Grade 5 Math

PA Core Mathematics Standards
Module 1 

• CC.2.1.5.B.1 Students acquire the knowledge and skills needed to: Apply place-value concepts to show an understanding of operations and rounding as they pertain to whole numbers and decimals. 
  • M05.A-T.1.1.1 Demonstrate an understanding that in a multi-digit number, a digit in one place represents 1/10 of what it represents in the place to its left.
  • M05.A-T.1.1.2 Explain patterns in the number of zeros of the product when multiplying a number by powers of 10 and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10.

Module 1-3

• CC.2.1.5.B.2 Students acquire the knowledge and skills needed to: Extend an understanding of operations with whole numbers to perform operations including decimals.
  • M05.A-T.1.1.2 Explain patterns in the number of zeros of the product when multiplying a number by powers of 10 and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. 
  • M05.A-T.2.1.1 Multiply multi-digit whole numbers (not to exceed three-digit by three-digit).
  • M05.A-T.2.1.2 Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors.
  • M05.A-F.2.1.1 Solve word problems involving division of whole numbers leading to answers in the form of fractions (including mixed numbers).

Module 4

• CC.2.2.5.A.1 Students acquire the knowledge and skills needed to: Interpret and evaluate numerical expressions using the order of operations. 
  • M05.B-O.1.1.1 Use multiple grouping symbols (parentheses, brackets, or braces)  in numerical expressions and evaluate expressions containing these symbols. 
  • M05.B-O.1.1.2 Write simple expressions that model calculations with numbers and interpret numerical expressions without evaluating them.

Module 5 

•  CC.2.4.5.A.5 Students acquire the knowledge and skills needed to: Apply concepts of volume to solve problems and relate volume to multiplication and to addition.
  • M05.D-M.3.1.1 Apply the formulas V = l × w × h and V = B × h for rectangular prisms to find volumes of right rectangular prisms with whole-number edge lengths in the context of solving real-world and mathematical problems. Formulas will be provided.
  • M05.D-M.3.1.2 Find volumes of solid figures composed of two non-overlapping right rectangular prisms.

Module 1

• A digit in a multi-digit whole number represents ten times what the digit represents in the place to its right.
• A digit in a multi-digit whole number represents 1/10 of what the digit represents in the place to its left.
• Patterns in the number of zeros can be used to multiply by powers of 10.
• Powers of 10 are written using whole-number exponents.
• Fluency in basic multiplication facts is the foundation for multi-digit multiplication.
• Multi-digit multiplication by 1-digit numbers is the first step to multiplying by 2- and 3-digit numbers.
• A variety of methods and strategies can assist in multiplying multi-digit whole numbers.
• Place value understanding is important when multiplying by multi-digit numbers.

Module 2/3

• A variety of methods and strategies can assist in dividing multi-digit whole numbers.
• Fluency in basic division facts is the foundation for division using the standard algorithm.
• Compatible numbers help to determine the reasonableness of quotients.

Module 4

• Comprehending a word problem is essential to modeling it using a numerical expression.
• Real-world situations can be represented by numerical expressions.
• Grouping symbols indicate what operations should be done first in an expression.
• There is an order to solve expressions.

Module 5

• Volume is the space that an object occupies.
• Area can be used to determine volume.
• A formula helps solve volume problems.
• The volume of one right rectangular prism can assist in determining the volume of a figure composed of multiple right rectangular prisms.

• Understanding place value relationships is a foundational skill in identifying numbers and performing estimation and computation with whole numbers.
• Patterns and rules help us make sense of complex problems.
• Fluent recall of multiplication and division facts aids in solving computational problems using the standard algorithm with multi-digit numbers.
• Formulas can be used to solve problems.
   

Module 1 

• Recognize the 10 to 1 relationship among place-value positions.
• Write and evaluate repeated factors in exponent form.
• Mentally multiply by multiples of 10, 100, and 1,000 using a basic fact and a pattern.
• Multiply multi-digit numbers by a 1-digit number.
• Multiply by multi-digit numbers.
• Fluently multiply multi-digit whole numbers to solve multistep problems.

Module 2 

•  Use multiplication to solve division problems.
•  Model division of whole numbers by 2-digit divisors using an area model.
•  Estimate quotients involving 2-digit divisors using compatible numbers.
• Divide whole numbers by 2-digit divisors using partial quotients.

Module 3

• Divide whole-number dividends by 2-digit divisors using the standard algorithm.
• Solve division problems and decide when to write the remainder as a fraction.
• Adjust the whole number quotient if the estimate is too high or too low.
• Represent a problem with a bar model or an equation, and solve a division problem.

Module 4

• Write numerical expressions.
• Compare numerical expressions without evaluating them.
• Use the order of operations to evaluate numerical expressions.
• Determine in what order operations must be evaluated when there are grouping symbols.

Module 5 

• Understand unit cubes and how they can be used to build a solid figure.
• Find volume by counting the number of unit cubes that fill a right rectangular prism.
• Estimate the volume of a right rectangular prism.
• Find the volume of a right rectangular prism.
• Use a formula to find the volume of a right rectangular prism.
• Find the volume of composed right rectangular prisms.

• How does understanding place value help us multiply and divide multi-digit whole numbers?
• What strategies or models can we use to multiply and divide using multi-digit whole numbers?
• Why is it important to follow the order of operations when solving numerical expressions?
• How can we apply volume and area concepts to solve real-world problems involving rectangular prisms?
• What role do patterns and rules play in helping us make sense of complex problems?
   

• L1.1    How can I describe place-value relationships in multi-digit whole numbers?
• L1.2    How can I rewrite expressions using the product of a 1-digit number and a power of 10 as a whole number?
• L1.3    How can I use mental math to multiply by multiples of 10, 100, 1,000?
• L1.4    How can I multiply multi-digit numbers by 1-digit numbers using regrouping and place value?
• L1.5    How can I multiply multi-digit numbers by 2-digit or 3-digit numbers?
• L1.6    How can I set up and solve multistep problems with at least two steps?
• L2.1    How can I use an array or an area model to solve a division problem?
• L2.2    How can I use visual models to find quotients of four-digit numbers divided by 2-digit divisors?
• L2.3    How can compatible numbers help me estimate quotients of division problems?
• L2.4    How can I use partial products to divide a multi-digit whole number by a 2-digit divisor?
• L3.1      Can I use place value strategies to divide 3- and 4-digit dividends by 2-digit divisors?
• L3.2      How can I solve a division problem, then use the context of the problem to interpret the remainder?
• L3.3      How can I adjust a digit in a whole number quotient based on whether an estimate is too low or too high?
• L3.4      How can I use a bar model or an equation to solve a division problem?
• L4.1      How can I write and solve a numerical expression that models a real-world situation?
• L4.2      How can I compare numerical expressions without evaluating them?
• L4.3      How can I use the order of operations to solve a numerical expression?
• L4.4      How can I use grouping symbols in a numerical expression so that it has a given value?    
• L5.1      How can I build solid figures using unit cubes?
• L5.2      How can I use unit cubes to find the volume of a right rectangular prism?
• L5.3      How can I estimate the volume of a right rectangular prism using an everyday object?
• L5.4      Can I find the volume of a right rectangular prism using the area of the base and the height?
• L5.5      Can I use a formula to find the volume of a right rectangular prism?
• L5.6      How can I find the volume of a figure composed of right rectangular prisms?
   

• Into Math Modules 1-5
• IXL Skill Plan
• Base-ten blocks
• Connecting cubes
• Square tiles
• Grid paper
• Two-color counters
• Square tiles
• Centimeter cubes
• Connecting cubes
• Reflex Math

• base
• divisor
• partial quotients
• sum
• dimension
• cubic unit
• exponent
• inverse operations
• estimate (verb)
• evaluate
• edge
• unit cube
• compatible numbers
• quotient
• difference
• numerical expression
• face
• volume
• dividend
• remainder
• product
• order of operations
• right rectangular prism

• Are You Ready?
• Module 1 Assessment Form A
• *Module 3 Assessment Form A
• Module 4 Assessment Form A
• Module 5 Assessment Form A
• Reteach/Review with Test Form B as needed
• *Module 3 Assessment assesses Modules 2 and 3

PA Core Mathematics Standards
Module 6-7 

• CC.2.1.5.C.1 Students acquire the knowledge and skills needed to: Use the understanding of equivalency to add and subtract fractions.
  • M05.A-F.1.1.1 Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.)

Module 6

• Visual models can be used to identify and create equivalent fractions.
• Fractions need same-sized parts to complete addition and subtraction tasks.
• Multiples can be used to find a common denominator for fractions with different-sized parts.

Module 7

1. Benchmarks used to estimate fractions are 0, ½, and 1.
2. Benchmark fractions are used to estimate sums and differences of fractions with unlike denominators.
3. Estimation of fractions helps to assess the reasonableness of sums and differences.
4. Mixed numbers are made up of a whole number and a fraction.
5. Mixed numbers can be written as improper fractions.
6. Improper fractions can be written as mixed numbers.
7. Renaming and regrouping can be used to subtract mixed numbers.
8. Properties of addition can be used to add fractions and mixed numbers.
9. Equations can model word problems when finding sums and differences of fractions.

• The ability to add and subtract fractions with unlike denominators is necessary for everyday activities such as cooking, baking, measuring, and financial literacy.
• Patterns and rules help us make sense of complex problems.
   

Module 6

• Generate fractions having the same-sized parts using visual models in addition and subtraction expressions when the fractional parts are not the same size.
• Add and subtract fractions with different-sized parts using visual models.
• Rewrite pairs of fractions to equivalent fractions using a common denominator.

Module 7

• Estimate sums and differences of fractions with unlike denominators using benchmark fractions.
• Add and subtract fractions with unlike denominators using common denominators.
• Add and subtract mixed numbers with unlike denominators.
• Rename to find the difference of two mixed numbers.
• Add fractions and mixed numbers with unlike denominators using properties.
• Write equations to solve addition and subtraction problems.
   

•  How can visual models help us understand, add, and subtract fractions with different-sized parts?
•  In what ways do models and equivalent fractions help us solve real-world problems with fractions?
   

• L6.1    How can visual models help me represent the addition or subtraction of fractions with different-sized parts?
• L6.2    How can I represent the sum of fractions with different-sized parts using a visual model?
• L6.3    How can I represent the difference between fractions with different-sized parts using a visual model?
• L6.4    How can I create equivalent fractions for a given fraction using a common denominator?
• L7.1      How can I use benchmarks to estimate a sum or difference of fractions with unlike denominators?
• L7.2      How can I assess the reasonableness of fraction sums and differences?
• L7.3      How can I assess the reasonableness of mixed number sums and differences?
• L7.4      How can I use renaming to subtract mixed numbers?
• L7.5      How can properties of addition help me add fractions and mixed numbers?
• L7.6      How can I use an equation to model a word problem and solve when adding or subtracting fractions?

• Into Math Modules 6-7
• IXL Skill Plan
• Fraction Circles
• Fraction Strips
• Number Lines
• Pattern Blocks
• Reflex Math
   

• equivalent fractions
• commutative property of addition
• common denominator
• associative property of addition
• benchmark

• Are You Ready?
• *Module 7 Assessment Form A
• Reteach & Reassess with Test Form B as needed
• *Module 7 Assessment assesses Modules 6 and 7
   

PA Core Mathematics Standards
Module 8-9 

• CC.2.1.5.C.2 Students acquire the knowledge and skills needed to: Apply and extend previous understandings of multiplication and division to multiply and divide fractions. 
  • M05.A-F.2.1.2 Multiply a fraction (including mixed numbers) by a fraction.
  • M05.A-F.2.1.3 Demonstrate an understanding of multiplication as scaling (resizing). 

Module 8 

• Visual models can represent a fractional part of a group.
• Visual models can help find the product of a fraction and a whole number.
• Visual models can represent the product of unit fractions.
• Compare and explain why a product is greater than, less than, or equal to one factor.
• Write and solve an equation to model a problem that involves multiplying a whole number by a fraction.

Module 9 

• Find the area of a rectangle with mixed-number side lengths.
• Solve real-world problems involving the multiplication of mixed numbers by using visual models or equations to represent the problem.
• Solve area problems involving multiplicative comparisons with fractions and mixed numbers.

• Patterns and rules help us make sense of complex problems.
• The ability to multiply fractions and mixed numbers is necessary for everyday activities such as cooking, baking, measuring, and financial literacy.

Module 8 

• Represent a fractional part of a group.
• Represent the multiplication of a whole number by a fraction.
• Multiply fractions using an area model.
• Multiply fractions by multiplying the numerators and denominators.

Module 9 

• Multiply mixed numbers using an area model and the standard algorithm.
• Solve area problems with fractions and mixed numbers.

• How can I use what I know about multiplication to solve real-world problems with fractions and mixed numbers?
   

• L8.1    How can I use groups of equal shares to show multiplication?
• L8.2    How can I represent multiplication of whole numbers and fractions?
• L8.3    How can I represent multiplication with unit fractions?
• L8.4    How can I represent multiplication of fractions?
• L8.5    How can I use representations of area to develop procedures?
• L8.6    How can I interpret fraction multiplication as scaling?    
• L8.7    How can I multiply fractions?
• L9.1    How can I use an area model to multiply mixed numbers?
• L9.2    How can I solve real-world problems with the multiplication of mixed numbers by writing an equation to model the problem?
• L9.3    How can I solve a real-world problem by writing a multiplication equation to model the problem?
• L9.4    How can I solve multiplication problems with fractions and mixed numbers to find the area of  rectangles?

• Into Math Modules 8-9
• IXL Skill Plan
• Two-Color Counters
• Number Lines
• Fraction Strips
• Pattern Blocks
• Fraction Circles
• Grid Paper
• Reflex Math

• area
• scaling
• multiplication
• unit fraction
• mixed number

• Are You Ready?
• Module 8 Assessment Form A
• Module 9 Assessment Form A
• Reteach/Review with Test Form B as needed

PA Core Mathematics Standards
Module 10-11 

• CC.2.1.5.C.2 Students acquire the knowledge and skills needed to: Apply and extend previous understandings of multiplication and division to multiply and divide fractions. 
  • M05.A-F.2.1.1 Solve word problems involving division of whole numbers leading to answers in the form of fractions (including mixed numbers).
  • M05.A-F.2.1.4 Divide unit fractions by whole numbers and whole numbers by unit fractions.

Module 12

• CC.2.4.5.A.1 Students acquire the knowledge and skills needed to: Solve problems using conversions within a given measurement system. 
  • M05.D-M.1.1.1 Convert between different-sized measurement units within a given measurement system. A table of equivalencies will be provided.
• CC.2.4.5.A.2 Students acquire the knowledge and skills needed to: Represent and interpret data using appropriate scale. 
• CC.2.4.5.A.4 Students acquire the knowledge and skills needed to: Solve problems involving computation of fractions using information provided in a line plot. 
  • M05.D-M.2.1.1 Solve problems involving computation of fractions by using information presented in line plots.
  • M05.D-M.2.1.2 Display and interpret data shown in tallies, tables, charts, pictographs, bar graphs, and line graphs, and use a title, appropriate scale, and labels. A grid will be provided to display data on bar graphs or line graphs. *This is taught in Grade 3 Into Math Module 18

Module 10 

• Represent a fraction as the product of a whole number and a unit fraction.
• Visual models can help find the quotient of a whole number and a unit fraction.

Module 11 

• Multiply fractions by whole numbers using visual models and equations.
• Compare fractions with different numerators and denominators.

Module 12

• Express customary units of length, liquid volume, and weight in a larger unit in terms of a smaller unit.
• Use line plots to display fractional measurement data.
• Solve problems by adding and subtracting fractional measurements in line plots.
• Solve elapsed time problems.

• Fractions can be interpreted as the division of two whole numbers.
• Dividing fractions allows us to solve everyday problems involving sharing or measuring.
• Customary measurement is the standard system used for measurements in everyday life.
• Unit conversions are used in life to help you change measurements so things make sense when you cook, build, travel, or shop.
   

Module 10 

• Interpret fractions as division.
• Represent and find the size and number of equal parts.
• Use representations of division of unit fractions by whole numbers.
• Use representations of division of whole numbers by unit fractions.

Module 11 

• Relate multiplication and division of fractions.
• Divide whole numbers by unit fractions.
• Divide unit fractions by whole numbers.
• Solve division problems using visual models and equations.

Module 12

• Compare and convert customary units of measurement.
• Convert measurement units to solve multistep problems.
• Make and use line plots with data given in fractions to solve problems.
• Convert units of time to solve elapsed time problems.

• What does it mean to divide with fractions, and how can I use it to solve real-world problems?
• How are different customary units related, and how can I convert between them to solve measurement problems?
   

• L10.1    How can I interpret fractions as representing division of whole numbers? 
• L10.2    How can I divide a unit fraction by a whole number using a visual fraction model?
• L10.3    How can I create a story context and use a visual model to interpret the division of a unit fraction by a whole number?
• L10.4    How can I divide a whole number by a unit fraction using a visual fraction model?
• L10.5    How can I create a story context and use a visual fraction model to interpret the division of a whole number by a unit fraction?
• L11.1    How can I divide a whole number by a unit fraction or a unit fraction by a whole number using a related multiplication equation?
• L11.2    How can I represent division of a whole number by a unit fraction using visual models and equations?
• L11.3    How can I create a story context for a given equation and use a visual fraction model to represent the quotient?
• L11.4    How can I represent division of a unit fraction by a whole number using visual models and equations?
• L11.5    How can I create a story context for a given equation and use a visual fraction model to represent the quotient?
• L11.6    How can I solve problems involving the division of fractions and whole numbers? 
• L12.1    How can I compare and convert customary units of measurement?
• L12.2    How can I solve multistep problems that include customary measurement conversions?
• L12.3    How can I make a line plot to display data in fractional measurements and use the line plot to solve problems? 
• L12.4    How can I solve elapsed time problems by converting units of time? 
   

• Into Math Modules 10-12
• IXL Skill Plan
• Fraction Strips
• Pattern Blocks
• Fraction Circles
• Inch Ruler
• 5th Grade PSSA Formula Sheet
• Reflex Math
   

• dividend
• unit fraction
• weight
• divisor
• elapsed time
• quotient
• line plot
• divide
• liquid volume

• Are You Ready?
• *Module 11 Assessment Form A
• Module 12 Assessment Form A
• Reteach/Review with Test Form B as needed
• *Module 11 Assessment assesses Modules 10 and 11
   

PA Core Mathematics Standards
Module 13 

• CC.2.1.5.B.1 Students acquire the knowledge and skills needed to: Apply place value concepts to show an understanding of operations and rounding as they pertain to whole numbers and decimals. 
  • M05.A-T.1.1.1 Demonstrate an understanding that in a multi-digit number, a digit in one place represents 1/10 of what it represents in the place to its left.
  • M05.A-T.1.1.3 Read and write decimals to thousandths using base-ten numerals,  word form, and expanded form.
  • M05.A-T.1.1.5 Round decimals to any place (limit rounding to ones, tenths,  hundredths, or thousandths place).
  • M05.A-T.1.1.4 Compare two decimals to thousandths based on meanings of the digits in each place using >, =, and < symbols.

Module 14 

• CC.2.1.5.B.2 Students acquire the knowledge and skills needed to: Extend an understanding of operations with whole numbers to perform operations including decimals. 
  • M05.A-T.2.1.3 Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals).

Module 13 

• The value of a digit is determined by its position in a number.
• In a multi-digit decimal number, a digit in one place represents ten times the value it would have in the place to its right.
• Decimal numbers can be written in different forms for different purposes.
• When comparing decimal numbers, distinguish the meaning between the > and < symbols.
• Apply the rules of rounding (number-line, place value understanding) in multi-digit decimal numbers.

Module 14 

• An estimate can help determine if an answer is reasonable.
• When adding larger numbers, addends need to be aligned by place value, and then adding begins with the digits in the smallest place value, moving one place to the left at a time, regrouping when necessary.
• When subtracting, align the two numbers by place value and begin subtracting starting in the smallest place value, moving left one place at a time, regrouping when necessary.
• Identifying the unknown value in a problem helps determine which operation (addition or subtraction) to use to find the solution.

• Understanding decimals helps us make informed decisions with money, measurements, and everyday estimates quickly and accurately.

Module 13 

• Understand thousandths.
• Read and write decimals to thousandths.
• Round decimals.
• Compare and order decimals.

Module 14 

• Represent decimal addition using concrete models or drawings.
• Represent decimal subtraction using concrete models or drawings.
• Assess the reasonableness of decimal sums and differences.
• Add decimals using a written method and strategies based on place value.
• Subtract decimals using a written method and strategies based on place value.
• Use strategies based on properties and reasoning to add and subtract decimals. 

• How does understanding place value help me read, write, and compare decimals?
• How can I use place value to accurately add and subtract decimals in real-life situations?
   

• L13.1    What is the relationship among decimal place value positions?
• L13.2    How can I read and write decimals to thousandths?
• L13.3    How can I round decimals?
• L13.4    How can I compare and order decimals?
• L14.1    How can I use concrete models or drawings to represent decimal addition?
• L14.2    How can I use concrete models or drawings to represent decimal subtraction?
• L14.3    How can I use benchmarks or rounding to check the reasonableness of decimal sums and differences?  
• L14.4    How can I use a written method and strategies based on place value to add decimals?
• L14.5    How can I use a written method and strategies based on place value to subtract decimals?
• L14.6    How can I add and subtract decimals by using reasoning and strategies involving addition properties or friendly numbers? 

• Into Math Modules 13-14
• IXL Skill Plan
• Place Value Charts
• Number Lines
• Base-Ten Blocks
• Decimal Models
   

• greater than (>)
• benchmark
• thousandth
• less than (<)
• round
• associative property of addition
• commutative property of addition

• Are You Ready? 
• Module 13 Assessment Form A
• Module 14 Assessment Form A
• Reteach/Review with Test Form B as needed
   

PA Core Mathematics Standards
Module 15-16

• CC.2.1.5.B.1 Students acquire the knowledge and skills needed to: Apply place value concepts to show an understanding of operations and rounding as they pertain to whole numbers and decimals. 
  • M05.A-T.1.1.2 Explain patterns in the number of zeros of the product when multiplying a number by powers of 10 and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. 
  • M05.A-T.2.1.3 Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals).
• CC.2.1.5.B.2 Students acquire the knowledge and skills needed to: Extend an understanding of operations with whole numbers to perform operations including decimals.  

Modules 15 and 16

• Recognize that a digit in a decimal number represents 10 times what it represents in the place to the right.
• Multiply fractions by whole numbers.
• Multiply whole numbers up to four digits by 1 and 2-digit whole numbers.

• Understanding multiplication of decimals helps us make informed decisions with money, measurements, and everyday estimates quickly and accurately.

Module 15

• Understand decimal multiplication patterns.
• Represent multiplication with decimals and whole numbers.
• Assess the reasonableness of products.
• Multiply decimals by 1 and 2-digit whole numbers.
• Solve problems using bar models.

Module 16

• Use a visual model to multiply decimals.
• Place the decimal point in decimal multiplication.
• Multiply decimals with zeros in the product.

• How does multiplying decimals help me solve real-world problems with money, measurement, and precision?
   

• L15.1    How can I multiply decimals by a power of 10 that is both greater than and less than 1?
• L15.2    How can I represent the product of a decimal less than one and a whole number using a visual model? 
• L15.3    How can I assess the reasonableness of the product of a decimal less than one and a whole number?
• L15.4    How can I multiply a decimal by a 1-digit whole number using the Distributive Property, partial products, and an area model?
• L15.5    How can I use an area model and place-value patterns to multiply a decimal by a 2-digit whole number?
• L15.6    How can I use a bar model to solve a multistep problem that uses multiplication?
• L16.1    How can I find the product of two decimals to the tenths place by using a decimal model?
• L16.2    How can I multiply two decimal numbers by applying an understanding of place value?
• L16.3    How can I write the correct number of zeros in the product of two decimal numbers?

• Into Math Modules 15-16
• IXL Skill Plan
• Decimal Models
• Place Value Charts
• Base-Ten Blocks
• Colored Pencils
• Two-Color Counters
   

• distributive property
• product
• estimate (noun)
• estimate (verb)
• place value

• Are You Ready?
• *Module 16 Assessment Form A
• Reteach/Review with Test Form B as needed
• *Module 16 Assessment assesses Modules 15 and 16

PA Core Mathematics Standards
Module 17 

• CC.2.1.5.B.1 Students acquire the knowledge and skills needed to: Apply place value concepts to show an understanding of operations and rounding as they pertain to whole numbers and decimals. 
  • M05.A-T.1.1.2 Explain patterns in the number of zeros of the product when multiplying a number by powers of 10 and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use  whole-number exponents to denote powers of 10. 
• CC.2.1.5.B.2 Students acquire the knowledge and skills needed to: Extend an understanding of operations with whole numbers to perform operations including decimals.
  • M05.A-T.2.1.3 Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals).

Module 18 

• CC.2.4.5.A.1 Students acquire the knowledge and skills needed to: Solve problems using conversions within a given measurement system. 
  • M05.D-M.1.1.1 Convert between different-sized measurement units within a given measurement system. A table of equivalencies will be provided.

Module 17 

• Find whole-number quotients and remainders with dividends up to four digits and one-digit divisors.
• Use equations, rectangular arrays, and area models to explain division calculations.
• Divide using strategies based on place value, the properties of operations, and the relationship between multiplication and division.

Module 18 

• Understand the relative sizes of customary and metric units of measurement.
• Express measurements in a larger unit in terms of a smaller unit.

• Understanding the division of decimals helps us make informed decisions with money, measurements, and everyday estimates quickly and accurately.
• Unit conversions are used in life to help you change measurements so things make sense when you cook, build, travel, or shop.

Module 17 

• Understand decimal division patterns.
• Represent division of decimals by whole numbers.
• Assess the reasonableness of quotients.
• Divide decimals by whole numbers.

Module 18 

• Compare and convert metric units.
• Solve problems involving customary and metric conversions.
• Convert measurement units to solve multistep problems.

• How can I use decimal division to solve real-world problems accurately and efficiently?
• How are different metric units related, and how can I convert between them to solve measurement problems?
   

• L17.1    How can I use patterns to place the decimal point in a quotient?
• L17.2    How can I use a concrete or visual model to divide a decimal by a whole number?
• L17.3    How can I estimate the quotient of a decimal division problem by using compatible numbers?
• L17.4    How can I divide decimals by whole numbers?
• (L17.5-L17.7 are not taught in fifth grade. These lessons are based on sixth-grade standards.)
• L18.1    How can I convert between any two metric units of length, liquid volume, or mass?
• L18.2    How can I solve problems involving conversions within the same system of measurement?
• L18.3    How can I solve a multistep problem that includes measurement conversions?
   

• Into Math Modules 17-18
• IXL Skill Plan
• Place Value Charts
• Base-Ten Blocks
• Decimal Models
• Reflex Math
   

• dividend
• gram
• divisor
• liter
• estimate
• meter
• quotient

• Are You Ready? 
• Modified Module 17 Assessment (Does not have the sixth-grade standards dividing with a decimal in the divisor)
• Module 18 Assessment Form A
• Reteach/Review with Test Form B as needed
   

PA Core Mathematics Standards
Module 19 

• CC.2.3.5.A.1 Students acquire the knowledge and skills needed to: Graph points in the first quadrant on the coordinate plane and interpret these points when solving real-world and mathematical problems. 
  • M05.C-G.1.1.1 Identify parts of the coordinate plane (x-axis, y-axis, and the origin) and the ordered pair (x-coordinate and y-coordinate). Limit the coordinate plane to quadrant I.
  • M05.C-G.1.1.2 Represent real-world and mathematical problems by plotting points in quadrant I of the coordinate plane and interpret coordinate values of points in the context of the situation.
• CC.2.2.5.A.4 Students acquire the knowledge and skills needed to: Analyze patterns and relationships using two rules.
  • M05.B-O.2.1.1 Generate two numerical patterns using two given rules. 
  • M05.B-O.2.1.2 Identify apparent relationships between corresponding terms of two patterns with the same starting numbers that follow different rules.
• Module 20 
• CC.2.3.5.A.2 Students acquire the knowledge and skills needed to: Classify two-dimensional figures into categories based on an understanding of their properties. 
  • M05.C-G.2.1.1 Classify two-dimensional figures in a hierarchy based on properties.

Module 19 

• Identify points, lines, line segments, rays, angles and perpendicular and parallel lines in plane figures.
• Generate a number pattern following a given rule.
• Identify features of a number pattern that were not explicit from the given rule.

Module 20 

• Identify right triangles.
• Identify and recognize the relationship between categories of figures, including quadrilaterals.

• Coordinate planes can be used in the real world to find and describe exact locations—like reading maps, planning buildings, designing video games, or graphing data in math and science.
• Knowing the difference between quadrilaterals can help you recognize and use the right shapes when building, designing, solving problems, or understanding how things fit together in real life.

Module 19 

• Identify and describe a point in a coordinate system.
• Graph points on a coordinate grid and interpret the coordinate values.
• Use coordinate graphing to represent and solve problems.
• Use two rules to generate numerical patterns. 
• Identify the relationship between corresponding terms in patterns.

Module 20 

• Identify and classify polygons.
• Classify and draw triangles using their attributes.
• Classify and compare quadrilaterals using their attributes.
• Compare and classify two-dimensional figures using Venn diagrams.
   

• How can we use coordinate graphs to represent and analyze relationships between quantities in real-world situations?
• How can we use the properties of 2-dimensional figures to classify and understand their relationships?
   

• L19.1    How can I identify and describe a point in a coordinate system?
• L19.2    How can I graph a point on a coordinate grid and understand the coordinate values?
• L19.3    How can I use coordinate graphing to represent and solve problems? 
• L19.4    How can I use two rules to create numerical patterns? How can I write ordered pairs using corresponding terms? How can I identify relationships between corresponding terms? 
• L19.5    How can I write and graph ordered pairs on a coordinate grid using two numerical patterns? 
• L20.1    How can I identify and classify polygons? 
• L20.2    How can I classify triangles?
• L20.3    How can I classify and compare quadrilaterals? 
• L20.4    How can I compare and classify two-dimensional figures using Venn diagrams?

• Into Math Modules 19-20
• IXL Skill Plan
• 1-cm Grid Paper
• Venn Diagram
• Reflex Math
   

• axes
• x-axis
• congruent
• nonagon
• coordinate grid
• y-coordinate
• equilateral triangle
• regular polygon
• coordinate system
• y-axis
• heptagon
• scalene triangle
• ordered pair
• y-coordinate
• isosceles triangle
• trapezoid (exclusive)
• trapezoid (inclusive)

• Are You Ready?
• Module 19 Assessment Form A
• Module 20 Assessment Form A
• Reteach/Review with Test Form B as needed