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District OverviewThe mathematics curriculum provides sequential and comprehensive K-12 instruction in a collaborative, student-centered learning environment that fosters critical thinking, creativity, skillful problem-solving, and effective communication in order to enable all students to adapt to an ever-changing, global society and increase college and career readiness. An emphasis has been placed on conceptual understanding, higher-order thinking, and problem solving skills to prepare students for 21st century careers. This is further embedded through the integrated use of technology into daily lessons. Instruction focuses on meaningful development of mathematical ideas at each grade level where students are given the opportunity to explore, engage, and take risks with content as they build and expand their knowledge and understanding of mathematics. Students will experience mathematics as a coherent and useful subject within the context of real-life situations. In all, the curriculum aims to reach high standards while encouraging curiosity and building confidence in a collaborative atmosphere.

Grade 5 DescriptionThe core instructional model for enVisionmath 2.0 is based on two steps: Problem-based learning and Visual Learning.

Problem-based learning introduces concepts and procedures with a problem-solving experience. Visual learning makes the important mathematics explicit with enhanced direct instruction which connects to the Problem-based

learning.In grade 5, instructional time should focus on the following core domains:

Operations and Algebraic Thinking Number and Operations in Base Ten Number and Operations-Fractions Measurement and Data Geometry

Throughout the 5th grade program, students will address the following standards for mathematical practice: make sense of problems and persevere in solving them reason abstractly and quantitatively construct viable arguments and critique the reasoning of others model with mathematics use appropriate tools strategically attend to precision look for and make use of structure look for and express regularity in repeated reasoning

The program is organized to help students focus on clusters of Common Core standards within a grade. It achieves coherence across grades through careful learning progressions. The core instructional model facilitates conceptual understanding and uniquely builds the depth of understanding, fluency, and proficiency with math practices needed for success on assessments.

Grade 5 Units: Topic 1: Understand Place Value Topic 2: Add and Subtract Decimals to Hundredths Topic 3: Fluently Multiply Multi-Digit Whole Numbers Topic 4: Use Models and Strategies to Multiply Decimals Topic 5: Use Models and Strategies to Divide Whole Numbers Topic 6: Use Models and Strategies to Divide Decimals Topic 7: Use Equivalent Fractions to Add and Subtract Fractions Topic 8: Apply Understanding of Multiplication to Multiply Fractions Topic 9: Apply Understanding of Division to Divide Fractions Topic 10: Understand Volume Concepts Topic 11: Convert Measurements Topic 12: Represent and Interpret Data Topic 13: Algebra: Write and Interpret Numerical Expressions Topic 14: Graph Points on the Coordinate Plane Topic 15: Algebra: Analyze Patterns and Relationships Topic 16: Geometric Measurement: Classify Two-Dimensional Figures

Subject: Math Grade: 5 Suggested Timeline: 8 DAYS

Unit Title: Topic 1: Understand Place Value

Unit Overview/Essential Understanding: Basic facts and place-value patterns can be used to find products when on factor is a multiple of 10, 100, or 1,000; and exponent with 10

as the base can be used to represent powers of 10. Understanding each digit’s place value in a number provides a way to understand the number’s value. Our number system is based on powers of 10. Whenever we get 10 in one place value, we move to the next greater place value. Each digit within a decimal number has place value that helps determine the value of the number. Place value can be used to compare and order whole numbers and decimals. Rounding is a process for finding the multiple of 10, 100, and so on, or of 0.1, 0.01, and so on, closest to a given number. Good math thinkers look for relationships in math to help solve problems.

Unit Objectives: At the end of this topic, students will be able to independently use their learning to:

use exponents to write powers of 10 and calculate products read and write whole numbers using standard form, expanded form and number names represent decimals to thousandths as fractions and fractions with denominators of 1,000 as decimals read and write decimals through thousandths in different ways use place value to compare decimals through thousandths round decimals to different places use the structure of the decimal place-value system to solve problems involving patterns

Focus Standards Addressed in this Unit: CC.2.1.5.B.1 – Apply place value concepts to show an understanding of operations and rounding as they pertain to whole numbers and

decimals

Important Standards Addressed in this Unit:N/A

Misconceptions: Some students may have difficulty recognizing a number in its exponential form. Some students may have difficulty determining which zeros can be omitted and which zeros must be written in decimal numbers.

Students sometimes have difficulty writing a number in expanded form when one of the digits is zero. Students sometimes think that they automatically start comparing by looking at the left-most digit. Remind students that decimal place values differ from whole number place values.

Concepts/Content: Exponents Place Value Comparing Numbers Rounding Numbers

Competencies/Skills: Write whole numbers in

expanded form Read and write decimals Compare and round decimals

Description of Activities: Daily Common Core Review Center Games Solve and Share Math Tools Practice Buddy Online Practice Quick Check Another Look Video Visual Learning Bridge Vocabulary Cards and Activity

Assessments: Practice Buddy Quick Check Online Topic Assessment Topic Assessment

Interdisciplinary Connections: Math and Science Activity

Additional Resources: Pearson Realize www.pearsonrealize.com IXL www.ixl.com/Math/grade-5 Pearson, enVisionmath2.0

Subject: Math Grade: 5 Suggested Timeline: 7 Days

http://www.ixl.com/Math/grade-5

http://www.pearsonrealize.com/

Unit Title: Topic 2: Add and Subtract Decimals to Hundredths

Unit Overview/Essential Understanding: There’s more than one way to do a mental calculation. Mental addition and subtraction involve changing one or more numbers so that

the calculations are easy to do. A sum or difference can be estimated by replacing numbers with other numbers that are easier to add or subtract mentally. Models and algorithms for adding or subtraction multi-digit decimals are just an extension of models and algorithms for adding and

subtraction whole numbers. Adding multi-digit decimals is similar to adding multi-digit whole numbers. Subtraction multi-digit decimals is similar to subtraction multi-digit whole numbers. Adding and subtraction decimals is similar to adding and subtraction whole numbers. Algorithms and models can be used to complete

the calculations. Good math thinkers choose and apply math they know to show and solve problems from everyday life.


use properties of addition and strategies to solve problems mentally use rounding or compatible numbers to estimate sums and differences model sums and differences of decimals add decimals to the hundredths using the standard algorithm subtract decimals to the hundredths using the standard algorithm add and subtract decimals use prior math knowledge and equations or bar diagrams to solve problems

Focus Standards Addressed in this Unit: CC.2.1.5.B.2 – Extend an understanding of operations with whole numbers to perform operations including decimals


Misconceptions: Students may not understand that there may be several ways to use mental math to solve problems. Point out that the compatible numbers do not need to be multiples of 100. Any estimates that are easy to add and close to the original

numbers can be compatible numbers.

Some students may think that annexing a zero to the end of a decimal changes its value. Explain to students that annexing a zero is necessary so that each place has a digit.

Concepts/Content: Add and Subtract Decimals Multiply Decimals Divide Multi-digit Whole Numbers

and Decimals

Competencies/Skills: Multiply Multi-digit Whole

Numbers Divide Multi-digit Whole Numbers Perform Computations with

Decimals






Unit Title:



Topic 3: Fluently Multiply Multi-Digit Whole Numbers

Unit Overview/Essential Understanding: Place-value patterns and mental math can be used to write the product of a whole number and a power of 10 by simply annexing the

correct number of zeros to the whole number factor. Estimation products is a useful technique to quickly solve mathematical problems and understand the value of numbers used in real-

world situations. There is more than one way to estimate a product. Multiply 3-digit numbers by 2-digit numbers by combining equal groups. Rounding to the nearest 10 or using compatible numbers helps

estimate with greater accuracy when multiplying with greater numbers. The process for multiplying factors with zeros is always the same regardless of the size of the numbers with zeros. Estimation is a

strategy that can be used to check the final product for reasonableness. No matter the size of the numbers, the standard algorithm for multiplying whole numbers is always based on properties of operations

and can be used to solve problems. Using a bar diagram and writing an equation are two strategies that can be used to solve multi-step problems. Good math thinkers use math to explain why they are right. They can talk about the math that others do, too.


use place-value understanding and patterns to mentally multiply whole numbers and powers of 10 use rounding and compatible numbers to estimate products multiply 3-digit by 2-digit numbers by combining equal groups and adding partial products use knowledge about place value and multiplying with 2-digit and 3-digit numbers to multiply with zeros use properties and the standard algorithm for multiplication to find the product of multi-digit numbers use models and strategies to solve word problems critique the reasoning of others by asking questions, looking for flaws, and using prior knowledge of estimating products


decimals CC.2.1.5.B.2 – Extend and understanding of operations with whole numbers to perform operations including decimals

Important Standards Addressed in this Unit:N/AMisconceptions:

If students forget that when they multiply by 12, they are multiplying by 10 + 2, not by 1 and 2, their product will be much smaller that their estimate.

Make sure that students either put a zero in the second partial product or leave a space. Remind them that they are multiplying by 10, not 1.


and Decimals



Decimals






Unit Title: Topic 4: Use Models and Strategies to Multiply Decimals



Unit Overview/Essential Understanding: Patterns can be identified and used to multiply decimals by 10, 100, and 1,000. Representations such as symbols, diagrams, and words

can help you multiply and communicate mathematical ideas. You can estimate the product of a decimal and a whole number by using compatible numbers and rounding. Comparing two strategies

can help you decide which strategy provides an estimate that is closer to the exact answer. The standard multiplication algorithm used with decimals is an extension of the standard algorithm used when multiplying whole

numbers. You can use models to represent multiplication problems and communicate ideas to others. The steps involved in multiplying a decimal by a whole number are similar to the steps used in multiplying tow whole numbers. Place

value in the factors determines the placement of the decimal point in the product. Steps for multiplying decimals are similar to steps for multiplying whole numbers. Place value determine s the placement of the decimal

point in a product. The partial products process for multiplying whole numbers can be used for multiplying with decimals. You can use models and other

strategies to find the answer and determine if it is reasonable. The Associative and Commutative Properties can be used to break apart and identify two decimals.


use knowledge about place value and patterns to find the product of a decimal number and a power of 10 use rounding and compatible numbers to estimate the product of a decimal and a whole number use models to represent multiplying a decimal and a whole number use place-value understanding and the standard multiplication algorithm to multiply a decimal by a whole number use grids to model decimals and find the product of a decimal and a decimal multiply decimals using partial products and models use properties to multiply decimals


decimals CC.2.1.5.B.2 – Extend an understanding of operations with whole numbers to perform operations including decimals


Students may be confused that the two methods of estimation show different results. Explain that estimates may be greater than or less than the exact answer.

Some students may confuse aligning the decimal point to add or subtract and think that they can simply “bring down” the decimal point

from the factors to the product. Some students may have difficulty placing the decimal point. Remind them to compare the product with the estimate.


and Decimals



Decimals






Unit Title: Topic 5: Use Models and Strategies to Divide Whole Numbers

Unit Overview/Essential Understanding: Division problems with dividends and divisors that are multiples of ten can be solved using basic facts and patterns. Multiplication can



be used to check whether quotients are reasonable. Using compatible numbers is one of many estimation strategies that can be used to estimate a quotient. Multiplication can be used to

check whether quotients are reasonable. Area models and arrays are two ways to represent division with multi-digit whole numbers. Dividing with 2-digit divisors is just an extension of the steps for dividing with 1-digit divisors. Estimation and place value can help

determine the placement of digits in the quotient. Compatible numbers can be used to simplify division problems involving dividing 3-digit dividends by 2-digit multiples of ten. Estimation

and number sense can be used to check whether quotients are reasonable. Estimation can place-value understanding can be used to determine where to place the first digit in a quotient. Dividing by 2-digit divisors is an extension of the standard algorithm for dividing with 1-digit divisors. Estimation can help determine the

placement of digits and be used to check whether quotients are reasonable. Good math thinkers make sense of problems and think of ways to solve them. If they get stuck, they don’t give up.


use place-value patterns and mental math to find quotients use compatible numbers and place-value patterns to estimate quotients use models to find quotients solve division problems using partial quotients find the quotient when the divisor is a multiple of 10 decide where to place the first digit of the quotient when dividing whole numbers use estimation to decide whether a quotient is reasonable when dividing by 2-digit divisors make sense of problems and keep working

Focus Standards Addressed in this Unit: CC.2.1.5.B.2 – Extend an understanding of operations with whole numbers to perform operations including decimals


Misconceptions: Some students may be puzzled by how to choose compatible numbers. Explain that there is often more than one choice of compatible

numbers that can be used to find an estimate. Some students may have difficulty relating the area model to the division algorithm. Connect the numbers, such as the partial products,

that appear in both places.


and Decimals



Decimals






Topic 6: Use Models and Strategies to Divide Decimals

Unit Overview/Essential Understanding: Place-value patterns can be used to divide decimals by powers of 10. Rounding and compatible numbers can be used to estimate quotients with decimals. The standard algorithm used for dividing decimals is an extension of the standard algorithm for dividing whole numbers. Place-value

blocks can be used as a tool to show this connection. The standard algorithm used for dividing decimals is an extension of the standard algorithm for dividing whole numbers. When dividing



by a whole number, place the decimal point in the quotient directly above the decimal point in the dividend. An area model uses the inverse relationship between multiplication and division to show dividing a decimal by a 2-digit whole number. Number sense and reasoning can be used to place the decimal point in the quotient when dividing a decimal by a decimal. When dividing with decimals, it is sometimes necessary to annex zeros to the dividend so you can keep dividing until there is no

remainder. Good math thinkers know how to think about words and umbers to solve problems.

Unit Objectives:At the end of this topic, students will be able to independently use their learning to:

use mental math and place-value patterns to divide a decimal by a power of 10 use reason and strategies such as rounding and compatible numbers to estimate quotients in problems with decimals use models to help find quotients in problems involving decimals use the standard algorithm for division to divide decimals by a whole number use models to visualize the relationship between division and multiplication to divide decimals by a 2-digit whole number use number sense and reasoning to place the decimal point in the quotient when dividing two decimals use the standard algorithm and place-value patterns to divide a decimal by another decimal use the standard algorithm to divide decimals, annexing zeros as needed use reasoning to solve problems by making sense of quantities and relationships in the situation


decimals CC.2.1.5.B.2 – Extend an understanding of operations with whole numbers to perform operations including decimals


Misconceptions: Students may not understand where to place the decimal point in the quotient. Discuss how to write the decimal point directly above

the decimal point in the dividend. If students have difficulty lining up the decimal, have them use grid paper with each digit in a grid square.

Concepts/Content: Add and Subtract Decimals Multiply Decimals


Numbers

Description of Activities: Daily Common Core Review Center Games

Divide Multi-digit Whole Numbers and Decimals

Divide Multi-digit Whole Numbers Perform Computations with

Decimals

Solve and Share Math Tools Practice Buddy Online Practice Quick Check Another Look Video Visual Learning Bridge Vocabulary Cards and Activity





Unit Title: Topic 7: Use Equivalent Fractions to Add and Subtract Fractions

Unit Overview/Essential Understanding: A number line can be used to determine if estimates are reasonable. Fractions with unlike denominators can be represented using equivalent fractions with like denominators. Fractions with unlike denominators can be added by replacing them with equivalent fractions that have common denominators. Fractions with unlike denominators can be subtracted by replacing them with equivalent fractions that have common denominators. Addition and subtraction of fractions may both be needed to solve a problem.



Sums and differences of mixed numbers can be estimated by rounding to the nearest whole number, or by using benchmark fractions. Models can be used to show different ways of adding mixed numbers. Adding mixed numbers is an extension of adding fractions. Models can be used to show different ways of subtracting mixed numbers. Subtracting mixed numbers is an extension of subtracting fractions. Addition and subtraction of mixed numbers may both be needed to solve problems. Good math thinkers choose and apply math they know to show and solve problems from everyday life.


estimate sums and differences of fractions by using the nearest half or whole number find common denominators for fractions with unlike denominators add fractions with unlike denominators using equivalent fractions with a common denominator subtract fractions with unlike denominators write equivalent fractions to add and subtract fractions with unlike denominators estimate sums and differences of fractions and mixed numbers add mixed numbers using models add mixed numbers using equivalent fractions and a common denominator use models to subtract mixed numbers subtract mixed numbers using equivalent fractions and a common denominator add and subtract mixed numbers using equivalent fractions and common denominator represent a problem situation with a mathematical model

Focus Standards Addressed in this Unit: CC.2.1.5.C.1 – Use the understanding of equivalency to add and subtract fractions


Misconceptions:1. Remind students that they are not rounding to the nearest whole number as they did with decimals. They need to compare how close

the given fractions are to 0, ½, and 1 in order to find the closest estimate.2. Students may not realize that they can still find an equivalent fraction even after regrouping. Remind them that when working with

fractions, they should always check to see if the numerator and denominator have a common factor and divide to find and equivalent fraction.

Concepts/Content: Competencies/Skills: Description of Activities:

Sums and Differences of Fractions and Mixed Numbers

Conceptual Development of Addition and Subtraction

Add and Subtract Fractions and Mixed Numbers with Unlike Denominators

Daily Common Core Review Center Games Solve and Share Math Tools Practice Buddy Online Practice Quick Check Another Look Video Visual Learning Bridge Vocabulary Cards and Activity





Unit Title: Topic 8: Apply Understanding of Multiplication to Multiply Fractions

Unit Overview/Essential Understanding: Models can be used to show that the product of a whole number and a fraction can be interpreted as repeated addition. Multiplying a fraction and a whole number involves both multiplication and division. Models can be used to represent multiplying a

fraction by a whole number. Different methods can be used to multiply fractions and whole numbers. In one method, the whole number is renamed as a fraction,

the numerators are multiplied, and then the denominators are multiplied. Visual models, such as fraction strips, number lines, area models, and bar diagrams, can be used to represent multiplication of a fraction

by a fraction.



To find the product of tow fractions, multiple the numerators, and then multiply the denominators. Recognize when a product is less than or greater than 1.

An area model can be used to represent the product of two fractions. Multiplying mixed numbers is an extension of multiplying fractions. The relative size of the factors can be used to determine the relative size of the product. Good math thinkers make sense of problems and think of ways to solve them. If they get stuck, they don’t give up.


multiply a whole number by a fraction multiply a fraction by a whole number multiply fractions and whole numbers use models to multiply two fractions multiply two fractions find the area of a rectangle using fractions and diagrams use models, equations, and previously learned strategies to multiply mixed numbers compare the size of the product to the size of one factor without multiplying to consider multiplication as scaling use previously learned knowledge to make sense of problems and persevere in solving them

Focus Standards Addressed in this Unit: CC.2.1.5.C.2 Apply and extend previous understandings of multiplication and division to multiply and divide fractions


Some students may have difficulty remembering the Associative Property of Multiplication. Remind them that factors can be regrouped and the product still remains the same.

Some students may be puzzled by the fact that a whole number, like 7, can be written as a fraction, 7/1. Point out that a fraction can name a division of whole numbers. 7/1 actually means 7 divided by 1 and equals 7.

Some students may not understand equivalent fractions. Remind them that two fractions are equivalent if they name the same part of the whole. Point out that they can rename a fraction by multiplying or dividing the numerator and denominator by the same nonzero number.

Some students may be puzzled by how to label the area of a region. Remind them that the area is the number of square units needed to cover a surface. Area will be labeled in square units.

Concepts/Content: Meanings of Multiplication Understand Area Models of

Competencies/Skills: Fraction Multiplication

Description of Activities: Daily Common Core Review Center Games

Multiplication Meanings of Division

Solve and Share Math Tools Practice Buddy Online Practice Quick Check Another Look Video Visual Learning Bridge Vocabulary Cards and Activity





Unit Title: Topic 9: Apply Understanding of Division to Divide Fractions

Unit Overview/Essential Understanding: A fraction can be interpreted as division of the numerator by the denominator. A fraction or mixed number can represent the quotient of two whole numbers. Models can be used to show how dividing a whole number by a fraction relates to multiplication. Visual fraction models can be used to represent and solve problems involving whole numbers divided by unit fractions. Dividing a unit fraction by a non-zero whole number can be modeled by showing part of a whole divided into equal parts. Area models and number lines can be used to represent and solve division problems involving whole numbers and unit fractions. Some problems can be solved by first finding and solving one or more sub-problems and then using the answer to solve the original

problem.



Good math thinkers look for things that repeat, and they make generalizations.Unit Objectives: At the end of this topic, students will be able to independently use their learning to:

understand how fractions are related to division implement division of fractions to show quotients as fractions and mixed numbers use multiplication to divide a whole number by a unit fraction use models such as pictorial models or a number line to show dividing a whole number by a unit fraction use models to divide unit fractions by non-zero whole numbers use models to divide whole numbers and unit fractions. Check you answer using multiplication solve multi-step problems involving division with unit fractions notice repetition in calculations and generalize about how to divide whole numbers and unit fractions

Focus Standards Addressed in this Unit: CC.2.1.5.C.2 Apply and extend previous understandings of multiplication and division to multiply and divide fractions


Misconceptions: Some students may have difficulty understanding what each number represents in a division problem. If students have trouble understanding the relationship between 3 ÷1/8 =24 and 24 x 1/8 = 3, then show them as a simple relationship

like 20 ÷ 5 = 4 and 4 x 5 = 20. Explain that in both, dividend ÷ divisor = quotient and quotient x divisor = dividend. Students may think that they can divided the numerators and denominators the same way that they would multiply them. Remind

students that using a model, such as a number line, will help them understand that a problem like 5 ÷ 1/3 is equal to 5 x 3.Concepts/Content:

Meanings of Multiplication Understand Area Models of

Multiplication Meanings of Division

Competencies/Skills: Fraction Multiplication


Assessments:

Practice Buddy Quick Check Online Topic Assessment Topic Assessment




Unit Title: Topic 10: Understand Volume Concepts

Unit Overview/Essential Understanding: Volume can be measured by counting the number of cubic units needed to fill a three-dimensional figure. Formulas can be used to find the volume of rectangular prisms and cubes. Formulas can be used to find the volume of rectangular prisms and cubes. The volume of a solid figure composed of rectangular prisms can be found by adding the volumes of each rectangular prism. Some problems can be solved by first finding and solving one or more sub-problems and then using the answer(s) to solve the original

problem. Good math thinkers know how to pick the right tools to solve math problems.




find the volume of solid figures find the volume of rectangular prisms using a formula find the volume of prisms in different ways find the volume of a solid figure that is the combination of two or more rectangular prisms use models, prior knowledge of volumes, and preciously learned strategies to solve word problems involving volume use previously learned knowledge about volumes to choose the appropriate tools to solve volume problems

Focus Standards Addressed in this Unit: CC.2.4.5.A.6 Apply concepts of volume to solve problems and relate volume to multiplication and to addition


Misconceptions: Some students may think that volume can only be measured in cubic feet or cubic inches. Reinforce that volume can be measured in a

variety of standard and metric units but will always be expressed as cubic units to show that you are describing a three-dimensional space.

Concepts/Content: Connect Volume and a Formula

for Finding the Number of Cubes Relate Volume to Addition

Competencies/Skills: Use a Formula to Find the Volume

of a Rectangular Prism


Assessments: Practice Buddy Quick Check

Online Topic Assessment Topic Assessment




Unit Title: Topic 11: Convert Measurements

Unit Overview/Essential Understanding: Multiplication and division are used to convert among different units of length. Multiplication and division are used to convert among different units of capacity. Multiplication and division are used to convert among different units of weight. Multiplication and division are used to convert among different units of length. Multiplication and division are used to convert among different units of capacity. Multiplication and division are used to convert among different units of mass. Some problems can be solved by first finding and solving one or more sub-problems and then using the answer(s) to solve the original

problem. Good math thinkers are careful about what they write and say, so their ideas about math are clear.


convert customary units of length convert customary units of capacity convert customary units of weight



convert metric units of length convert metric units of capacity convert metric units of mass solve real-world problems with measurement conversions be precise when solving measurement problems

Focus Standards Addressed in this Unit: CC.2.1.5.B.2 – Extend and understanding of operations with whole numbers to perform operations including decimals CC.2.4.5.A.1 Solve problems using conversions within a given measurement system


Misconceptions: Students may automatically think that they should divide the greater number by the lesser number.

Concepts/Content: Understand Attributes Customary Units of Measure Metric Units of Measure

Competencies/Skills: Use Multiplication or Division to

Convert Units








Unit Title: Topic 12: Represent and Interpret Data

Unit Overview/Essential Understanding: Line plots are one way to organize and represent numerical data collected in a survey. You can use line plats to answer questions about

a data set. Line plots are one way to organize and represent numerical data. You can use a line plot to see how data are distributed. You can use line plots to solve problems that involve data. Good math thinkers use math to explain why they are right. They can talk about the math that others do, too.


read and analyze line plots organize and display data in a line plot solve problems using data in a line plot critique the reasoning of others using understanding of line plots and fractions

Focus Standards Addressed in this Unit: CC.2.1.5.C.1 Use the understanding of equivalency to add and subtract fractions CC.2.4.5.A.4 Solve problems involving computation of fractions using information provided in a line plot

Important Standards Addressed in this Unit:

N/A

Misconceptions:N/A

Concepts/Content: Number Lines and Line Plots Frequency Tables and Line Plots Outlier in a Line Plot

Competencies/Skills: Read and Analyze a Line Plot Make a Line Plot








Unit Title: Topic 13: Algebra: Write and Interpret Numerical Expressions

Unit Overview/Essential Understanding: There is an agreed upon order in which operations are carried out in a numerical expression. The value of a numerical expression can be found by using the order of operations. Numerical expressions can represent the calculations needed to solve a problem. Numerical expressions show relationships among the quantities involved which you can interpret without evaluating the expressions. Good math thinkers know how to think about words and numbers to solve problems.


use the order of operations to evaluate expressions evaluate expressions with parentheses, brackets, and braces write simple expressions that show calculations with numbers interpret numerical expressions without evaluating them use reasoning to solve problems by making sense of quantities and relationships in the situation

Focus Standards Addressed in this Unit: CC.2.2.5.A.1 Interpret and evaluate numerical expressions using order of operations

Important Standards Addressed in this Unit:

N/A

Misconceptions: Remind student to multiply and divide in order from left to right first.

Concepts/Content: Order of Operations Interpret Numerical Expressions

Without Calculating

Competencies/Skills: Use the Order of Operations to

Evaluate a Numerical Expression








Unit Title: Topic 14: Graph Points on the Coordinate Plane

Unit Overview/Essential Understanding: The coordinate system uses two perpendicular number lines intersecting at 0 to name the location of points in the plane. A coordinate grid has an x-axis and a y-axis that can be used to locate points in two dimensions. Points that lie on a line can be connected and extended to solve problems. Good math thinkers know how to think about words and numbers to solve problems.


locate points on a coordinate grid graph points on a coordinate grid solve real-world problems by graphing points use reasoning to solve problems by making sense of quantities and relationships in the situation

Focus Standards Addressed in this Unit: CC.2.3.5.A.1 Graph points in the first quadrant on the coordinate plane and interpret these points when solving real world and

mathematical problems


Misconceptions:

The biggest problem students have with graphing points is getting the coordinated mixed up. Keep reminding them that the first number tells how far to go right and the second number tells how far to go up.

Some students may confuse the x- and y- coordinates.

Concepts/Content: Coordinate Graph Ordered Pairs

Competencies/Skills: Graph Points








Unit Title: Topic 15: Algebra: Analyze Patterns and Relationships

Unit Overview/Essential Understanding: Two patterns can be extended using the same rule and there will be a relationship between the patterns. Tow patterns can be extended using rules and there will be a relationship between the patterns. A graph can show the relationship between two number sequences. Good math thinkers make sense of problems and think of ways to solve them. If they get stuck, they don’t give up.


analyze numerical patterns use tables to identify relationships between patterns analyze patterns and graph ordered pairs generated from number sequences make sense of problems and persevere in solving them

Focus Standards Addressed in this Unit: CC.2.2.5.A.4 Analyze patterns and relationships using two rules


Misconceptions:N/A

Concepts/Content: Understand Relationships

Competencies/Skills: Extend Patterns Graph Relationships








Unit Title: Topic 16: Geometric Measurement: Classify Two-Dimensional Figures

Unit Overview/Essential Understanding: Triangles are classified by their sides and by their angles. Quadrilaterals are classified by their sides and by their angles. Good math thinkers use math to explain why they are right.


classify triangles by their angles and sides classify quadrilaterals by their properties classify quadrilaterals using hierarchy construct arguments about geometric figures

Focus Standards Addressed in this Unit: CC.2.3.5.A.2 Classify two-dimensional figures into categories based on an understanding of their properties


Misconceptions: Remind students that triangles can be classified by the lengths of their sides and by the measures of their angles. The terms right, acute,

and obtuse are used to classify triangles by their angle measures, not by the length of their sides.

Concepts/Content: Hierarchy of Quadrilaterals

Competencies/Skills: Classify Shapes







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