
MAFS.7.EE.2.3: (DOK 2) Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation. [procedural, application]
Generate equivalent fractions to find like denominators.
Rewrite an expression in an equivalent form in order to provide insight about how quantities are related in a problem context.
MAFS.7.NS.1.2: (DOK 2) Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.
a. Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (–1)(–1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts. [conceptual, application]
b. Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers, then – (p/q) = (–p)/q = p / (–q). Interpret quotients of rational numbers by describing real-world contexts. [conceptual, application]
c. Apply properties of operations as strategies to multiply and divide rational numbers. [conceptual, procedural]
Describe situations in which opposite quantities combine to make 0.
Represent and explain how a number and its opposite have a sum of 0 and are additive inverses
Demonstrate and explain how adding two numbers, p + q, if q is negative, the sum of p and q will be |q| spaces to the left of p on the number line.
Interpret sums of rational numbers by describing real-world contexts.
Explain and justify why the sum of p + q is located a distance of |q| in the positive or negative direction from p on a number line.
Identify subtraction of rational numbers as adding the additive inverse property to subtract rational numbers, p - q = p + (-q).
Apply and extend previous understanding to represent addition and subtraction problems of rational numbers with a horizontal or vertical number line.
Represent the distance between two rational numbers on a number line is the absolute value of their difference and apply this principle in real-world contexts.
Apply the principle of subtracting rational numbers in real-world contexts.
MAFS.7.EE.2.3: (DOK 2) Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation. [application]
Generate equivalent fractions to find like denominators.
Rewrite an expression in an equivalent form in order to provide insight about how quantities are related in a problem context
Learning Goal: / Module 17:
The student is expected to represent real-world quantities with integers, and then solve the problems by finding the sums or differences of the integers.
Module 18:
The student is expected to represent real-world quantities with integers, and then solve the problems by finding the products or quotients of integers.
Assessments / Pre Assessment : LakecountySchoology.com
Formative Assessments: MARS Task, EngageNY, IXL, HMH Quiz, Illustrative Mathematics,
Summative Assessment: eduphoria, schoology, HMH online Test
Essential Question(s): / Module 17:
1. How do you add integers with the same sign?
2. How do you add integers with different signs?
3. How do you subtract integers?
4. How do you solve multi-step problems involving addition and subtraction of integers?
5. How can you use addition and subtraction of integers to solve real-world problems?
Module 18:
1. How do you multiply integers?
2. How do you divide integers?
3. How can you use integer operations to solve real-world problems?
4. How can you use multiplication and division of integers to solve-real world problems?
Progress Monitoring/ Feedback Loop / Pre-assessment, PL Flow, May do’s, Must do’s, Thinking maps, and post test.
Higher Order Question(s) / Module 17
Why did you choose that mathematical tool?
Why is it helpful to use_____?
What is the relationship of the quantities?
What are some other strategies you might try?
Module 18
What properties could we use to find a solution?
In what ways does this problem connect to other mathematical concepts?
How would you represent ______?
Key Vocabulary / Module 17:
Absolute value Additive inverse Expression Model Higher Order
Module 18:
Divide Dividend Divisor Integers Multiply Negative Numbers Operation Opposites Positive Number Product Quotient
Monday / Unit: 8 Module: 17 / Rigor Level: 2
Daily Agenda
Daily Objective / · I can add positive and negative numbers
BELL RINGER / · On board
I DO: / · Review Bellwork
· Explain new flow
· Model adding integers with chips
WE DO: / · Model addition of integers using chips
· Practice problems within your group from page 498
YOU DO: / · Develop a rule for adding integers with same sign/different sign
· Begin Working on Personalized learning flow
Homework / ·
Tuesday /
Unit: 8 Module: 17
/ Rigor Level: 2Daily Agenda
Daily Objective / · I can add positive and negative numbers
BELL RINGER / · On board
I DO: / · Review Bellwork
· Small group with students who need remediation
WE DO: / · Watch video on adding integers
· PL Day
YOU DO: / · PL Day
Homework / · n/a (you may work on your flow)
Wednesday / Unit: 8 Module: 17 / Rigor Level: 2
Daily Agenda
Daily Objective / · I can add positive and negative numbers
BELL RINGER / · On board
I DO: / · Review Bellwork
· Small group with students who need remediation
WE DO: / · Begin working on your flow
YOU DO: / · PL Day
Homework / · n/a (you may work on your flow)
Thursday / Unit: 8 Module: 17 / Rigor Level: 2
Daily Agenda
Daily Objective / · I can subtract positive and negative numbers
BELL RINGER / · On board
I DO: / · Review Bellwork
· Small group with students who need remediation
WE DO: / · Take notes on subtracting negative numbers
· Watch video from PBSmath on adding and subtracting negative numbers
YOU DO: / · Practice modeling subtraction of negative numbers
Homework / · n/a (you may work on your flow)
Friday / Unit: 8 Module: 17 / Rigor Level: 2
Daily Agenda
Daily Objective / · I can subtract positive and negative numbers
BELL RINGER / · On board
I DO: / · Review Bellwork
· Small group on subtracting negative numbers
WE DO: / · Create a tree map on the operation for adding & subtracting integers
· PL Day
You DO: / · PL Day
Homework / · n/a
Note: Learning Scales and Accommodations are below.
WICR Strategies used during each unit.Writing
Writing activities that help
students understand the
content / Inquiry
Questioning strategies
that help students
understand the content / Collaboration
Working together with a
partner or in a group of
students to understand, to
problem solve, or to
complete a task/project / Reading
Any strategies in reading
that help students
understand
Writing-to-Learn
• summaries
Process writing
• using a rubric as evaluation
On-demand/Timed writing
• writing that is completed in class within a set amount of time
• grade is evaluated using a rubric
Cornell Notes
• taking notes on the most important information
• summarizing
• using the notes to study
Reflective writing
• students write about what they have learned and what they still need / Higher level questioning
in classes
• Costa’s Level 1: Students
find the answers right there
in the text.
• Costa’s Level 2: Students
must figure out the answer
from information in the
text.
• Costa’s Level 3: Students
apply what they have
learned or use what they
have learned to evaluate or
create. / Think Pair Share
Sharing ideas with a
partner or in a group
Carousel/Gallery Walk
Problem solving in groups
Projects in groups / Before reading activities
• vocabulary activities
• accessing prior knowledge
• making predictions
During reading activities
• marking the text
• Cornell notes
• graphic organizers
After reading strategies
• summarizing
• group projects
Accommodations used daily on an individual basis in accordance with IEP and 504 plans and ELL Students
· Read directions for the student
· Check for understanding
· Allow to leave class for assistance
· Extra time for exams
· Daily agenda / · Allow student time to step out to de-escalate
· Testing in small groups
· Use of a planner/binder for organization
· English Language Dictionary / · Extended time on assignments =1 day
· Preferential seating
· Written direction given
· Break directions into chunks / · Read Aloud to Students
· Visual manipulatives
· Cooperative Learning,
· Vocabulary, Description, Introduction,
.
Student Friendly Mathematical Practice Statements
MAFS.K12.MP.1.1 Make sense of problems and persevere in solving them.
• Make a plan!
• Try different approaches when your problem is hard.
• Solve your problem in more than one way.
• Check whether your solution makes sense.
MAFS.K12.MP.2.1 Reason abstractly and quantitatively.
• Explain the meanings of the numbers, words, pictures, symbols, and objects you and others use
MAFS.K12.MP.3.1 Construct viable arguments and critique the reasoning of others.
• Explain both what to do and why it works.
• Work to make sense of others’ mathematical thinking.
MAFS.K.12.MP.4.1 Model with mathematics.
• Apply math to real-world situations.
• Use models such as graphs, drawings, tables, symbols, numbers, and diagrams to solve problems.
MAFS.K12.MP.5.1 Use appropriate tools strategically.
• Choose appropriate tools for your problem.
• Use mathematical tools correctly and efficiently.
• Estimate and use what you know to check the answers you find using tools.
MAFS.K12.MP.6.1 Attend to precision.
• Communicate your mathematical thinking clearly and precisely.
• Use the level of precision you need for your problem.
• Be accurate when you count, measure, and calculate.
MAFS.K12.MP.7.1 Look for and make use of structure.
• Find, extend, analyze, and create patterns.
• Use patterns and structures to solve problems.
MAFS.K12.MP.8.1 Look for and express regularity in repeated reasoning.
• Use patterns and structures to create and explain rules and shortcuts.
• Use properties, rules, and shortcuts to solve problems.
• Reflect on your thinking before, during, and after you solve a problem.