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Curriculum Map: Compacted 5/6
Course: Grade 5/6 Compacted
Sub-topic: Uncategorized
Grade(s): None specified
Unit: Creating a Community of Mathematical Thinkers
Subject: Mathematics
Timeline: Week 1
Purpose:
The purpose of the Establishing a Community of Mathematical Thinkers Module is to launch the important mathematical processes and
practices that will support the growth and independence of our students as mathematical thinkers in a learning community.
Stage One - Desired Results
Enduring Understandings:What will students understand (about
Essential Questions:What arguable, recurring, and thoughtwhat big ideas) as a result of the unit? "Students will understand
provoking questions will guide inquiry and point toward the big ideas
that..."
of the unit?
Mathematical thinkers effectively use their understanding,
knowledge and skills.
Mathematical thinkers learn through collaboration and problem
solving.
Why problem solve (or why think mathematically)?
How does participation in a community of learners support
thinking and learning?
How do structures, strategies, and routines in problem solving
support thinking and learning?
How does productive mathematical thinking support critical
thinking, growth and independence?
Learning Targets:
I can attack a math problem and solve it (MP1)
I can make sense of a problem (MP2)
I can prove my answer (MP3)
I can assist others when I do not agree with their answer (MP3)
I can use the appropriate vocabulary and symbols to represent a problem or solution (MP4)
I can use math tools to help me solve/show how I solved a problem (MP5)
I can explain the steps I used to solve a problem, and I am careful in my calculations (MP6)
I can use what I already know to help me solve a new problem (MP7)
I can use multiple ways to find a solution to a problem (MP8)
STANDARDS
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Unit: Unit 1 Expressions, Equations & Volume
Subject: Mathematics
Timeline: Week 2 to 6
Purpose:
The purpose of this learning unit is for students to build multiplicative thinking with an emphasis on order of operations and the affects on the outcome of
computation problems. Students will also apply and extend previous understandings of numeric expressions to algebraic expressions with an emphasis on
vocabulary development with a justification of equivalent expressions using mathematical properties.
Stage One - Desired Results
Enduring Understandings:What will students understand (about
Essential Questions:What arguable, recurring, and thoughtwhat big ideas) as a result of the unit? "Students will understand
provoking questions will guide inquiry and point toward the big ideas
that..."
of the unit?
● Computational fluency includes understanding not only the
meaning, but also the appropriate use of numerical operations.
● Mathematical rules and expressions depict mathematical
relationships
● Expressions and equations are composed of terms including
variables that represent unknown numbers.
● Expressions can be simplified while equations are solved. ● Formulas can be used to find volume of rectangular prisms.
Exponents indicate repeated multiplication, where multiplication
indicates repeated addition.
Expressions can be rewritten as equivalent expressions to make
sense of a context.
How do the properties of multiplication contribute to algebraic
understanding?
How can order of operations change the outcome of a problem?
What makes a strategy both effective and efficient? How do you know if your solution is reasonable?
How can volume be used to solve problems and relate to
multiplication and addition?
How can properties of operations create equivalent expressions?
How can you write and evaluate an expression that represents a
real-life problem?
How do you know if two expressions are equivalent?
When simplifying an expression with multiple operations, how
do you know what operation to do first?
Learning Targets:
I can multiply multi-digit whole numbers. (M05.A-T.2.1.1)
I can find whole number quotients of whole numbers with up to four-digit dividends and two-digit divisors. (M05-A-T.2.1.2)
I can solve word problems involving division of whole numbers leading to answers in the form of fractions (including mixed numbers).
(M05.A-F.2.1.1)
I can use multiple grouping symbols (parentheses, brackets, or braces) in numerical expressions and evaluate expressions containing
these symbols. (M05.B-O.1.1.1)
I can write simple expressions that model calculations with numbers and interpret numerical expressions without evaluating them.
(M05.B-O.1.1.2)
I can apply the formulas V=l x v x h and V = B x h for rectangular prisms to find volumes of right rectangular prisms with wholenumber edge lengths in the context of solving real-world and mathematical problems. Formulas will be provided. (M05.D-M.3.1.1)
I can write algebraic expression from verbal descriptions.
I can evaluate expressions at specific values of their variables, including expressions that arise from formulas used in real world
problems. I can apply the properties of operations to generate equivalent expressions. ​
I can write and evaluate numerical expressions involving whole number exponents. I can describe the parts of an expression using math vocabulary words, such as sum, term, product, factor, quotient, and coefficient.
STANDARDS
STATE: PA Core Standards (2014)
CC.2.1.5.B.2 (Practiced)
Extend an understanding of operations with whole numbers to perform operations
including decimals.
CC.2.2.5.A.1 (Practiced)
Interpret and evaluate numerical expressions using order of operations.
CC.2.2.6.B.1 (Practiced)
Apply and extend previous understandings of arithmetic to algebraic expressions.
CC.2.2.6.B.2 (Practiced)
Understand the process of solving a one-variable equation or inequality and apply it to realworld and mathematical problems.
CC.2.4.5.A.5 (Practiced)
Apply concepts of volume to solve problems and relate volume to multiplication and to
addition.
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Unit: Unit 2 Computation of Fractions
Subject: Mathematics
Timeline: Week 7 to 11
Purpose:
The purpose of this learning unit is for students to add and subtract fractions with unlike denominators, with an emphasis on a variety of
strategies to find common denominators. The students will also apply and extend previous knowledge of finding common factors and
multiples through solving real world problems.
Stage One - Desired Results
Enduring Understandings:What will students understand (about
Essential Questions:What arguable, recurring, and thoughtwhat big ideas) as a result of the unit? "Students will understand
provoking questions will guide inquiry and point toward the big ideas
that..."
of the unit?
Computational fluency includes understanding the meaning and
appropriateness of numerical operations.
There are multiple representations for any number.
Numbers have a finite number of factors, but an infinite number
of multiples.
How do fractions show the relationship between operations?
How can equivalent fractions help find sums and differences?
What makes an answer reasonable?
How do you determine what algorithm (including operations,
GCF, LCM, and distributive property) is appropriate when
solving a word problem?
Learning Targets:
I can solve word problems involving addition and subtraction of fractions. (MO5.A-F.1.1/2.1.5.C.1)
I can add and subtract fractions with unlike denominators, including mixed numbers. (MO5.A-F.1.1.1/2.1.5.C.1)​
I can solve and estimate the answers to story problems involving addition and/or subtraction of fractions and mixed numbers.
I can use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers, (MP5)
I can rewrite fractions with unlike denominators as equivalent fractions with a common denominator in order to find their sum or
difference.
I can identify the greatest common factor of two whole numbers up to 100.
I can identify the least common multiple of two whole numbers up to 12.
I can use the distributive property to find the sum of two numbers that share a common factor. (example:36 + 8= 4(9 + 2).
STANDARDS
STATE: PA Core Standards (2014)
CC.2.1.5.C.1 (Focus)
Use the understanding of equivalency to add and subtract fractions.
CC.2.1.5.C.2 (Practiced)
Apply and extend previous understandings of multiplication and division to multiply and
divide fractions.
CC.2.1.6.E.3 (Practiced)
Develop and/or apply number theory concepts to find common factors and multiples.
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Unit: Unit 3 Place Value and Decimals
Subject: Mathematics
Timeline: Week 12 to 16
Purpose:
The purpose of this learning unit is for students to establish a foundation for number operations by building understanding of our base ten
place value system, with an emphasis on what place value represents, patterns in placement, and to read, write, compare, round and
compute decimals. Students will then apply their decimal computation skills to solve algebraic equations and check for accuracy.
Stage One - Desired Results
Enduring Understandings:What will students understand (about
Essential Questions:What arguable, recurring, and thoughtwhat big ideas) as a result of the unit? "Students will understand
provoking questions will guide inquiry and point toward the big ideas
that..."
of the unit?
Place Value is the foundation of all numbers
Number systems are made up of patterns
Numbers can be represented in many ways
Computational fluency includes understanding not only the
meaning, but also the appropriate use of numerical operations.
An equation is composed of two expressions.
Equations can be solved using reasoning, fact families, and
inverse operations.
How does understanding of base ten show the relationship
between place values?
How can measurement conversions be applied in real life
situations?
How can numbers in different forms be compared or computed?
What is the difference between an expression and an equation?
Learning Targets:
I can demonstrate an understanding that in a multi-digit number, each digit represents ten times what it represents in the place to its
right and each digit represents one-tenth what it represents in the place to its left. (M05.A-T.1.1.1)
I can explain patterns in the number of zeros of the product when multiplying a number by powers of 10 and I can explain patterns in
the placement of the decimal point when multiplied or divided by a power of 10.( M05.A-T. 1.1.2)
I can read and write decimals to thousandths represented with base-ten numerals, number names and expanded form. (M05.AT.1.1.3)
I can compare pairs of decimals to thousandths, based on an understanding of what the digit in each place represents; use <, =, and
> symbols to record comparisons.(M05.A-T.1.1.4)
I can round decimals to the nearest one, tenth, and hundredth. (M05.A-T.1.1.5)
I can find whole number quotients of whole numbers with up to four digit dividends and two digit divisors. (M05.A-T.2.1.2)
I can add and subtract decimals to hundredths, and I can use written numbers and symbols to represent strategies for computing with
decimals to hundredths. (M05-A.T.2.1.3)
I can explain reasoning behind strategies for computing with decimals to hundredths.
I can convert among different-sized standard measurement units withing a given measurement system. (M05.D-M1.1.1)
I can solve a real world problem or mathematical problem using an equation that contains positive numbers and one variable.
I can solve problems involving operations with whole numbers, decimals, straight computation, or word problems. (M06.A-N.2.1.1)
I can solve real-world and mathematical problems by writing and solving equations. (M06.B-E.2.1.3)
I can convert between fractions and decimals.
STANDARDS
STATE: PA Core Standards (2014)
CC.2.1.5.B.1 (Focus)
Apply place-value concepts to show an understanding of operations and rounding as they
pertain to whole numbers and decimals.
CC.2.1.5.B.2 (Focus)
Extend an understanding of operations with whole numbers to perform operations
including decimals.
CC.2.1.6.E.2 (Practiced)
Identify and choose appropriate processes to compute fluently with multi-digit numbers.
CC.2.2.6.B.1 (Focus)
Apply and extend previous understandings of arithmetic to algebraic expressions.
CC.2.2.6.B.2 (Practiced)
Understand the process of solving a one-variable equation or inequality and apply it to realworld and mathematical problems.
CC.2.4.5.A.1 (Practiced)
Solve problems using conversions within a given measurement system.
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Unit: Unit 4 Multiplying and Dividing Whole Numbers & Decimals
Subject: Mathematics
Timeline: Week 17 to 21
Purpose:
The purpose of this learning unit is for students to work with whole number and decimal computation and to extend this knowledge to
solving equations. Stage One - Desired Results
Enduring Understandings:What will students understand (about
Essential Questions:What arguable, recurring, and thoughtwhat big ideas) as a result of the unit? "Students will understand
provoking questions will guide inquiry and point toward the big ideas
that..."
of the unit?
Computational fluency includes understanding the meaning and
appropriateness of numerical operations.
Attributes of 3-D shapes develop an understanding of volume.​
Numbers can be represented in multiple ways.
Knowing the reasonableness of an answer comes from using
good number sense and estimation strategies.
Equations can be solved using reasoning, fact families, and
inverse operations.
How are multiplication and division related?
How does place value effect the properties of operations and
their relationships?
How can volume be used to solve problems?
Learning Targets:
I can multiply multi-digit whole numbers (not to exceed three-digit by three-digit). (M05.A-T.2.1.1)
I can find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors. (M05.A-T.2.1.2)
I can add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals). (M05.A-T.2.1.3)
I can apply the formulas V= l x w x h and V= B x h for rectangular prisms to find the volumes of right rectangular prisms with wholenumber edge lengths in the context of solving real-world and mathematical problems. Formulas will be provided. (M05.D-M.3.1.1) I can find volumes of solid figures composed of two non-overlapping right rectangular prisms. (M05.D-M.3.1.2)
I can solve problems involving operations (+, -, x, ) with whole numbers, decimals, straight computation, or word problems. I can solve multi-digit division problems using the standard algorithm. (long division)
I can solve real-world and mathematical problems by writing and solving equations of the form x + p =q and px=q for cases in which
p, q, and x are all non-negative rational numbers. ​​
STANDARDS
STATE: PA Core Standards (2014)
CC.2.1.5.B.2 (Focus)
Extend an understanding of operations with whole numbers to perform operations
including decimals.
CC.2.1.6.E.2 (Focus)
Identify and choose appropriate processes to compute fluently with multi-digit numbers.
CC.2.2.6.B.2 (Practiced)
Understand the process of solving a one-variable equation or inequality and apply it to realworld and mathematical problems.
CC.2.4.5.A.5 (Practiced)
Apply concepts of volume to solve problems and relate volume to multiplication and to
addition.
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Unit: Unit 5 Multiplication and Division of Fractions
Subject: Mathematics
Timeline: Week 22 to 27
Purpose:
The purpose of this learning unit is for students to extend their understandings of multiplication and division to working with fractions with
an emphasis on understanding visual models and their connection to the algorithm. Students will then apply the computation skills of
fractions to solve equations.
Stage One - Desired Results
Enduring Understandings:What will students understand (about
Essential Questions:What arguable, recurring, and thoughtwhat big ideas) as a result of the unit? "Students will understand
provoking questions will guide inquiry and point toward the big ideas
that..."
of the unit?
Mathematical rules and expressions depict mathematical
relationships. Computational fluency includes understanding the meaning and
appropriateness of numerical operations.
There are multiple representations for any number.
Knowing the reasonableness of an answer comes from using
good number sense and estimation strategies.
Equations can be solved using reasoning, fact families, and
inverse operations
How can models and representations depict mathematical
relationships?
What effect do ​operations ​have on the relationship between
fractions?
What does it mean to multiply and divide fractions?​
Learning Targets:
I can solve world problems involving division of whole numbers leading to answers in the form of fractions (including mixed
numbers). (M05.A-F.2.1.1)
I can multiply a fraction (including mixed numbers) by a fraction). (M05.A-F-2.1.2)
I can demonstrate an understanding of multiplication as scaling (resizing). (M05.A-F.2.1.3)
I can divide unit fractions by whole numbers and whole numbers by unit fractions. (M05.A-F.2.1.4)
I can convert between different -sized measurement units within a given measurement system. A table of equivalencies will be
provided. (M05.D-M.1.1.1)
I can solve problems involving computation of fractions by using information presented in line plots. (M05.D-M.2.1.1)
I can display and interpret data shown in tallies, tables, charts, pictographs, bar graphs, and line graphs, and use a title , appropriate
scale, and labels. A grid will be provided to display data on bar graphs or line graphs. (M05.D-M.2.1.2)
I can interpret and compute quotients of fractions ( including mixed numbers), and solve word problem involving division of fractions
by fractions. I can solve real-world and mathematical problems by writing and solving equations of the form x + p =q and px=q for cases in which
p, q, and x are all non-negative rational numbers.
STANDARDS
STATE: PA Core Standards (2014)
CC.2.1.5.C.2 (Focus)
Apply and extend previous understandings of multiplication and division to multiply and
divide fractions.
CC.2.1.6.E.1 (Focus)
Apply and extend previous understandings of multiplication and division to divide fractions by fractions.
CC.2.2.6.B.2 (Practiced)
Understand the process of solving a one-variable equation or inequality and apply it to real- world and mathematical problems.
CC.2.4.5.A.1 (Practiced)
Solve problems using conversions within a given measurement system.
CC.2.4.5.A.2 (Practiced)
Represent and interpret data using appropriate scale.
CC.2.4.5.A.4 (Practiced)
Solve problems involving computation of fractions using information provided in a line plot. Page 7 of 10
Unit: Unit 6 Graphing, Geometry & Volume
Subject: Mathematics
Timeline: Week 27 to 30
Purpose:
The purpose of this learning unit is for students to work on geometry with an emphasis on new geometric concepts, including coordinate
graphing in all four quadrants and the use of hierarchies to classify two-dimensional shapes by their properties.
Stage One - Desired Results
Enduring Understandings:What will students understand (about
Essential Questions:What arguable, recurring, and thoughtwhat big ideas) as a result of the unit? "Students will understand
provoking questions will guide inquiry and point toward the big ideas
that..."
of the unit?
Geometry is all around us in 2-D and 3-D figures. Patterns and relationships can be represented numerically,
graphically and symbolically. 2-D geometric relationships develop reasoning and justification
skills.
Attributes of 3-D shapes develop an understanding of volume.
How can patterns be used to make predictions?
How do I express a pattern to show a relationship?
How are geometric shapes and objects classified and related?
How can volume be used to solve problems and relate to
multiplication and addition?
Learning Targets:
I can generate two numerical patterns using two given rules. (M05.B-O.2.1.1)
I can identify apparent relationships between corresponding terms of two patterns with the same starting numbers that follow different
rules. (M05.B-O.2.1.2)
I can identify parts of the coordinate plane (x-axis, y-axis, and the origin) and the ordered pair (x-coordinate and y-coordinate). Limit
the coordinate plane to quadrant 1. (M05.C-G.1.1.1)
I can represent real-world and mathematical problems by plotting points in quadrant 1 of the coordinate plane and interpret coordinate
values of points in the context of the situation. (M05.C-G.1.1.2)
I can classify two-dimensional figures in a hierarchy based on properties. (M05.C-G.2.1.1)
I can convert between different-sized measurement units within a given measurement system. A table of equivalencies will be
provided. (M05.D-M.1.1.1)
I can apply the formulas V= l x w x h and V= B x h for rectangular prisms to find the volumes of right rectangular prisms with wholenumber edge lengths in the context of solving real-world and mathematical problems. Formulas will be provided. (M05.D-M.3.1.1) I can find volumes of solid figures composed of two non-overlapping right rectangular prisms. (M05.D-M.3.1.2)
I can locate and plot integers and other rational numbers on a horizontal or vertical number line; locate and plot pairs of integers and
other rational numbers on a coordinate grid. I can solve real-world and mathematical problems by plotting points in all four quadrants of the coordinate plane. I can use coordinates and absolute value to find distances between points with the same first coordinate or the same second
coordinate.
STANDARDS
STATE: PA Core Standards (2014)
CC.2.1.6.E.4 (Practiced)
Apply and extend previous understandings of numbers to the system of rational numbers.
CC.2.2.5.A.4 (Practiced)
Analyze patterns and relationships using two rules.
CC.2.3.5.A.1 (Focus)
Graph points in the first quadrant on the coordinate plane and interpret these points when
solving real world and mathematical problems.
CC.2.3.5.A.2 (Focus)
Classify two-dimensional figures into categories based on an understanding of their
properties.
CC.2.4.5.A.1 (Practiced)
Solve problems using conversions within a given measurement system.
CC.2.4.5.A.5 (Practiced)
Apply concepts of volume to solve problems and relate volume to multiplication and to
addition.
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Unit: Unit 7 Rational Numbers
Subject: Mathematics
Timeline: Week 32 to 34
Purpose:
The purpose of this Learning Module is for students to apply and extend previous understandings of numbers with an emphasis on the
system of rational numbers and a focus on understanding ordering and absolute value of rational numbers.
Stage One - Desired Results
Enduring Understandings:What will students understand (about
Essential Questions:What arguable, recurring, and thoughtwhat big ideas) as a result of the unit? "Students will understand
provoking questions will guide inquiry and point toward the big ideas
that..."
of the unit?
How can you classify numbers? Positive and negative numbers are often used to solve problems
How can you use rational numbers to solve real-world
in everyday life.
problems?
How are integers and absolute value used in the real world
situations?
Learning Targets:
I can represent quantities in real-world contexts using positive and negative numbers, explain the meaning of 0 in each situation.
I can determine the opposite of a number and recognize that the opposite of the opposite of a number is the number itself. I can locate and plot integers and other rational numbers on a horizontal or vertical number line; locate and plot pairs of integers and
other rational numbers on a coordinate grid. I can write, interpret and explain statements of order for rational numbers in real-world contexts. I can interpret the absolute value of a rational number as its distance from 0 on a number line and as a magnitude for a positive or
negative quantity in a real-world situation. STANDARDS
STATE: PA Core Standards (2014)
CC.2.1.6.E.4 (Focus)
Apply and extend previous understandings of numbers to the system of rational numbers.
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Unit: Unit 8-Inequalities and Functions
Subject: Mathematics
Timeline: Week 35 to 37
Purpose:
The purpose of this learning unit is for students to apply and extend previous understandings of algebraic equations to analyze and express
the relationship between variables. Students will also apply and extend their previous knowledge of number lines to write and graph
inequalities.
Stage One - Desired Results
Enduring Understandings:What will students understand (about
Essential Questions:What arguable, recurring, and thoughtwhat big ideas) as a result of the unit? "Students will understand
provoking questions will guide inquiry and point toward the big ideas
that..."
of the unit?
What are the similarities and differences between equations and
Inequalities can be used to represent constraints or conditions
inequalities?
What are the different ways to solve an equation or inequality?
of a situation, and can have an infinite number of solutions.
How do you know if your solution is reasonable?
Functions and their representations are used to model and
How are functions useful?
analyze real-world relationships.
Linear equations are used to solve real world problems. Learning Targets:
I can use substitution to determine whether a given number in a specified set makes an inequality true. I can write an inequality in the form x > c or x < c to represent a constraint or condition in real-world or mathematical problems
and/or represent solutions of such inequalities on number lines. I can write an equation to express the relationship between the dependent and independent variables
I can analyze the relationship between the dependent and the independent variables using graphs and tables and /or relate these to an
equation. STANDARDS
STATE: PA Core Standards (2014)
CC.2.2.6.B.2 (Focus)
Understand the process of solving a one-variable equation or inequality and apply it to real- world and mathematical problems.
CC.2.2.6.B.3 (Focus)
Represent and analyze quantitative relationships between dependent and independent
variables.
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