Grade 3 Math
Course Description
In this course, students will deepen their understanding of mathematical concepts through hands-on activities and real-world applications. Emphasizing problem-solving and critical thinking, the course covers:
- Understand Multiplication and Area: Students learn that multiplication is a way to show equal groups and can be represented using repeated addition, arrays, number lines, and bar models. They explore how factors are the numbers being multiplied and the product is the answer, and they discover that the order of factors can be switched (commutative property) without changing the product. Students also build a strong understanding of area by using unit squares, arrays, and by breaking larger shapes into smaller rectangles (distributive property) to find the total area.
- Multiplication and Division: Students explore multiplication as repeated addition and division as repeated subtraction, using tools like skip counting, arrays, number lines, and bar models to solve and understand problems. They learn important multiplication and division properties: identifying patterns in fact families and learning how to break apart or group factors to solve more complex problems. Students also use place value and rules for multiplying by tens, recognize how multiplication and division are inverse operations, and apply strategies to solve one- and two-step word problems, including those with unknown values represented by letters or symbols.
- Addition and Subtraction Strategies & Applications: Students build a strong understanding of addition and subtraction by exploring patterns, properties like the commutative and associative properties, and using place value strategies to solve multi-digit problems. They learn how to round and estimate to check the reasonableness of answers and solve real-world problems involving time, money, and measurement. Students also explore geometry by measuring perimeter, identifying polygons, and understanding how shapes can have the same area but different perimeters, or vice versa.
- Fractions: Students develop a deep understanding of fractions as numbers that represent equal parts of a whole or a group. They learn how to read and write fractions, identify numerators and denominators, and represent fractions using number lines, models, and real-world examples. Students also compare fractions using strategies like benchmark fractions and explore equivalent fractions, mixed numbers, and how equal parts have equal areas.
- Measurement and Data: Students learn to measure liquid volume and mass using both standard (cups, quarts, gallons, pounds) and metric units (liters, grams, kilograms). They use addition, subtraction, multiplication, and division to solve real-world measurement problems. Students also collect, represent, and interpret data using picture graphs, bar graphs, and line plots—including plotting fractional data on a number line.
- Geometry: Students explore the attributes of shapes and learn how to describe and compare them. They discover that different shapes can share attributes, which helps group them into larger categories like quadrilaterals. Students also learn to identify and draw examples of quadrilaterals, including rhombuses, rectangles, and squares.
Course Big Ideas
- Multiplication involves combining equal groups where each factor has a specific meaning: the first factor represents the number of groups, and the second factor represents the number of objects in each group. Using concrete and visual models helps illustrate this relationship and shows that the product is the total number of objects across all groups.
- Visual tools like arrays demonstrate multiplication concepts and reveal properties such as the Commutative Property, showing that factors can switch places without changing the product. Building on known multiplication facts allows students to derive new facts, deepening their understanding and fluency.
- Addition/subtraction and multiplication/division are connected through related facts that show how one operation undoes the other, and understanding place value supports using strategies to solve both.
- Using strategies and properties helps build fluency in learning basic facts, which, together with fluency, makes solving computational problems easier.
- Rounding and estimation are essential strategies that help students check the reasonableness of answers.
- Understanding measurement concepts like perimeter, money, and time supports practical problem solving and comparison.
- Fractions represent equal parts of a whole or a group and can be shown in many different ways, such as number lines, shapes, or sets. Understanding that all parts must be the same size helps us read, write, and compare fractions accurately. Fractions greater than one can be written as mixed numbers.
- Understanding and using standard and metric units to measure volume, mass, and other quantities, combined with fluency in basic math facts, helps solve a variety of measurement problems.
- Collecting, displaying, and interpreting data using picture graphs, bar graphs, and line plots supports solving one- and two-step problems and deepens understanding of measurement concepts.
- Shapes have different attributes, such as the number of sides or angles, that help us describe and classify them. Recognizing shared and unique attributes helps understand relationships between shapes and sort them into categories.
Course Essential Questions
- How can we use multiplication and division, along with visual models and properties, to understand equal groups, build fact fluency, and solve problems?
- In what ways do addition and subtraction work together, and how can strategies like rounding and estimation help us check answers and solve real-world problems involving measurement, money, and time?
- What are fractions, and how can we represent, compare, and understand them as equal parts of a whole or group using different models and symbols?
- How do we measure, organize, and describe objects and data using standard and metric units, graphs, and shape attributes to solve problems and classify shapes?
Course Competencies
- Accurately perform addition, subtraction, multiplication, and division with whole numbers to estimate, round, find area and perimeter, and apply these skills to solve real-world problems.
- Measure length, mass, and liquid volume using customary and metric units, create and interpret line plots, tell time to the nearest minute, solve elapsed time problems, count money and make change, and connect math operations to real-life contexts through strategic problem solving.
- Understand and represent fractions as parts of a whole, compare and order fractions with like numerators or denominators, recognize and generate equivalent fractions, and demonstrate understanding of symmetry by partitioning shapes into equal parts.
- Use visual models to collect, organize, and interpret data using charts, graphs, and tables to represent mathematical situations.
- Identify, classify, and draw polygons by their attributes (sides, angles).
- Use mathematical vocabulary and tools (manipulatives, drawings, technology) to support understanding and explain the reasoning clearly.
Course Assessments
- Growth Measure Benchmarks
- Acadience Math Assessments
- Are You Ready?
- Module 1 Assessment
- Module 2 Assessment
- Module 3 Assessment
- Module 4 Assessment
- Module 5 Assessment
- Module 6 Assessment
- Module 7 Assessment
- Module 8 Assessment
- Module 9 Assessment
- Module 10 Assessment
- Module 11 Assessment
- Module 12 Assessment
- Module 13 Assessment
- Module 14 Assessment
- Module 15 Assessment
- Module 16 Assessment
- Module 17 Assessment
- Module 18 Assessment
- Module 19 Assessment
- Module 20 Assessment
Course Units
- Unit 1: Understand Multiplication and Area
- Unit 2: Multiplication and Division
- Unit 3: Addition and Subtraction Strategies & Applications
- Unit 4: Fractions
- Unit 5: Measurement and Data
- Unit 6: Geometry
Unit 1: Understand Multiplication and Area
- Standards
- Know
- Understanding/Key Learning
- Do
- Unit Essential Questions
- Lesson Essential Questions
- Materials/Resources
- Vocabulary
- Assessments
Standards
PA Core Mathematics Standards
Module 1
- CC.2.2.3.A.1 Students acquire the knowledge and skills needed to: Represent and solve problems involving multiplication and division.
- M03.B-O.1.1.1 Interpret and/or describe products of whole numbers (up to and including 10 × 10).
- M03.B-O.1.2.1 Use multiplication (up to and including 10 × 10) and/or division (limit dividends through 50 and limit divisors and quotients through 10) to solve word problems in situations involving equal groups, arrays, and/or measurement quantities.
- CC.2.2.3.A.2 Students acquire the knowledge and skills needed to: Understand properties of multiplication and the relationship between multiplication and division.
- M03.B-O.2.1.1 Apply the commutative property of multiplication (not identification or definition of the property).
- M03.B-O.2.1.2 Apply the associative property of multiplication (not identification or definition of the property).
Module 2
- CC.2.4.3.A.5 Students acquire the knowledge and skills needed to: Determine the area of a rectangle and apply the concept to multiplication and to addition.
- M03.D-M.3.1.1 Measure areas by counting unit squares (square cm, square m, square in., square ft, and non-standard square units).
- M03.D-M.3.1.2 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.
Know
- Equal groups can be represented by concrete and visual models.
- Multiplication is repeated addition.
- Arrays show equal groups.
- Factors are the numbers in a multiplication problem.
- Product is the answer to a multiplication problem.
- Commutative property of multiplication states that you can multiply the factors in any order and still get the same product.
- Multiplication can be represented on a number line or bar model.
- Area is the measure of the number of unit squares needed to cover a surface.
- A unit square has an area of 1 square unit.
- Area can be found by counting unit squares.
- Arrays can be used to find area.
- Figures can be broken apart into smaller rectangles to find the area of combined figures.
Understanding/Key Learning
- Understand a factor is a number that is multiplied by another number to find a product.
- Create concrete and visual models using groups of objects to illustrate how each factor has a specific meaning in multiplication.
- Understand the first factor represents the number of groups and the second factor represents the number of objects in each group.
- Understand the product represents the total number of objects.
- Demonstrate the array model to build understanding of the Commutative Property of Multiplication.
- Derive new facts from facts already known.
Do
Module 1
- Use concrete and visual models to represent and solve problems when you know the number of equal groups and the number of objects in each group.
- Use concrete and visual models or drawings to write related addition and multiplication equations.
- Use multiplication within 100 to solve word problems in situations involving equal groups and arrays.
- Apply properties of operations as strategies to multiply.
Module 2
- Recognize area as an attribute of plane figures and understand concepts of area measurement.
- Measure area by counting unit squares.
- Relate area to the operation of multiplication and addition.
- Break apart a composite figure into smaller rectangles to find the area of combined figures.
Unit Essential Questions
Module 1
- How can you use equal groups to find the total number of objects in a multiplication problem?
- In what ways can addition and multiplication equations help us solve problems involving equal groups?
- How do arrays, number lines, and bar models help us represent and solve multiplication problems?
- What does the Commutative Property of Multiplication tell us about the relationship between different multiplication equations?
Module 2
- How do unit squares help you understand and measure area?
- What does it mean to measure an area using square units?
- How can repeated addition or multiplication help us find the area of a rectangle?
- What strategies can you use to find the area when side lengths are missing or when shapes are combined?
Lesson Essential Questions
- L1.1 How can you count equal groups to find the total number of objects when each group is given?
- L1.2 How can you write an addition equation and multiplication equation to help find a total to solve problems about equal groups?
- L1.3 How can arrays represent problems about equal groups?
- L1.4 How do you use the Commutative Property of Multiplication to write and relate multiplication equations?
- L1.5 How can you use number lines to represent problems about equal groups and to write multiplication equations?
- L1.6 How can you use bar models to represent problems about equal groups and to write multiplication equations?
- L2.1 How can unit squares help me find an area?
- L2.2 How can you measure and describe an area using square units?
- L2.3 How can repeated addition or multiplication be used to find the area of a rectangle?
- L2.4 What ways can areas be found with missing side lengths?
- L2.5 How can you find the area of combined rectangles?
Materials/Resources
Vocabulary
Assessments
Unit 2: Multiplication and Division
- Standards
- Know
- Understanding/Key Learning
- Do
- Unit Essential Questions
- Lesson Essential Questions
- Materials/Resources
- Vocabulary
- Assessments
Standards
PA Core Mathematics Standards
Module 3
- CC.2.2.3.A.1 Students acquire the knowledge and skills needed to: Represent and solve problems involving multiplication and division.
- M03.B-O.1.2.1 Use multiplication (up to and including 10 × 10) and/or division (limit dividends through 50 and limit divisors and quotients through 10) to solve word problems in situations involving equal groups, arrays, and/or measurement quantities.
Module 4
- CC.2.2.3.A.2 Students acquire the knowledge and skills needed to: Understand properties of multiplication and the relationship between multiplication and division.
- M03.B-O.2.1.1 Apply the commutative property of multiplication (not identification or
- definition of the property).
- M03.B-O.2.1.2 Apply the associative property of multiplication (not identification or definition of the property).
- CC.2.2.3.A.3 Students acquire the knowledge and skills needed to: Demonstrate multiplication and division fluency.
- CC.2.2.3.A.4 Students acquire the knowledge and skills needed to: Solve problems involving the four operations, and identify and explain patterns in arithmetic.
- M03.B-O.3.1.5 Identify arithmetic patterns (including patterns in the addition table or multiplication table) and/or explain them using properties of operations.
Module 5
- CC.2.1.3.B.1 Students acquire the knowledge and skills needed to: Apply place-value understanding and properties of operations to perform multi-digit arithmetic.
- M03.A-T.1.1.3 Multiply one-digit whole numbers by two-digit multiples of 10 (from 10 through 90).
- CC.2.2.3.A.1 Students acquire the knowledge and skills needed to: Represent and solve problems involving multiplication and division.
- CC.2.4.3.A.5 Students acquire the knowledge and skills needed to: Determine the area of a rectangle and apply the concept to multiplication and to addition.
- M03.B-O.1.1.1 Interpret and/or describe products of whole numbers (up to and including 10 × 10).
Module 6
- CC.2.2.3.A.1 Students acquire the knowledge and skills needed to: Represent and solve problems involving multiplication and division.
- M03.B-O.1.1.2 Interpret and/or describe whole-number quotients of whole numbers (limit dividends through 50 and limit divisors and quotients through 10).
Module 7
- CC.2.2.3.A.1 Students acquire the knowledge and skills needed to: Represent and solve problems involving multiplication and division.
- M03.B-O.1.2.2 Determine the unknown whole number in a multiplication (up to and including 10 × 10) or division (limit dividends through 50 and limit divisors and quotients through 10) equation relating three whole numbers.
Module 8
- CC.2.2.3.A.2 Students acquire the knowledge and skills needed to: Understand properties of multiplication and the relationship between multiplication and division.
- M03.B-O.2.2.1 Interpret and/or model division as a multiplication equation with an unknown factor.
- M03.B-O.3.1.2 Represent two-step word problems using equations with a symbol standing for the unknown quantity. Limit to problems with whole numbers and having whole-number answers.
- M03.B-O.3.1.6 Create or match a story to a given combination of symbols (+, –, ×, ÷, <, >, and =) and numbers.
- CC.2.2.3.A.4 Students acquire the knowledge and skills needed to: Solve problems involving the four operations, and identify and explain patterns in arithmetic.
- M03.B-O.3.1.1 Solve two-step word problems using the four operations (expressions are not explicitly stated). Limit to problems with whole numbers and having whole-number answers.
- M03.B-O.3.1.2 Represent two-step word problems using equations with a symbol standing for the unknown quantity. Limit to problems with whole numbers and having whole-number answers.
- M03.B-O.3.1.3 Assess the reasonableness of answers. Limit problems posed with whole numbers and having whole-number answers.
Know
- Multiplication is repeated addition and facts can be memorized by skip counting.
- Factors from a multiplication problem can be represented in a rectangular array where the first factor is the number of rows and the second factor is the number in each row (example: 2x6 = 2 rows of 6).
- Multiplication problems can be solved by learning to skip count by a factor along the number line.
- Multiplication problems can be represented by drawings (bar models, equal groups, arrays).
- When a story problem talks about the number of objects and groups, the information can be represented by a multiplication problem (# of groups x # of objects = total objects).
- Any number multiplied by zero the product is zero (0 X 3=3).
- Any number multiplied by one the product is the same number (example: 8x1=8).
- Factors can be multiplied in any order to get the same product.
- A big multiplication problem can be split into two smaller problems and then added together to get the product (example 6x7= (6x3)+(6x4)).
- Three or more factors can be grouped in any order using parentheses and multiplied to get the same product (example: 2x (3x4)= (2x3)x4).
- The numbers in a multiplication table follow a pattern. Each row and column is a fact family.
- The product of a multiplication problem can be found by tracing the row and column of each factor to find where they intersect.
- Missing information in a multiplication problem can be found using properties of multiplication or fact families.
- Place value aids understanding that numerical value of a number (example: 30=3 tens).
- When multiplying by a multiple of ten one can take away the zero in the ones place to multiply the basic fact. Then add the zero back to the product to reach its full value (30x4= (3x4)x10).
- Division is repeated subtraction and facts can be memorized by skip counting backwards.
- Division problems can be solved by learning to skip count backwards by a factor along the number line.
- Division problems can be represented by drawings (bar models, equal groups, arrays).
- Multiplication and division are related like fact families called inverse operations (2x3=6, 6÷3=2).
- Missing information in a division problem can be found using properties of division or fact families.
- Zero divided by any number the quotient is zero (0 ÷ 3=0).
- Any number divided by one the product is the same number (example: 8÷1=8).
- Missing information in a division problem can be found using strategies or fact families.
- Letters can represent the unknown number in equations.
- A two-step word problem is where you solve one thing, then use that to solve another.
- A growing pattern changes by the same amount from one number to the next.
- A rule is an instruction that tells you the correct way to do something. It can be used to describe a growing pattern.
Understanding/Key Learning
- Multiplication and division facts are related. Related facts illustrate the inverse relationship between multiplication and division and can be used to find an unknown number in another related fact.
- Place value understanding is a key component of multiplication and division.
- Using strategies and properties of multiplication and division help build fact fluency.
- Fluent recall of addition, subtraction, multiplication, and division facts aids in solving computational problems.
- Strategies can be used to solve multiplication problems and the strategy can be used in reverse for division problems.
Do
Module 3
- Create equal groups to solve multiplication problems within 100.
- Create arrays to solve multiplication problems within 100.
- Use number lines and skip counting to solve multiplication problems within 100.
- Create bar models to solve multiplication problems within 100.
- Self-select the strategy that works best for solving multiplication problems.
- Derive the unknown facts from known facts.
- Identify the multiplication equation represented by information shared in a word problem.
Module 4
- Apply properties of operations as strategies to multiply (identity, zero, commutative, distributive, and associative properties.).
- Use strategies to fluently multiply within 100.
- Identify arithmetic patterns in the multiplication table and explain them using properties of operations.
- Write equations to represent multiplication problems with missing information.
Module 5
- Multiply one-digit whole numbers by multiples of 10 in the range 10–90 using strategies based on place value and properties of operations.
- Represent multiples of tens by the number of tens (example: 60 = 6 tens)
- Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each.
- Use multiplication within 100 to solve word problems.
- Use area models to represent the distributive property in mathematical reasoning.
Module 6
- Interpret whole-number quotients of whole numbers as the number of objects in each share or as the number of equal shares.
- Use 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.
Module 7
- Use multiplication and division within 100 to solve word problems.
- Determine the unknown whole number in a multiplication or division equation.
- Apply properties of operations as strategies to multiply and divide.
- Understand division as an unknown- factor problem.
- Fluently multiply and divide within 100.
Module 8
- Solve two-step problems using the four operations, and equations with letters.
- Identify arithmetic patterns.
*Standards Success Lesson: Expressions and Equations Use after Lesson 8.2 Available online in printable formats only.
Unit Essential Questions
- How can understanding multiplication and division help us solve real-world problems involving equal groups, arrays, and measurements?
- What strategies and properties of operations (identity, zero, commutative, distributive, associative) help us multiply and divide numbers fluently and solve problems?
- How can the rules for multiplying and dividing, and knowing about place value, help us solve problems when a number is missing?
- How do multiplication and division patterns help us understand numbers better and solve one- and two-step word problems using different strategies?
Lesson Essential Questions
- L.3.1 How can you use different strategies to multiply with the factors 2 and 4 and solve equal groups problems?
- L.3.2 How can you use different strategies to multiply with the factors 5 and 10 and solve equal groups problems?
- L.3.3 How can you use different strategies to multiply with the factors 3 and 6 and solve equal groups problems?
- L.4.1 How can you use the Identity Property and Zero Property of Multiplication as strategies to multiply with 1 and 0?
- L.4.2 How can you understand and know how to use the Distributive Property to decompose factors as a strategy to multiply one-digit numbers?
- L.4.3 How can you multiply three factors by using the Associative and Commutative Properties of Multiplication?
- L.4.4 How can you use several multiplication strategies to multiply with 7?
- L.4.5 How can you alternate between strategies and properties to multiply with 8? How can you determine the best strategy to use for different factors and problems?
- L.4.6 How can you apply the Distributive Property with multiplication and addition or subtraction? How can you use patterns and strategies to multiply with 9?
- L.4.7 How can you identify arithmetic patterns in the multiplication table and explain them by using the properties of operations? How can you use patterns and properties to find products in a table and to identify products as odd or even?
- L.5.1 How can you use the Distributive Property to find a product when one factor is a multiple of 10?
- L.5.2 How can you use the Associative Property to find a product when one factor is a multiple of 10?
- L.5.3 How can you use place value to find a product when one factor is a multiple of 10?
- L.5.4 How can you use properties, place value, regrouping, and concrete and visual models to find a product when one factor is a multiple of 10?
- L.6.1 How can you use the information in a division problem to find the number of groups or the number in each group?
- L.6.2 How can you separate objects into equal groups to find the number of objects in each group?
- L.6.3 How can you separate a number of objects into equal groups of a given size to find the number of equal groups?
- L.6.4 How can you show how subtraction and division are related? How can repeated subtraction or a number line be used to solve a division problem?
- L.6.5 How can making or drawing an array to solve division problems help find the number of objects in each row or the number of rows?
- L.6.6 How can creating a bar model to represent and solve a division problem support writing a division problem?
- L.6.7 How can using properties and visual models assist in applying the rules for dividing with 1 and 0?
- L.7.1 How can you use related multiplication and division equations to solve problems?
- L.7.2 How can you write related multiplication and division equations to solve problems?
- L.7.3 How can you use more than one strategy to solve multiplication and division problems with 2, 4, and 8 as factors and divisors?
- L.7.4 How can you use more than one strategy to solve multiplication and division problems with 5 and 10 as factors and divisors?
- L.7.5 How can you use more than one strategy to solve multiplication and division problems with 3 and 6 as factors and divisors?
- L.7.6 How can you use more than one strategy to solve multiplication and division problems with 7 and 9 as factors and divisors?
- L.7.7 How can you use more than one strategy to recall multiplication and division facts to solve problems?
- L.8.1 How can you identify and extend patterns and use patterns to solve problems?
- L.8.2 How can you use multiplication and division equations with unknown numbers to solve problems?
- *Standard Success Lesson How can you use expressions and equations to model situations with numbers?
- L.8.3 How can you represent and solve problems using multiplication and division and unknown numbers?
- L.8.4 How can you write equations using the four operations with an unknown to solve two-step problems?
- L.8.5 How can you write equations with unknowns using the four operations to solve one- and two-step word problems?
Materials/Resources
Vocabulary
Assessments
Unit 3: Addition and Subtraction Strategies & Applications
- Standards
- Know
- Understanding/Key Learning
- Do
- Unit Essential Questions
- Lesson Essential Questions
- Materials/Resources
- Vocabulary
- Assessments
Standards
PA Core Mathematics Standards
Module 9
- CC.2.1.3.B.1 Students acquire the knowledge and skills needed to: Apply place-value understanding and properties of operations to perform multi-digit Arithmetic.
- M03.A-T.1.1.2 Add two-and three-digit whole numbers (limit sums from 100 through 1,000) and/or subtract two- and three-digit numbers from three-digit whole numbers.
- M03.B-O.3.1.2 Represent two-step word problems using equations with a symbol standing for the unknown quantity. Limit to problems with whole numbers and having whole-number answers.
- M03.B-O.3.1.3 Assess the reasonableness of answers. Limit problems posed with whole numbers and having whole-number answers.
- M03.B-O.3.1.1 Solve two-step word problems using the four operations (expressions are not explicitly stated). Limit to problems with whole numbers and having whole-number answers.
- M03.A-T.1.1.1 Round two- and three-digit whole numbers to the nearest ten or hundred, respectively.
- M03.A-T.1.1.4 Order a set of whole numbers from least to greatest or greatest to least (up through 9,999, and limit sets to no more than four numbers).- this is for the extra PA lesson
Module 10
- CC.2.1.3.B.1 Students acquire the knowledge and skills needed to: Apply place-value understanding and properties of operations to perform multi-digit arithmetic.
- M03.A-T.1.1.2 Add two- and three-digit whole numbers (limit sums from 100 through 1,000) and/or subtract two- and three-digit numbers from three-digit whole numbers.
- M03.B-O.3.1.7 Identify the missing symbol (+, –, ×, ÷, <, >, and =) that makes a number sentence true.
- M03.B-O.3.1.1 Solve two-step word problems using the four operations (expressions are not explicitly stated). Limit to problems with whole numbers and having whole-number answers.
- M03.B-O.3.1.2 Represent two-step word problems using equations with a symbol standing for the unknown quantity. Limit to problems with whole numbers and having whole-number answers.
- M03.B-O.3.1.3 Assess the reasonableness of answers. Limit problems posed with whole numbers and having whole-number answers.
- M03.B-O.3.1.4 Solve two-step equations using order of operations (equation is explicitly stated with no grouping symbols).
Module 11
- CC.2.4.3.A.6 Students acquire the knowledge and skills needed to: Solve problems involving perimeters of polygons and distinguish between linear and area measures.
- M03.D-M.4.1.1 Solve real-world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, exhibiting rectangles with the same perimeter and different areas, and exhibiting rectangles with the same area and different perimeters. Use the same units throughout the problem.
Module 12
- CC.2.4.3.A.3 Students acquire the knowledge and skills needed to: Solve problems and make change involving money using a combination of coins and bills.
- M03.D-M.1.3.2 Make change for an amount up to $5.00 with no more than $2.00 change given (penny, nickel, dime, quarter, and dollar).
- M03.D-M.1.3.1 Compare total values of combinations of coins (penny, nickel, dime, and quarter) and/or dollar bills less than $5.00.
- M03.D-M.1.3.3 Round amounts of money to the nearest dollar.
- CC.2.4.3.A.2 Students acquire the knowledge and skills needed to: Tell and write time to the nearest minute and solve problems by calculating time intervals.
- M03.D-M.1.1.1 Tell, show, and/or write time (analog) to the nearest minute.
- M03.D-M.1.1.2 Calculate elapsed time to the minute in a given situation (total elapsed time limited to 60 minutes or less).
Know
- Patterns can be found in an addition table.
- Numbers can be ordered based on value.
- Any number plus zero is that number (example: 8+0=8).
- Two or more numbers can be added in any order to get the same sum (4+3=7, 3+4=7).
- Various strategies can be used to solve multi-digit addition and subtraction problems.
- Addends can be grouped in different ways and still get the same sum (4+(9+6)= 19 (4+9)+6=19).
- An understanding of place value helps to round whole numbers the nearest ten or hundred.
- Drawing and equations can be used with a symbol for the unknown number to represent the problem.
- Rounding and estimation help us quickly check if an answer makes sense by simplifying numbers to the nearest ten or hundred and comparing our estimate to the actual result.
- Perimeter is the distance around a figure.
- A polygon is a closed shape with all straight sides.
- Two shapes can cover the same amount of space inside but have different lengths all around their edges and vice versa.
- Count, read, write, add, subtract, compare, and round money amounts using collections of coins and bills.
- Analog and digital clocks can be used to tell and write time to the nearest minute.
- Time intervals in minutes can be represented in many ways (number line diagram, making jumps on the clock).
Understanding/Key Learning
- Addition and subtraction facts are related. Related facts illustrate the inverse relationship between addition and subtraction and can be used to find an unknown number in another related fact.
- Using strategies and properties of addition and subtraction help build fact fluency.
- Fluent recall of addition, subtraction, multiplication, and division facts aids in solving computational problems.
- Strategies can be used to solve addition problems and the strategy can be used in reverse for subtraction problems.
- Rounding gives a general idea of how much or how many to check the reasonableness of an answer.
- Estimation is rounding to add or subtract to assess an answer.
- Perimeter can be found when side lengths are given or unknown sides can be found when relevant measurements are provided.
- Develop skills to understand, work with, and compare different money amounts using coins and bills, including counting, calculating, and estimating.
- Time can be calculated to the nearest minute on a digital and analog clock.
- Strategies can be used to find time intervals.
Do
Module 9
- Use place value to round whole numbers to the nearest 10 and 100.
- Order numbers based on value to 10,000 (from least to greatest or greatest to least).
- Fluently add and subtract within 1,000 using strategies based on place value, properties, and/or the relationship between addition and subtraction.
- Identify arithmetic patterns for addition and subtraction.
*Standards Success Lesson: Compare and Order Numbers to 10,000 Use after Lesson 9.1 Available online in printable formats only.
Module 10
- Fluently add and subtract within 1,000.
- Use strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction.
- Assess reasonableness of answers through mental computation and estimation.
- Solve two-step word problems using the four operations; represent problems using equations with a letter standing for the unknown quantity.
*Standards Success Lesson: Describe Relationships Use before Lesson 10.6 Available online in printable formats only.
*Standards Success Lesson: Order of Operations Use after Lesson 10.6 Available online in printable formats only.
Module 11
- Find the perimeter of polygons.
- Find unknown side lengths of polygons.
- Show rectangles with the same perimeter and different areas or with the same area and different perimeters.
Module 12
- Add and subtract money amounts.
- Compare money from collections of coins and bills.
- Count, read, and write amounts of coins and bills.
- Round money to the nearest dollar.
- Tell and write time from analog and digital clocks to the nearest minute.
- Measure time intervals in minutes.
- Solve word problems involving addition and subtraction of time intervals in minutes.
*Standards Success Lesson: Count Coins and Bills Use before Lesson 12.1 Available online in printable formats only.
*Standards Success Lesson: Compare Amounts of Money Use before Lesson 12.1 Available online in printable formats only.
*Standards Success Lesson: Add and Subtract Money Amounts Use before Lesson 12.1 Available online in printable formats only.
*Standards Success Lesson: Round to the Nearest Dollar Use before Lesson 12.1 Available online in printable formats only.
*Standards Success Lesson: Make Change Use before Lesson 12.1 Available online in printable formats only.
Unit Essential Questions
- How can understanding place value help us add, subtract, and round numbers easily and accurately?
- What strategies can we use to solve multi-step word problems with addition, subtraction, multiplication, and division?
- How do we find the perimeter of shapes and use that to explore relationships between side lengths and areas?
- How can we count, compare, and calculate money and time to solve real-life problems?
Lesson Essential Questions
- L9.1 How can you identify number patterns on an addition table, and use the identity and Commutative Property of Addition to complete equations?
- L9.2 How can you use mental math strategies to add and subtract with 2 and 3-digit numbers?
- L9.3 How can you use the Commutative and Associative Properties of Addition to find the sum of more than two addends?
- *Standard Success Lesson What are some ways you can compare and order numbers to 10,000?
- L9.4 How can you use mental math to determine the reasonableness of statements and answers?
- L9.5 How can you use and explain how to use place value to round whole numbers to the nearest ten or hundred?
- L9.6 How can you use rounding and compatible numbers to estimate sums and differences and solve problems?
- L10.1 How can you use expanded for and partial sums to add 2- and 3-digit numbers?
- L10.2 How can you use place value and regrouping to add 2- and 3-digit numbers?
- L10.3 How can you combine place values and use flexible grouping to subtract 2- and 3-digit numbers?
- L10.4 How can you regroup first and then use place value to subtract 2- and 3-digit numbers?
- L10.5 How can you apply strategies to solve addition and subtraction problems?
- *Standards Success Lesson How can you describe the relationship between two expressions = or ≠?
- L10.6 How can you write equations with letters for unknown quantities to solve two-step problems?
- *Standards Success Lesson Why are there rules such as the order of operations?
- L11.1 How can you count or use addition or multiplication to find the distance around a polygon
- L11.2 How can you measure the lengths of the sides of polygons using inch or centimeter units to find the perimeter of a polygon and/or add the side lengths to find perimeter?
- L11.3 How can you find the unknown side length of a polygon when you know the other side lengths and the perimeter of a polygon, using addition, subtraction, multiply or divide to find the unknown side length?
- L11.4 How can you use perimeter to compare rectangles with the same area?
- L11.5 You can use area to compare rectangles with the same perimeter?
- *Standards Success Lesson How can you count, read, and write money amounts for groups of coins and bills?
- *Standards Success Lesson How can you compare the total values of collections of coins and bills?
- *Standards Success Lesson How can you add and subtract money amounts?
- *Standards Success Lesson How can you round to the nearest dollar?
- *Standards Success Lesson How can you make change by counting on?
- L12.1 How can you tell and write time to the nearest minute?
- L12.2 How can you use a.m. and p.m. to describe time?
- L12.3 How can you find elapsed time when I know the start time and the end time?
- L12.4 How can you find the start time or the end time when I know the elapsed time?
- L12.5 How can you use a number line to find the end time or the start time when I know two amounts of elapsed time?
Materials/Resources
Vocabulary
Assessments
Unit 4: Fractions
- Standards
- Know
- Understanding/Key Learning
- Do
- Unit Essential Questions
- Lesson Essential Questions
- Materials/Resources
- Vocabulary
- Assessments
Standards
PA Core Mathematics Standards
Module 13
- CC.2.1.3.C.1 Students acquire the knowledge and skills needed to: Explore and develop an understanding of fractions as numbers.
- M03.A-F.1.1.1 Demonstrate that when a whole or set is partitioned into y equal parts, the fraction 1/y represents 1 part of the whole and/or the fraction x/y represents x equal parts of the whole (limit denominators to 2, 3, 4, 6, and 8; limit numerators to whole numbers less than the denominator; and no simplification necessary).
- CC.2.3.3.A.2 Students acquire the knowledge and skills needed to: Use the understanding of fractions to partition shapes into parts with equal areas and express the area of each part as a unit fraction of the whole.
- M03.C-G.1.1.3 Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole.
- M03.A-F.1.1.2 Represent fractions on a number line (limit denominators to 2, 3, 4, 6, and 8; limit numerators to whole numbers less than the denominator; and no simplification necessary).
- M03.A-F.1.1.4 Express whole numbers as fractions, and/or generate fractions that are equivalent to whole numbers (limit denominators to 1, 2, 3, 4, 6, and 8).
- M03.D-M.1.2.3 Use a ruler to measure lengths to the nearest quarter inch or centimeter.
- M03.D-M.2.1.3 Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Display the data by making a line plot, where the horizontal scale is marked in appropriate units—whole numbers, halves, or quarters
Module 14
- CC.2.3.3.A.2 Students acquire the knowledge and skills needed to: Use the understanding of fractions to partition shapes into parts with equal areas and express the area of each part as a unit fraction of the whole.
- M03.C-G.1.1.3 Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole.
Module 15
- CC.2.1.3.C.1 Students acquire the knowledge and skills needed to: Explore and develop an understanding of fractions as numbers.
- M03.A-F.1.1.5 Compare two fractions with the same denominator (limit denominators to 1, 2, 3, 4, 6, and 8), using the symbols >, =, or <, and/or justify the conclusions.
Module 16
- CC.2.1.3.C.1 Students acquire the knowledge and skills needed to: Explore and develop an understanding of fractions as numbers.
- M03.A-F.1.1.3 Recognize and generate simple equivalent fractions (limit the denominators to 1, 2, 3, 4, 6, and 8 and limit numerators to whole numbers less than the denominator).
- M03.A-F.1.1.3 Recognize and generate simple equivalent fractions (limit the denominators to 1, 2, 3, 4, 6, and 8 and limit numerators to whole numbers less than the denominator).
Know
- A whole is all of the parts that make up one shape or group.
- If all the parts of a whole are the same size, then the whole is divided into equal parts.
- A fraction is a number that names part of a whole or part of a group.
- A unit fraction is 1 equal part of a whole or a group.
- The numerator tells how many parts are being counted.
- The denominator tells how many equal parts are in the whole or in the group.
- A fraction can be represented in many different ways (number line, ruler, parts of a group, parts of a whole).
- A fraction can be greater than one as a mixed number represented as a whole and a fraction.
- Equal parts of a whole have equal areas.
- Benchmark fractions can be used to compare the relative size of fractions (number line, part of a whole, parts of a group, and bar model).
- When comparing two fractions with the same numerator, the smaller denominator creates the larger fraction.
- When comparing two fractions with the same denominator, the larger numerator creates the larger fraction.
- Equivalent fractions are fractions that represent the same amount.
Understanding/Key Learning
- A fraction shows part of a whole or part of a group.
- When all the parts are the same size, the whole is divided into equal parts.
- Fractions can be shown in different ways, like on a number line, with shapes, or as part of a group, and they can also be greater than one when written as mixed numbers.
- Fractions can be compared using greater than, less than, or equal to.
Do
Module 13
- Partition shapes into equal areas.
- Understand a fraction 1/b when a whole is partitioned into b equal parts; represent a fraction 1/b on a number line; represent fraction a/b; understand equivalent fractions; express whole numbers as fractions; measure lengths in halves and fourths of an inch.
Module 14
- Partition shapes into parts with equal areas.
- Write unit fractions to describe the area of each equal part of a whole.
Module 15
- Compare two fractions by reasoning about their size.
- Compare two fractions with the same numerator or the same denominator.
Module 16
- Understand that two fractions are equivalent if they are the same size or the same point on a number line.
- Using a model, recognize and generate equivalent fractions with denominators of 2, 3, 4, 6, and 8.
Unit Essential Questions
Lesson Essential Questions
- L13.1 How can you draw and name equal parts of a whole that is divided in different ways?
- L13.2 How can you represent and identify one equal part of a whole group as a unit fraction?
- L13.3 How can you use a fraction to name an equal part of a whole or an equal part of a group?
- L13.4 How can you identify, describe, represent, and locate fractions on a number line?
- L13.5 How can you draw visual models to show how to write fractions that name whole numbers?
- L13.6 How can you identify fractions greater than 1 on a number line and write them in fraction form and as mixed numbers?
- L13.7 How can you measure lengths to the nearest half or fourth of an inch using a ruler?
- L14.1 How can you use a fraction to show that equal parts of a whole shape have the same area?
- L14.2 How can you divide shapes into parts with equal areas and write each equal part as a fraction?
- L14.3 How can you write a unit fraction to represent the area of each part of a whole shape?
- L15.1 How can you use concrete and visual models to compare fractions?
- L15.2 How can you compare fractions that are divided into an equal number of same-sized parts?
- L15.3 How can you compare fractions that count the same number of equal parts when the whole is divided into a different number of equal parts?
- L15.4 How can you use different reasoning strategies to compare fractions?
- L16.1 How can you represent a fraction with equal parts that are smaller in size than the equal parts of an equivalent fraction?
- L16.2 How can you represent a fraction with equal parts that are larger in size than the equal parts of an equivalent fraction?
- L16.3 How can you represent a fraction with equal parts that are smaller or larger in size than the equal parts of an equivalent fraction?
Materials/Resources
Vocabulary
Assessments
Unit 5: Measurement and Data
- Standards
- Know
- Understanding/Key Learning
- Do
- Unit Essential Questions
- Lesson Essential Questions
- Materials/Resources
- Vocabulary
- Assessments
Standards
PA State Mathematics Standards
Module 17
- CC.2.4.3.A.1 Students acquire the knowledge and skills needed to: Solve problems involving measurement and estimation of temperature, liquid volume, mass, and length.
- M03.D-M.1.2.1 Measure and estimate liquid volumes and masses of objects using standard units (cups [c], pints [pt], quarts [qt], gallons [gal], ounces [oz.], and pounds [lb]) and metric units (liters [l], grams [g], and kilograms [kg]).
- M03.D-M.1.2.2 Add, subtract, multiply, and divide to solve one-step word problems involving masses or liquid volumes that are given in the same units.
- CC.2.2.3.A.4 Students acquire the knowledge and skills needed to: Solve problems involving the four operations, and identify and explain patterns in arithmetic.
- M03.B-O.3.1.1 Solve two-step word problems using the four operations (expressions are not explicitly stated). Limit to problems with whole numbers and having whole-number answers.
- M03.B-O.3.1.2 Represent two-step word problems using equations with a symbol standing for the unknown quantity. Limit to problems with whole numbers and having whole-number answers.
- M03.B-O.3.1.3 Assess the reasonableness of answers. Limit problems posed with whole numbers and having whole-number answers.
- CC.2.4.3.A.4 Students acquire the knowledge and skills needed to: Represent and interpret data using tally charts, tables, pictographs, line plots, and bar graphs.
- M03.D-M.2.1.1 Complete a scaled pictograph and a scaled bar graph to represent a data set with several categories (scales limited to 1, 2, 5, and 10).
- M03.D-M.2.1.2 Solve one- and two-step problems using information to interpret data presented in scaled pictographs and scaled bar graphs (scales limited to 1, 2, 5, and 10).
Module 18
- CC.2.2.3.A.4 Students acquire the knowledge and skills needed to: Solve problems involving the four operations, and identify and explain patterns in arithmetic.
- M03.B-O.3.1.1 Solve two-step word problems using the four operations (expressions are not explicitly stated). Limit to problems with whole numbers and having whole-number answers.
- M03.B-O.3.1.2 Represent two-step word problems using equations with a symbol standing for the unknown quantity. Limit to problems with whole numbers and having whole-number answers.
- M03.B-O.3.1.3 Assess the reasonableness of answers. Limit problems posed with whole numbers and having whole-number answers.
- CC.2.4.3.A.4 Students acquire the knowledge and skills needed to: Represent and interpret data using tally charts, tables, pictographs, line plots, and bar graphs.
- M03.D-M.2.1.1 Complete a scaled pictograph and a scaled bar graph to represent a data set with several categories (scales limited to 1, 2, 5, and 10).
- M03.D-M.2.1.2 Solve one- and two-step problems using information to interpret data presented in scaled pictographs and scaled bar graphs (scales limited to 1, 2, 5, and 10).
- M03.D-M.2.1.4 Translate information from one type of display to another. Limit to pictographs, tally charts, bar graphs, and tables.
- M03.D-M.2.1.3 Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Display the data by making a line plot, where the horizontal scale is marked in appropriate units—whole numbers, halves, or quarters.
Know
- Liquid volume is measured in metric and standard units (cups, pint, quarts, gallons, liters).
- Mass is measured in metric and standard units (ounces, pounds, grams, kilograms).
- The four operations can be used to solve measurement problems.
- Picture graphs, bar graphs, and line plots collect and display data.
- Fractions can be graphed on a line plot.
Understanding/Key Learning
- Liquids (volume) and solids (mass) are measured in metric and standard units.
- Fluent recall of addition, subtraction, multiplication, and division facts aids in solving measurement problems.
- Picture graphs, bar graphs, and line plots can be used to collect and show data to solve one and two-step problems.
- Measurement data can be visually displayed on a line plot.
Do
Module 17
- Measure and estimate liquid volume using cups, pints, quarts, gallons, liters.
- Measure and estimate mass using ounces, pounds, grams, kilograms.
- Use the four operations to solve one-step word problems involving liquid volumes or masses given in the same units.
* Standards Success Lesson: Estimate and Measure Customary Liquid Volume Use before Lesson 17.1 Available online in printable formats only.
* Standards Success Lesson: Estimate and Measure Weight Use before Lesson 17.1 Available online in printable formats only.
Module 18
- Draw scaled picture graphs.
- Draw scaled bar graphs.
- Use picture and bar graphs to solve one- and two-step comparison problems.
- Generate data by measuring lengths in fractions of an inch and display in line plots.
- Fluently add and subtract within 1,000.
Unit Essential Questions
Lesson Essential Questions
*Standards Success Lesson How can you estimate and measure liquid volume in customary units?
*Standards Success Lesson How can you estimate and measure weight using pounds?
- L17.1 How can you use metric units to estimate and measure liquid volume?
- L17.2 How can you use metric units to estimate and measure the mass of objects?
- L17.3 How can you solve word problems that involve liquid volume and mass?
- L18.1 How can you use data in a picture graph to solve how many more and how many less problems?
- L18.2 How can you draw a scaled picture graph to solve how many more and how many less problems?
- L18.3 How can you use data in a scaled bar graph to solve how many more and how many less problems?
- L18.4 How can you draw a scaled bar graph to solve how many more and how many less problems?
- L18.5 How can you use a line plot to display measurement data?
- L18.6 How can you measure lengths to the nearest quarter inch and make a line plot to display the data?
- L18.7 How can you use data in picture graphs, bar graphs, and line plots to solve one- and two-step how many more and how many less problems?
Materials/Resources
Vocabulary
Assessments
Unit 6: Geometry
- Standards
- Know
- Understanding/Key Learning
- Do
- Unit Essential Questions
- Lesson Essential Questions
- Materials/Resources
- Vocabulary
- Assessments
Standards
PA Core Mathematics Standards
Modules 19 and 20
- CC.2.3.3.A.1 Students acquire the knowledge and skills needed to: Identify, compare, and classify shapes and their attributes.
- M03.C-G.1.1.1 Explain that shapes in different categories may share attributes and that the shared attributes can define a larger category.
- M03.C-G.1.1.2 Recognize rhombi, rectangles, and squares as examples of quadrilaterals and/or draw examples of quadrilaterals that do not belong to any of these subcategories.
Know
Understanding/Key Learning
Do
Module 19
- Understand that shapes in different categories may share attributes, and that the shared attributes can define a larger category.
- Recognize rhombuses, rectangles, and squares as examples of quadrilaterals.
Module 20
- Understand that shapes in different categories may share attributes.
- Understand that the shared attributes of shapes can define a larger category.
- Recognize rhombuses, rectangles, and squares as types of quadrilaterals.
- Draw examples of quadrilaterals that do not belong to any of these subcategories (rhombuses, rectangles, and squares)
Unit Essential Questions
Lesson Essential Questions
- L19.1 How can you describe shapes as open or closed, as polygons, and by the number of sides and the number of angles?
- L19.2 How can you identify angles that are right angles, greater than a right angle, or less than a right angle in shapes?
- L19.3 How can you identify whether the sides of a shape are equal or not equal in length and identify parallel sides of a shape?
- L19.4 How can you use the number of sides, the number of angles, the number of sides of equal length, and the number of right angles to describe and identify quadrilaterals?
- L20.1 How can you draw a quadrilateral given descriptions of the sides and angles in the shape, and group quadrilaterals using the side lengths or number of right angles?
- L20.2 How can you identify whether a shape belongs in a group by the number of sides, number of angles, sides that are equal length, parallel sides, and by some shape names and attributes?
- L20.3 How can you identify whether a plane shape belongs in a category by the number of parallel sides, sides of equal length, and right angles?
