Download Unit 1 Numerical Expressions Math 6

Unit 1 Numerical Expressions
Math 6
Unit Goals – Stage 1
Number of Days: 29 days
9/6/16 – 10/14/16
Unit Description: Students expand their understanding of the number system and build their fluency in arithmetic operations. Students learned in 5th
grade to divide whole numbers by unit fractions and unit fractions by whole numbers. Now, they apply and extend their understanding of multiplication and
division to divide fractions by fractions. The meaning of this operation is connected to real‐world problems as students are asked to create and solve
fraction division word problems. Students continue (from fifth grade) to build fluency with adding, subtracting, multiplying, and dividing multi-digit decimal
numbers using the standard algorithms. Students will continue their work with order of operations and expanding it with exponents in numerical
expressions.
Materials: fraction manipulatives, fraction tiles kit*
(* Paper tool available at LBUSD Curriculum Intranet  Instructional Tools  Middle School  Mathematical Tools)
Standards for Mathematical Practice
Transfer Goals
SMP 1
Make sense of problems and
Students will be able to independently use their learning to…
persevere in solving them.
• Make sense of never-before-seen problems and persevere in solving them.
SMP 2
Reason abstractly and
• Construct viable arguments and critique the reasoning of others.
quantitatively.
Making Meaning
SMP 3
Construct viable arguments and UNDERSTANDINGS
ESSENTIAL QUESTIONS
critique the reasoning of others. Students will understand that…
Students will keep considering…
SMP 4
Model with mathematics.
• Whole numbers, decimals, and fractions are all numbers and
• How are operations with whole
SMP 5
Use appropriate tools
can be represented on the number line.
numbers, decimals, and fractions
strategically.
similar?
• Order of operations is an agreed upon convention to help
SMP 6
Attend to precision.
mathematicians have a common answer.
• Why are order of operations
SMP 7
Look for and make use of
necessary?
• The properties of multiplication and division that students
structure.
learn when working with whole numbers apply to fractions.
• How do you divide fractions by
SMP 8
Look for and express regularity
fractions?
• Using standard algorithms help fluently compute multi-digit
in repeated reasoning.
numbers and decimals.
Standards for Mathematical Content
Clusters Addressed
[m] 6.NS.A Apply and extend previous
understandings of
multiplication and division to
divide fractions by fractions.
[a] 6.NS.B Compute fluently with multi‐
digit numbers and find
common factors and
multiples.
[m] 6.EE.A Apply and extend previous
understandings of arithmetic
to algebraic expressions.
LONG BEACH UNIFIED SCHOOL DISTRICT
2016-2017
KNOWLEDGE
Students will know…
• The definition of academic vocabulary
words, such as least common
multiple, greatest common factor, and
numerical expressions.
• Exponents represent repeated
multiplication.
1
Acquisition
SKILLS
Students will be skilled at and/or be able to…
• Fluently divide multi‐digit numbers using the standard
algorithm.
• Write and evaluate numerical expressions involving whole‐
number exponents.
• Create equivalent expressions using order of operations.
• Find the greatest common factor and the least common
multiple.
• Divide fractions by fractions using visual models equations.
• Fluently add, subtract, multiply, and divide decimals using
the standard algorithm.
Posted 6/9/16
Unit 1 Numerical Expressions
Math 6
Assessed Grade Level Standards
Standards for Mathematical Practice
SMP 1
Make sense of problems and persevere in solving them.
SMP 2
Reason abstractly and quantitatively.
SMP 3
Construct viable arguments and critique the reasoning of others.
SMP 4
Model with mathematics.
SMP 5
Use appropriate tools strategically.
SMP 6
Attend to precision.
SMP 7
Look for and make use of structure.
SMP 8
Look for and express regularity in repeated reasoning.
Standards for Mathematical Content
[m] 6.NS.A
Apply and extend previous understandings of multiplication and division to divide fractions by fractions.
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. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction
model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9
is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How
many 3/4‐cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?
[a] 6.NS.B
Compute fluently with multi‐digit numbers and find common factors and multiples.
6.NS.2
Fluently divide multi‐digit numbers using the standard algorithm.
6.NS.3
Fluently add, subtract, multiply, and divide multi‐digit decimals using the standard algorithm for each operation.
6.NS.4
Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers
less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple
of a sum of two whole numbers with no common factor. For example, express 36 + 8 as 4 (9 + 2).
[m] 6.EE.A
Apply and extend previous understandings of arithmetic to algebraic expressions.
6.EE.1
Write and evaluate numerical expressions involving whole‐number exponents.
6.EE.2
Write, read, and evaluate expressions in which letters stand for numbers.
b. Identify parts of an expression using mathematical terms (sum, term, product, factor quotient, coefficient); view one or more parts of
an expression as a single entity. For example, describe the expression 2 (8 + 7) as a product of two factors; view (8 + 7) as both a
single entity and a sum of two terms.
c. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world
problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there
are no parentheses to specify a particular order (Order of Operations). For example, use the formulas V = s3 and A = 6 s2 to find
the volume and surface area of a cube with sides of length s = 1/2.
Key: [m] = major clusters; [s] = supporting clusters; [a] = additional clusters
LONG BEACH UNIFIED SCHOOL DISTRICT
2016-2017
2
Posted 6/9/16
Unit 1 Numerical Expressions
Math 6
Evidence of Learning – Stage 2
Assessment Evidence
Unit Assessment
Students will complete selected response and constructed response items to indicate level of mastery/understanding of the unit standards as outlined in
this guide.
[m] 6.NS.A
• The student interprets quotients of fractions using visual fraction models and the relationship between multiplication and division.
• The student solves real-world and mathematical one-step problems involving division of fractions by fractions.
[a] 6.NS.B
• The student fluently divides multi‐digit numbers using the standard algorithm.
• The student fluently adds, subtracts, multiplies, and divides multi‐digit decimals using the standard algorithm for each operation.
• The student finds the greatest common factor of two whole numbers less than or equal to 100.
• The student finds the least common multiple of two whole numbers less than or equal to 12.
• The student uses the distributive property to rewrite a sum of two or more numbers as a product of their GCF and another number.
[m] 6.EE.A
• The student writes and evaluates numerical expressions involving whole‐number exponents.
• The student writes, reads, and evaluates expressions.
• The student identifies parts of an expression using mathematical terms.
For selected content, students will need to…
• Solve complex problems in pure and applied mathematics, making productive use of knowledge and problem solving strategies.
• Clearly and precisely construct viable arguments to support their own reasoning and critique the reasoning of others.
Other Evidence
Formative Assessment Opportunities
• Opening Tasks
• Informal teacher observations
• Checking for understanding using active participation strategies
• Exit slips/Summaries
• Modeling Lessons (SMP 4)
•
•
•
•
•
Tasks
Formative Assessment Lessons (FAL)
Quizzes/Chapter Tests
Big Ideas Math Performance Tasks
SBAC Interim Assessment Blocks
Access Using Formative Assessment for Differentiation for suggestions. Located on the LBUSD website – “M” Mathematics – Curriculum Documents
LONG BEACH UNIFIED SCHOOL DISTRICT
2016-2017
3
Posted 6/9/16
Unit 1 Numerical Expressions
Math 6
Learning Plan – Stage 3
Days
Learning Target
I will explore fractions by
participating in the
Opening Task.
1 day
I will divide multi-digit
numbers using the
standard algorithm by…
2-3
days
Suggested Sequence of Key Learning Events and Instruction
Big Ideas Math Course 1
Expectations
(Activities and Lessons)
OPENING TASK - Fraction Tiles Kit
This Opening Task is a create/explore activity.
Students will create fraction tile kits to use within this
unit. When students complete the fraction tile kit,
have them explore with the fractions. What do they
notice? Have them share as a whole group. This
activity will be a gateway into the entire unit of
numerical expressions and can be used throughout
the unit as a manipulative/visual model.
• Solving real world and mathematical problems with
or without a remainder.
• Writing the remainder as a fraction and interpreting
the remainder in a real world context. (SMP 2)
• Answering questions such as…
o How can you use multiplication to check that
your quotient is correct?
o When would you need to interpret the
remainder?
o When would you use division in the real world?
• Writing numerical expressions with whole number
exponents.
• Identifying parts of an expression using
mathematical terms.
• Evaluating numerical expressions using order of
operations including those with whole-number
exponents.
5-6
• Answering questions such as…
days
o What is the difference between an expression
and an equation?
o How can you generate write equivalent
expressions?
o Why is it important to agree on an order of
operations?
o What is the effect of inserting parantheses into
a numerical expression?
LONG BEACH UNIFIED SCHOOL DISTRICT
4
2016-2017
I will generate equivalent
numerical expressions
by…
Curriculum Intranet
Conceptual
Understanding:
• Fraction Tiles Kit
• Section 1.1
(Activities 1 and 2;
Examples 3 and 4)
• Section 1.2
(Activities 1 and 2;
Examples 1, 2, 3, and 4)
• Section 1.3
(Activities 1 and 2;
Examples 1, 2, 3, and 4)
Conceptual
Understanding:
• Order of Operations Task
Procedural Skills and
Fluency:
• Game Closet: More Fours
• Game Closet: 5 is Alive
• Game Closet: 6 Sticks
• Game Closet: 7 Not 11
• Game Closet: 8 is Great
• Game Closet: 9 is Fine
• Solo-Team-Teach: Order
of Operations
Posted 6/9/16
Unit 1 Numerical Expressions
Math 6
Learning Plan – Stage 3
Days
Learning Target
I will find the greatest
common factor and the
least common multiple
by…
•
•
•
•
•
Suggested Sequence of Key Learning Events and Instruction
Big Ideas Math Course 1
Expectations
(Activities and Lessons)
Using prime factorization.
• Section 1.4
(Activity 3;
Listing factors of two whole numbers less than or
Examples 1, 2, and 3)
equal to 100.
Listing multiples of two numbers less than or equal • Section 1.5
(Activities 1 and 3;
to 12.
Examples 1, 2, 3, and 4)
Solving real world and mathematical problems.
• Section 1.6
Answering questions such as…
(Activities 1 and 2;
o What can the GCF be used for?
Examples 1, 2, 3, and 4)
o What can the LCM be used for?
•
STEM Video: Filling
o When is GCF or LCM used in the real world?
Piñatas
3-4
days
I will check my
understanding of
numerical expressions by
participating in the FAL.
Curriculum Intranet
Procedural Skills and
Fluency:
• Dominoes: LCM
• Solo-Team-Teach: GCD
Application:
• Fruit Task
• The Florist Shop Task
• STEM Video Performance
Task: Setting the Table
• Modeling: How Many Hot
Dogs and Buns Should
He Buy? (SMP 4)
OPTION #1: FORMATIVE ASSESSMENT LESSON
• Finding Factors and Multiples
(SMP 1, 2, 3, 5, 6, 7, 8)
2-3
days
LONG BEACH UNIFIED SCHOOL DISTRICT
2016-2017
5
Posted 6/9/16
Unit 1 Numerical Expressions
Math 6
Learning Plan – Stage 3
Days
Learning Target
I will divide fractions by…
•
•
•
•
•
•
7-8
days
2-3
days
I will check my
understanding of
numerical expressions by
participating in the FAL.
Suggested Sequence of Key Learning Events and Instruction
Big Ideas Math Course 1
Expectations
(Activities and Lessons)
Using visual fraction models. (SMP 5)
• Section 2.2
(Activities 1 and 2;
Interpreting quotients of fractions in real world
Examples 1, 2, 3, and 4)
context. (SMP 2).
• Section 2.3
Explaining division of fractions by fractions using
(Activity 2;
the relationship between multiplication and
Examples 1, 2, and 4)
division. (SMP 3)
Using reciprocals to divide fractions.
Solving real world and mathematical problems.
Answering questions such as…
o What patterns do you notice when you divide
fractions?
o What happens when you divide by a fraction?
Does your answer get smaller or bigger?
Explain. (SMP 3)
o How do you use the visual models to represent
dividing fractions? (SMP 5)
o How is dividing fractions similar and different
than dividing other types of numbers?
o When in the real world would you divide
fractions?
Curriculum Intranet
Conceptual
Understanding:
• Cup of Rice Task
• Dan’s Division Strategy
Task
• Dividing Fractions
PowerPoint
Procedural Skills and
Fluency:
• Dividing Fractions Card
Game
• How Do They Fit?
Dividing Rational
Numbers
Application:
• Amusement Park Task
• Building Projects w/
Fractions
• Traffic Jam Task
• Video Game Credits Task
• Modeling: How Many
Biscuits Can You Make?
(SMP 4)
OPTION #2: FORMATIVE ASSESSMENT LESSON
• Interpreting Multiplication and Division
(SMP 1, 2, 3, 4, 5, 6, 7)
LONG BEACH UNIFIED SCHOOL DISTRICT
2016-2017
6
Posted 6/9/16
Unit 1 Numerical Expressions
Math 6
Learning Plan – Stage 3
Days
Learning Target
I will add, subtract, and
multiply decimals by…
•
•
•
•
•
Suggested Sequence of Key Learning Events and Instruction
Big Ideas Math Course 1
Expectations
(Activities and Lessons)
Fluently using the standard algorithm.
• Section 2.4
(Activity 4;
Connecting the digits in the decimal number to its
Examples 1, 2, 3, and 4)
place value.
• Section 2.5
Using estimation to check if answers are
(Examples 1, 2, 3, and 4)
reasonable when adding, subtracting, and
• STEM Video: Space is
multiplying decimals. (SMP 1)
Big
Solving real world and mathematical problems.
Answering questions such as…
o If you are multiplying by a number less than
one, what do you get? What about greater than
one? Explain. (SMP 3)
o How would you use estimation to check your
answer?
o When do you use decimals in the real world?
2-3
days
LONG BEACH UNIFIED SCHOOL DISTRICT
2016-2017
7
Curriculum Intranet
Conceptual
Understanding:
• Adding Decimals Task
• Adding Decimals to Make
them as Close to One as
Possible Task
• Which One Doesn’t
Belong? Multiplying
Decimals
• Modeling: How Much
Money Are The Coins
Worth? (SMP 4)
Procedural Skills and
Fluency:
• Game Closet: Amazing
Decimals
• Game Closet: Let’s Go
Shopping!
• I Have Who Has?:
Multiplying Decimals
• Product Game: Decimals
• Race to One
• Take a Risk! Multiplying
Decimals
• Target 1000 Game
• STEM Video Performance
Task: Space Explorers
Posted 6/9/16
Unit 1 Numerical Expressions
Math 6
Learning Plan – Stage 3
Days
Learning Target
I will divide decimals
by…
•
•
•
•
•
2-3
days
I will prepare for the unit
assessment on
numerical expressions
by...
Suggested Sequence of Key Learning Events and Instruction
Big Ideas Math Course 1
Expectations
(Activities and Lessons)
Fluently dividing decimals by a whole number.
• Section 2.6
(Examples 1, 2, 3, and 4)
Fluently dividing decimals by decimals.
Interpreting the quotient in a real world context.
(SMP 2)
Solving real world and mathematical problems.
Answering questions such as…
o Explain when it is necessary to move a decimal
in division. (SMP 3)
o When do you use divisions of decimals in the
real world?
• Incorporating the Standards for Mathematical
Practice (SMPs) along with the content standards
to review the unit.
1-2
days
1 day
LONG BEACH UNIFIED SCHOOL DISTRICT
2016-2017
• Ch. 1 Study Help (p. 22)
• Ch. 1 Review
(p. 45 – 47)
• Ch. 2 Study Help (p. 76)
• Ch. 2 Review
(p. 101 – 103)
Curriculum Intranet
Procedural Skills and
Fluency:
• Math Bingo: Dividing
Decimals
• Solo-Team-Teach:
Dividing Decimals
Application:
• Gold Task
• Sam’s Smoothies Task
Application:
• Band Competition
Performance Task
• Festival Treats
Performance Task
Unit Assessment
8
Posted 6/9/16