Evidence Outcomes:

1. Use place value understanding to round whole numbers to the nearest 10 or 100. (CCSS: 3.NBT.A.1)

2. Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction. (CCSS: 3.NBT.A.2)

3. Multiply one-digit whole numbers by multiples of 10 in the range 10–90 (e.g., 9 x 80, 5 x 60) using strategies based on place value and properties of operations. (CCSS: 3.NBT.A.3)

Transfer Goals: Based on the Evidence Outcomes, what will students transfer to new contexts/situations?

• Recognize patterns of place value within the base ten number system and apply to a new context

• Examine & apply a variety of strategies to accurately & effectively solve problems

Essential Understandings: In order to meet these transfer goals, the essential ideas and core processes students must understand are...

• Each successive place in a number has 10 times the value of the place to the right

• Each digit in a number holds value

• There are 4 basic operations: addition, subtraction, multiplication, division

• Multiple strategies can be applied to solve problems, often using different operations

• Relationships between and within operations

In order to meet these essential understandings, students must know...

Academic Vocabulary: digit, number, value, addend, sum, difference, rounding, algorithm, expanded form, fact family

Place Value:

• Different forms of numbers

• Numbers are constructed of digits that hold value

• Structure of place value

• Base ten number system

• Rounding is comparative

• Rounding can help to evaluate reasonable answers

• Base ten models/manipulatives can help with the understanding of place value

Add and Subtract:

• Addition and subtraction are related and can be used to check answers (fact families)

• How to apply place value understanding to a strategy

• Standard algorithm for addition and subtraction

• Know Commutative Property of Addition

• Four basic operations

Multiples of 10:

• Each successive place in a number has 10 times the value of the place to the right

• Basic multiplication facts (single-digit by single-digit)

In order to meet these essential understandings, students must be able to...

Place Value:

• Identify the value of a digit

• Recognize & generate numbers in different forms (standard, unit, word, expanded)

• Decompose numbers into expanded form

• Compose numbers from expanded form

• Round numbers to the nearest 10 and 100

Add and Subtract :

• Apply addition and subtraction relationship to check answers (Fact Families)

• Use multiple strategies to accurately solve addition and subtraction problems within 1000

• Use the standard algorithm to solve addition and subtraction within 1000

• Use Commutative Property of Addition: changing the order of the addends will not change the sum

Multiples of 10:

• Multiply 1 digit whole numbers by multiples of 10 in a range 10-90 using strategies based on place value and properties of operations

  • Identify familiar facts (9 x 80 is the same as (9 x 8) x 10)

  • Use familiar facts to solve

  • Generalize place value for powers of 10

• Fluently solve multiplication facts 1-10

• Justify & reason to support claims

• Make thinking visible to construct viable arguments

Evidence Outcomes:

1. Describe a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b. (CCSS: 3.NF.A.1)

2. Describe a fraction as a number on the number line; represent fractions on a number line diagram. (CCSS: 3.NF.A.2)

   • Represent a fraction 1/b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts. Recognize that each part has size 1/b and that the endpoint of the part based at 0 locates the number 1/b on the number line. (CCSS: 3.NF.A.2.a)

   • Represent a fraction a/b on a number line diagram by marking off a lengths 1/b from 0. Recognize that the resulting interval has size a/b and that its endpoint locates the number a/b on the number line. (CCSS: 3.NF.A.2.b)

3. Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. (CCSS: 3.NF.A.3)

   • Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line. (CCSS: 3.NF.A.3.a)

   • Recognize and generate simple equivalent fractions, e.g., 1/2 = 2/4, 4/6 = 2/3. Explain why the fractions are equivalent, e.g., by using a visual fraction model. (CCSS: 3.NF.A.3.b)

   • Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. Examples: Express 3 in the form 3 = 3/1; recognize that 6/1= 6; locate 4/4 and 1 at the same point of a number line diagram. (CCSS: 3.NF.A.3.c)

   • Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model. (CCSS: 3.NF.A.3.d)

Transfer Goals: Based on the Evidence Outcomes, what will students transfer to new contexts/situations?

• A whole is composed of, or decomposed into, equal parts

• Complex concepts can be represented visually in multiple ways

Essential Understandings: In order to meet these transfer goals, the essential ideas and core process students must understand are...

• Fractions represent a quantity that is a portion of any whole

• Fractions can be parts of a whole number or numbers themselves

• Fractions can be visually represented in multiple ways (number lines, models, diagrams, numbers)

• Fractions have a unique structure that changes to represent different quantities

• Mathematicians must explain their thinking visually and verbally

In order to meet these essential understandings, students must know...

Academic Vocabulary: numerator, denominator, whole, fraction, fractional units (halves, thirds, etc.), equivalent, partition, unit fraction, benchmark fractions

Describe Fractions:

• Structure of a fraction

• Whole numbers can be partitioned into equal parts

• The denominator in a fraction shows the number of unit fractions to create the whole

• Unit fractions

Fractions on a number line:

• Each segment on a number line is 1 unit fraction

• How to partition number lines into equal parts

• Each line on a number line represents a fractional part of a whole

Equivalent Fractions:

• Definition of equivalent

• To be equivalent we must compare the same whole (ie. 2 circles, or number lines, partitioned into different fractional units)

• Fractions can have the same value but be different sizes based on the size of the whole

Whole Numbers as Fractions:

• Whole numbers can be written as fractions (2/1)

• When the numerator and denominator are the same, you have a whole number

• When the numerator is a multiple of the denominator, you have a whole number

Comparing Fractions:

• Function and vocabulary of the comparative symbols

• Numerator determines how many pieces of the whole

• Denominator determines how many equal parts the whole is partitioned into

• The larger the denominator the smaller the pieces

• Fractions can have the same value but be different sizes based on the size of the whole

In order to meet these essential understandings, students must be able to...

Describe Fractions:

• Identify a fraction

• Write a fraction

• Draw a visual representation of a fraction (number line, segmenting a whole, partition of a whole)

• Unit fractions (numerator of 1) are 1 piece of a whole split into the number of parts shown by the denominator

• Compose fractions with the same denominator using unit fractions

Fractions on a number line:

• Partition a number line into a number of equal parts indicated by the denominator

• Recognize each segment on a number line as equal to the unit fraction

• Create and label a number line showing fractions between 0-1, partitioning unit fractions and labelling each with a cumulative numerator and same denominator

Equivalent Fractions:

• Demonstrate equivalent fractions by comparing them with a visual model and a number line

• Recognize and generate simple equivalent fractions

• Reason with situational fractions (real-life examples)

Whole Numbers as Fractions:

• Identify fractions with a denominator of 1 as a whole number

• Identify fractions with the same numerator and denominator as a whole

Comparing Fractions:

• Order benchmark fractions

• Compare 2 fractions with the same numerator and different denominators using symbols <, >, and = using a visual model

• Compare 2 fractions with the same denominator and different numerators using symbols <, >, and = using a visual model

• Compare the same fraction as is refers to different-sized wholes using a visual model

• Justify & reason to support mathematical claims

Evidence Outcomes:

1. Interpret products of whole numbers, e.g., interpret 5 x 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 x 7. (CCSS: 3.OA.A.1)

2. Interpret whole-number quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. For example, describe a context in which a number of shares or a number of groups can be expressed as 56 ÷ 8. (CCSS: 3.OA.A.2)

3. Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. (see Appendix, Table 2) (CCSS: 3.OA.A.3)

4. Determine the unknown whole number in a multiplication or division equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 x __ = 48, 5= __ ÷ 3, 6 x 6 = __ (CCSS: 3.OA.A.4)

Transfer Goals: Based on the Evidence Outcomes, what will students transfer to new contexts/situations?

• Organizing objects into equal groups allows us to solve complex problems

• Examine & apply a variety of strategies to accurately & effectively solve problems

Essential Understandings: In order to meet these transfer goals, the essential ideas and core processes students must understand are...

• Multiplication and division are equations that have their own structure and relate to one another

• Multiplication and division require us to reason about the number of groups and size of groups

• There are multiple strategies to multiply and divide

In order to meet these essential understandings, students must know...

Academic Vocabulary: equal groups, factor, product, multiple, divisor, dividend, quotient, partition, array, rows, columns

• Flexibly skip count (starting at any number)

• Multiplication and division have 3 components: number of groups (factor), amount in each group (factor), total number of objects (total)

• Visual representations are created based on the context of a problem

• Groups must be equal amounts in order to multiply or divide

• Division is partitioning the total amount into equal groups or placing objects equally into groups

• Unknown variables in equations are represented with a letter

• Arrays, equal groups, drawings (measurement quantity) can be used to represent multiplication and division

• Word problems require a process of analyzing context in order to generate a plan to solve

• Multiplication and division are related using fact families

• Fact families can be used to help us determine an unknown in a multiplication or division problem

In order to meet these essential understandings, students must be able to...

Multiplication:

• Interpret a product as the total number of objects arranged in equal groups (5 x 7 is 5 groups of 7 objects with a product of 35)

• Create an array that places the first factor listed as the number of rows (groups) and the second factor listed as the number of columns (Number in each group) (See Appendix table 2 in standards)

Division:

• Interpret quotients as the number of groups when a whole is partitioned into equal groups of objects (56 ÷ 8 is 56 objects partitioned into 8 equal groups: How many in each group?)

• Interpret quotients as the number in each group when a whole is partitioned into groups of equal amounts (56 ÷ 8 is 56 objects partitioned into groups of 8: How many groups?)

Word Problems:

• Make sense of word problems and determine important information needed to solve the problem

• Identify a mathematical equation from information within a word problem

• Write equations with a letter for the unknown quantity

• Use a visual model to support thinking

• Solve multiplication and division problems using:

  • Equal groups

  • Arrays

  • Measurement quantities (Drawings)

Determine unknowns:

• Apply fact families to determine the unknown whole number in multiplication or division

• Justify & reason to support claims

Evidence Outcomes:

1. Apply properties of operations as strategies to multiply and divide. (Students need not use formal terms for these properties.) Examples: If 6 × 4 = 24 is known, then 4 × 6 = 24 is also known. (Commutative property of multiplication.) 3 × 5 × 2 can be found by 3 × 5 = 15, then 15 × 2 = 30, or by 5 × 2 = 10, then 3 × 10 = 30. (Associative property of multiplication.) Knowing that 8 × 5 = 40 and 8 × 2 = 16, one can find 8 × 7 as 8 × (5 + 2) = (8 × 5) + (8 × 2) = 40 + 16 = 56. (Distributive property.) (CCSS: 3.OA.B.5)

2. Interpret division as an unknown-factor problem. For example, find 32 ÷ 8 by finding the number that makes 32 when multiplied by 8. (CCSS: 3.OA.B.6)

Transfer Goals: Based on the Evidence Outcomes, what will students transfer to new contexts/situations?

• Examine & apply a variety of strategies to accurately & effectively solve problems

• Organizing objects into equal groups allows us to solve complex problems

Essential Understandings: In order to meet these transfer goals, the essential ideas and core processes students must understand are...

• Multiplication and division relate to one another

• The properties of multiplication can be applied flexibly to solve multiplication and division problems

• Multiplication and division represent the relationship between the area of a rectangle and its side lengths

In order to meet these essential understandings, students must know...

Academic Vocabulary: commutative property, associative property, distributive property, equation vs. expression

Commutative Property:

• The product of a multiplication sentence is the same regardless of the order of the factors

Associative Property:

• When multiplying multi-factor problems, the order of operations does not apply

Distributive Property:

• Factors in a multiplication problem can be decomposed in order to create known facts

• Function of parentheses in mathematics

• Equations are formed by multiple expressions

• Applying fact families will help determine the unknown in a division problem

In order to meet these essential understandings, students must be able to...

Commutative Property:

• Recognize the commutative property in multiplication (5 groups of 7 has the same product as 7 groups of 5)

• Use known facts to solve the inverse problem

Associative Property:

• Solve multiplication problems with 3 single-digit factors by finding the product of two factors first, then multiplying that product by the final factor. (Example: 3 x 5 x 2 can be solved as 3 x 5 = 15, then 15 x 2 = 30)

Distributive Property:

• Deconstruct factors into simpler facts in order to create known multiplication facts (Example: Factor 7 = 2 + 5)

• Solve multiplication problems by breaking them into 2 known problems, then adding the products. (Example: 8 x 2 = 16 and 8 x 5 = 40, so 8 x 7 = 56)

• Demonstrate the accuracy of the distributive property using a visual model

• Use fact families to interpret the unknown in a division problem

• Justify & reason to support claims

Evidence Outcomes:

1. Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 x 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers. (CCSS: 3.OA.C.7)

Transfer Goals: Based on the Evidence Outcomes, what will students transfer to new contexts/situations?

• Examine & apply a variety of strategies to accurately & effectively solve problems

• Fluency of math facts leads to efficiency in solving problems

Essential Understandings: In order to meet these transfer goals, the essential ideas and core processes students must understand are...

• Multiple strategies can be used to build fluency and solve multiplication problems

• Relationships between and within operations

In order to meet these essential understandings, students must know...

• Deep understanding of fact families and the relationship it presents for multiplication and division

• Properties of operations

• Products of single-digit multiplication facts

In order to meet these essential understandings, students must be able to...

• Use fact families to solve multiplication and division problems

• Apply properties of operations in order to solve multiplication problems

• Know from memory all products of two single-digit numbers

• Justify & reason to support claims

Evidence Outcomes:

1. Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. (This evidence outcome is limited to problems posed with whole numbers and having whole-number answers; students should know how to perform operations in the conventional order of operations when there are no parentheses to specify a particular order.) (CCSS: 3.OA.D.8)

2. Identify arithmetic patterns (including patterns in the addition table or multiplication table) and explain those using properties of operations. For example, observe that 4 times a number is always even, and explain why 4 times a number can be decomposed into two equal addends. (CCSS: 3.OA.D.9)

Transfer Goals: Based on the Evidence Outcomes, what will students transfer to new contexts/situations?

• Based on an understanding of any problem, initiate a plan, execute it, and evaluate the reasonableness of the solution

Essential Understandings: In order to meet these transfer goals, the essential ideas and core process students must understand are...

• Various models can be used to solve problems in the four operations

• Rounding can help check for accuracy when solving problems

• Letters can be used to represent unknown values when writing & solving equations

In order to meet these essential understandings, students must know...

Academic Vocabulary: unknown variable

• Word problems require a process of analyzing the context in order to generate a plan to solve

• How to analyze multi-step word problems and compartmentalize information

• Visual models support making sense of and solving word problems

• Unknown variables in equations are represented with a letter

• Taking linear steps will help keep work organized

• Order of operations

• Understand that mathematicians check their answers for reasonableness using estimating and rounding

• How to round

• Odds/Evens

• Structure of addition and multiplication tables

• There are observable patterns in addition and multiplication tables

In order to meet these essential understandings, students must be able to...

• Make sense of word problems and determine important information needed to solve the problem

• Identify a mathematical equation from information within a word problem and use a letter to write an equation with an unknown quantity

• Identify the process of solving multi-step word problems

• Use a visual model to support their thinking

• Assess the reasonableness of answers using mental computation and estimation strategies including rounding

• Apply order of operations in equations without parentheses

• Interpret the structure of multiplication and addition tables

• Identify and explain patterns on addition & multiplication tables using properties of operations

• Apply patterns of multiplication tables to solve multiplication and division problems

• Justify & reason to support claims

Evidence Outcomes:

1. Tell and write time to the nearest minute and measure time intervals in minutes. Solve word problems involving addition and subtraction of time intervals in minutes, e.g., by representing the problem on a number line diagram. (CCSS: 3.MD.A.1)

2. Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l). (This excludes compound units such as command finding the geometric volume of a container.) Add, subtract, multiply, or divide to solve one-step word problems involving masses or volumes that are given in the same units, e.g., by using drawings (such as a beaker with a measurement scale) to represent the problem. (This excludes multiplicative comparison problems, such as problems involving notions of “times as much.” See Appendix, Table 2.) (CCSS: 3.MD.A.2)

Transfer Goals: Based on the Evidence Outcomes, what will students transfer to new contexts/situations?

• Ability to use appropriate tools to solve real-world problems

• Tell & manage time to be both personally responsible to the needs of others

Essential Understandings: In order to meet these transfer goals, the essential ideas and core processes students must understand are...

• Various models can be used to solve problems involving measurement and estimation of time, liquid volumes, and masses of objects

• Time and measurement are a real-world application of fractions

• Recognize that time is a quantity that can be measured with different degrees of precision

In order to meet these essential understandings, students must know...

Academic Vocabulary: interval, elapsed time, analog, digital, duration, volume, mass, liter, gram, kilogram, scale

Time:

• Structure and functions of time and clocks

• How to write time

• Difference between the hour and minute hand

• Time can be measured

• There are 24 hours in a day and we use 12-hour standard time (a.m. & p.m.)

• How to use tools to determine elapsed time (number line, tables, etc.)

Measurement:

• Different units of measurement

• Specific units are used dependent upon what is being measured

  • Liquid: liters

  • Solids: grams, kilograms

• Rounding to estimate

• Four operations

• Strategies for solving real-world problems

• Scale and how to accurately represent measurement in a drawing

In order to meet these essential understandings, students must be able to...

Time:

• Accurately read numbers on a clock as hours and minutes

• Accurately place the hands on an analog clock for a given time to the nearest minute

• Accurately write times in a digital format

• Measure time intervals in minutes

• Analyze word problems involving time to identify start time, end time, and duration

• Add and subtract time intervals in minutes within and across hour boundaries using a number line

Measurement:

• Accurately measure liquid volumes in liters

• Estimate liquid volumes in liters

• Accurately measure masses in grams and kilograms

• Estimate masses in grams and kilograms

• Reason using logical units (g, kg) for context

• Solve single-step word problems using the 4 operations involving masses or volumes in the same unit

• Use scale drawings to represent problems involving mass or volume

• Justify & reason to support claims

Evidence Outcomes:

1. Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step “how many more” and “how many less” problems using information presented in scaled bar graphs. For example, draw a bar graph in which each square in the bar graph might represent 5 pets. (CCSS: 3.MD.B.3)

2. Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units; whole numbers, halves, or quarters. (CCSS: 3.MD.B.4)

Transfer Goals: Based on the Evidence Outcomes, what will students transfer to new contexts/situations?

• Organize, represent and interpret data to make connections to real-world situations

• Use appropriate tools to deepen understanding of mathematical concepts

Essential Understandings: In order to meet these transfer goals, the essential ideas and core processes students must understand are...

• Data provides factual information in an organized way

• Different kinds of graphs have different purposes

• Systems of measurement have specific purposes

In order to meet these essential understandings, students must know...

Academic Vocabulary: scale, data, picture graph, bar graph, line plot, mixed number

Graphs:

• The purpose and function of picture graphs and bar graphs

• Location of information on picture and bar graphs

• Scale

• How to categorize

• Difference between “how many more” and “how many less” and what operation matches

• Process for solving multi-step problems

Measurement:

• Fractions on a ruler: ¼, ½, ¾

• How to use the ruler to measure an object

• Mixed numbers are whole numbers and parts of another

• Difference between plot and graph

• Representations of like information need to remain consistent in scale and precision

In order to meet these essential understandings, students must be able to...

Graphs:

• Identify scale on a graph

• Collect and organize information

• Transfer data to graph form

• Draw a scaled picture graph and scaled bar graph

• Monitor for Meaning to interpret information presented in a scaled bar graph

• Solve one- and two-step “how many more” and “how many less” problems using scaled bar graphs

Measurement:

• Accurately measure lengths using rulers to the nearest fourth inch

• Identify measurements as mixed numbers (whole number with additional fraction)

• Log data from practical examples

• Organize data on a line plot where the horizontal scale is marked in appropriate units (whole halves, quarters)

• Attend to precision when creating visual representations

• Justify & reason to support claims

Evidence Outcomes:

• Recognize area as an attribute of plane figures and understand concepts of area measurement. (CCSS: 3.MD.C.5)

  • A square with side length 1 unit, called “a unit square,” is said to have “one square unit” of area, and can be used to measure area. (CCSS: 3.MD.C.5.a)

  • A plane figure which can be covered without gaps or overlaps by n unit squares is said to have an area of n square units. (CCSS: 3.MD.C.5.b)

• Measure areas by counting unit squares (square cm, square m, square in, square ft., and improvised units). (CCSS: 3.MD.C.6)

• Use concepts of area and relate area to the operations of multiplication and addition. (CCSS: 3.MD.C.7)

  • Find the area of a rectangle with whole-number side lengths by tiling it, and show that the area is the same as would be found by multiplying the side lengths. (CCSS: 3.MD.C.7.a)

  • Multiply side lengths to find areas of rectangles with whole-number side lengths in the context of solving real-world and mathematical problems, and represent whole-number products as rectangular areas in mathematical reasoning. (CCSS: 3.MD.C.7.b)

  • Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b + c is the sum of a x b and a x c. Use area models to represent the distributive property in mathematical reasoning. (CCSS: 3.MD.C.7.c)

  • Recognize area as additive. Find areas of rectilinear figures by decomposing them into non- overlapping rectangles and adding the areas of the non-overlapping parts, applying this technique to solve real- world problems. (CCSS: 3.MD.C.7.d)

Transfer Goals: Based on the Evidence Outcomes, what will students transfer to new contexts/situations?

• Use appropriate tools/strategies to solve real-world problems

Essential Understandings: In order to meet these transfer goals, the essential ideas and core processes students must understand are...

• One dimensional measurement can be used to create two-dimensional measurements

• One dimension measurements use linear units, while two-dimensional measurements use square units

• Application of multiplication through arrays demonstrates measurement of area

• Properties of multiplication can be applied to measure the area

In order to meet these essential understandings, students must know...

Academic Vocabulary: attribute, area, square units

• • Concept of a square unit

  • Area is the amount of square units required to cover a figure (space)

  • Working practical definition of length and width

  • Arrays are a way to show a figure is covered in square units

  • Addition and multiplication can help find the area of a rectangle

  • Properties of operations can be used to find the area of rectangles

  • Rectilinear figures can be divided into regular figures

  • Areas of portions of a shape can be added to find the area of a whole

In order to meet these essential understandings, students must be able to...

• Recognize area as an attribute of two-dimensional plane figures

• Identify a “square unit” as a square with a side length of one unit

• Accurately measure area by counting unit squares (square cm, square m, square in, square ft, and improvised units)

• Find the area of a rectangle with whole-number side lengths through tiling

• Connect the tiled area to the area found by multiplying side lengths

• Name real-world applications of area

• Solve real-world problems by multiplying whole-number side lengths to find the area of a rectangles

• Apply the distributive property to solve problems involving area

• Decompose and find area of figures made of multiple rectangles

• Apply decomposition techniques to solve real-world problems

• Find the most efficient way to solve problems

• Justify & reason to support claims

Evidence Outcomes:

1. Solve real-world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters. (CCSS: 3.MD.D.8)

Transfer Goals: Based on the Evidence Outcomes, what will students transfer to new contexts/situations?

• Use appropriate tools/strategies to solve real-world problems

Essential Understandings: In order to meet these transfer goals, the essential ideas and core processes students must understand are...

• Perimeter is an attribute of plane figures

• Perimeter is a linear measurement

• Problem-solving with perimeter requires an application of geometric concepts

• Area and perimeter are related but separate attributes of plane figures

In order to meet these essential understandings, students must know...

Academic Vocabulary: attribute, perimeter, polygon, plane figure

• • Geometric concepts of rectangles

  • Strategies related to the four operations

  • Properties of operations

  • Working practical definition of length and width

  • Perimeter is the measurement of the continuous line forming the boundary of a figure - the sum of side lengths

  • The area is the amount of square units required to cover a figure (space)

In order to meet these essential understandings, students must be able to...

• Measure perimeter of polygons by measuring all sides

• Calculate the perimeter of a polygon given the side lengths

• Find the length of an unknown side (given perimeter and other side lengths)

• Apply properties of rectangles to label side lengths

• Apply properties of rectangles to find the perimeter

• Solve real-world problems involving perimeters of polygons

• Generate rectangles with a given perimeter, calculate their area

• Generate rectangles with a given area, calculate their perimeter

• Compare rectangles to determine the possibility of same perimeter and different area, or same area and different perimeter

• Justify & reason to support claims

Evidence Outcomes:

1. Explain that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories. (CCSS: 3.G.A.1)

2. Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. For example, partition a shape into 4 parts with equal area, and describe the area of each part as 1/4 of the area of the shape. (CCSS: 3.G.A.2)

Transfer Goals: Based on the Evidence Outcomes, what will students transfer to new contexts/situations?

• Categorizing enables the comparison of properties to identify polygons

• Spatial awareness is essential in determining equal areas

Essential Understandings: In order to meet these transfer goals, the essential ideas and core processes students must understand are...

• We categorize & classify polygons based on similarities in their attributes

• Polygons can be partitioned to show fractions

In order to meet these essential understandings, students must know...

Academic Vocabulary: attribute, characteristics, polygon, quadrilateral, rectangle, rhombus, square, parallel, perpendicular, partition

• Shapes are categorized based on characteristics

• Categorizing shapes requires visual and verbal reasoning

• Definitions of polygon, parallel, and perpendicular

• Properties of rectangle, rhombus, square and quadrilaterals

• Equally partitioning shapes creates unit fractions

In order to meet these essential understandings, students must be able to...

• Define what a polygon is and is not

• Closed shape

• Straight lines

• No overlapping lines

• No curves

• Identify the attributes of polygons at the appropriate level of complexity

• Number of sides

• Length of sides

• Placement of sides

• Generate and identify examples of parallel and perpendicular lines

• Accurately use the vocabulary of polygon classification

• Draw examples of polygons that fit in each subcategory of quadrilateral (rhombus, rectangle, square, no subcategory)

• Partition shapes into parts with equal areas

• Express the area of partitioned parts as a unit fraction of a whole

• Justify & reason to support claims