Grade 2 Math

PA Core Mathematics Standards
Module 1 

• CC.2.2.2.A.2 Students acquire the knowledge and skills needed to: Use mental strategies to add and subtract within 20. 

Module 2 

• CC.2.2.2.A.3 Students acquire the knowledge and skills needed to: Work with equal groups of objects to gain foundations for multiplication.

Module 3

•  CC.2.4.2.A.4 Students acquire the knowledge and skills needed to: Represent and interpret data using line plots, picture graphs, and bar graphs.

• Basic fact fluency within 20.
• Common strategies for adding and subtracting (doubles, making ten, number line). 
• Numbers are odd and even. 
• 2 even addends make an even sum.
• 2 odd addends make an even sum.
• 1 odd and 1 even addend, make an odd sum. 
• Arrays can be represented by addition equations.
• Data can be represented by different types of graphs (tally charts, picture graphs and bar graphs).

• Fluently add and subtract within 20 using mental strategies. By the end of grade 2, know from memory all sums of 2 one-digit numbers. 
• Determine whether a group of objects (up to 20) has an odd or even number of members, e.g., by pairing objects or counting them by 2s; write an equation to express an even number as a sum of two equal addends.
• Write an equation to express an even number as a sum of two equal addends.
• Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends.
• Draw a picture graph and bar graph (with single-unit scale) to represent a data set with up to four categories.  
• Solve simple put-together, take-apart, and compare problems using information in a bar graph.
   

Module 1

• Add fluently within 20 using mental strategies and properties.
• Subtract fluently within 20 using mental strategies.

Module 2

• Determine whether a group of objects has an odd or even number of members.
• Write an equation to express an even number as a sum of two equal addends
• Use addition to find the total number of objects arranged in rectangular arrays.
• Write an equation to express the total as a sum of equal addends.

Module 3

• Collect and record data in a tally chart
• Draw a picture graph and bar graph (with single-unit scale) to represent a data set with up to four categories
• Solve simple put-together, take-apart and compare problems using information presented in a picture graph or a bar graph 

Module 1

• How can I use mental math strategies to solve addition and subtraction problems quickly and accurately?
• What patterns or relationships can I find in numbers to help me add and subtract more efficiently?
• When is it helpful to use mental strategies instead of written methods?

Module 2

• How can putting objects into equal groups help me understand repeated addition?
• How can I use models or drawings to show equal groups and solve problems?

Module 3

• How can I collect, organize, and represent data to help others understand it?
• What do tally charts, picture graphs, and bar graphs show about data?
• How can I use graphs to answer questions and solve real-world problems?
   

• L1.1 How does a doubles fact help us solve an equation that is one more or one less? 
• L1.2 How do related facts help you solve equations?
• L1.3 How do you form other related facts using the same numbers?
• L1.4 How can related addition facts help you solve subtraction equations?
• L1.5 When might you choose to use “make a 10 a strategy” to solve an addition equation?
• L1.6 How do you use a number line to help you solve subtraction equations? 
• L1.7 How do you decide which 2 addends to use first, in a 3 addend equation? 
• L2.1 How does grouping objects help you determine if a number is odd or even?
• L2.2 How can you write an addition equation with 2 equal addends?
• L2.3 How can you use tools or drawings to show equal groups of objects?
• L2.4 How can you use a set number of objects to create an array? 
• L2.5 How can you create equal groups of objects to make an array for multiplication?
• L3.1 How can you collect, record, and use data in a tally chart? 
• L3.2 How do you read a picture graph?
• L3.3 How can you draw a picture graph to show data? 
• L3.4 How do you read a bar graph? 
• L3.5 How can you record and use data to draw a bar graph? 
   

• Into Math 2nd Grade Modules 1 - 3
• Two-color counters
• Connecting cubes
• Ten Frame
• Number line 0 - 20
• Square tiles
• Paper bag with 10 - 12 crayons inside
   

• Addends
• Count Back
• Count On
• Difference
• Doubles
• Related Facts
• Sum
• Addition Equation 
• Even
• Odd
• Array
• Bar Graph
• Picture Graph
• Tally Chart
• Tally Mark

• Are you ready? (For All Modules)
• Module Test form A (For All Modules)
  • If needed Reassess Test form B (For All Modules)
     

PA Core Mathematics Standards
Module 4

•  CC.2.1.2.B.1 Students acquire the knowledge and skills needed to: Use place-value concepts to represent amounts of tens and ones and to compare three-digit numbers.
• CC.2.1.2.B.2 Students acquire the knowledge and skills needed to: Use place-value concepts to read, write, and skip count to 1000.
• Module 5
•   CC.2.1.2.B.2 Students acquire the knowledge and skills needed to: Use place-value concepts to read, write, and skip count to 1000.

Module 6

• CC.2.1.2.B.2 Students acquire the knowledge and skills needed to: Use place-value concepts to read, write, and skip count to 1000. 
• CC.2.1.2.B.1 Students acquire the knowledge and skills needed to: Use place-value concepts to represent amounts of tens and ones and to compare three-digit numbers. 
   

• Basic fact fluency within 20.
• Ten, Tens make one hundred.
• The value of each digit changes depending on the position within the number. (6 in the tens place is 60)
• Numbers can be written in a variety of forms (expanded form, drawing, hundreds chart, standard form, and word form).
• Numbers are represented on a number line. 
• Skip counting follows number patterns.
• Numbers can be compared using symbols (<, >, =) or words (greater than, less than, equal too).

• 100 can be thought of as a bundle of ten tens - called a hundred. 
• Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones. 
• Read and write numbers to 1000 using base-ten numerals, number names, and expanded form. 
• Read and write numbers to 1,000 using base-ten numerals, number names, and expanded form.
• Count within 1000; skip count by 5s, 10s, and 100s.
• Mentally add 10 or 100 to a given number between 100 - 900, and mentally subtract 10 or 100 from a given number between 100 - 900.
• Compare 2 three-digit numbers based on the meanings of the hundreds, tens, and ones digit, using >, =, and < symbols to record the results of comparisons. 

• Module 4
  • Understand that the three digits in a three-digit number represent amounts of hundreds, tens, and ones.
  • Add and subtract within 20 fluently using strategies.
  • Read and write numbers to 1000 using base-ten-numerals, number names, and expanded form.
  • Reason that 100 is a bundle of ten tens.
  • Reason that decade numbers are whole number groups of hundreds.
  • Use place value models to show different numbers. 
  • Use concrete and visual models to show different numbers. 
• Module 5
  • Read and write numbers to 1,000 using base-ten numerals and expanded form. 
  • Name numbers to 1,000 using base-ten numerals.
  • Read and write numbers using base-ten numerals. 
  • Read and write numbers using expanded form.
  • Read and write numbers using number names. 
• Module 6
  • Count within 1,000.
  • Count by 5’s, 10’s, and 100’s within 900. 
  • Use mental math to add and subtract 10 or 100 to a given number within 900. 
  • Compare three-digit numbers using place value. 

Module 4

• How does understanding place value help us represent and compare numbers?
• What strategies can be used to determine the value of digits in a three-digit number?
• How can skip counting support our understanding of number patterns and structure within the base-ten system?

Module 5

• How does knowledge of place value help us read and write numbers up to 1000 accurately?
• What mathematical patterns are revealed through skip counting?

Module 6

• How do place-value concepts support reasoning when comparing and ordering numbers?
• What role does the value of each digit play in representing and understanding three-digit numbers?

• L4.1 How can you group 10 to make 100?
• L4.2 How can you write three-digit numbers in different ways?
• L4.3 How can you use drawings or objects to show the value of a three-digit number?
• L4.4 How can you write a three-digit number in expanded form?
• L4.5 How can you explain the value of each digit in a number up to 1,000?
• L5.1 How can you write a three-digit number in expanded form?
• L5.2 How can you write a three-digit number in word form?
• L5.3 How can you write three-digit numbers in different ways?
• L5.4 How can you write three-digit numbers in different ways?
• L5.5 How do you identify a three-digit number on a number line?
• L6.1 How do you skip by ones, fives, tens, and hundreds? 
• L6.2 How can you add or subtract 10 or 100 from a three-digit number?
• L6.3 How do you identify and continue a given pattern? 
• L6.4 How can you use concrete models to compare three-digit numbers?
• L6.5 How can you use <, >, = to compare three-digit numbers? 
   

•      Into Math 2nd Grade Modules 4 - 6
• Base ten blocks
• Connecting cubes 
• Counters
• Pencils
• Crayons
• Place Value Charts
• 3-digit number cards
• Symbol cards

• Ones
• Tens
• Hundreds
• Thousands
• Is equal to (=)
• Is greater than (>)
• Is less than (<)

• Are you ready? (For All Modules)
• Module Test form A (For All Modules)
  • If needed Reassess Test form B (For All Modules)
     

  PA Core Mathematics Standards
Module 7 

•  CC.2.4.2.A.3 Students acquire the knowledge and skills needed to: Solve problems and make change using coins and paper currency with appropriate symbols.

Module 8 

•  CC.2.4.2.A.3 Students acquire the knowledge and skills needed to: Solve problems and make change using coins and paper currency with appropriate symbols.

Module 9

•  CC.2.4.2.A.2 Students acquire the knowledge and skills needed to: Tell and write time to the nearest five minutes using both analog and digital clocks.

• Money can be shown and written using tens and ones. 
• Coins have different values.
• A coin combination can be represented in several different ways.
• Coins combined make a dollar. 
• Bills have different values. 
• Hands on a clock represent minutes or hours. 
• Skip count by 5’s to sixty. 
• Time is written using an analog or digital clock. 
• Time can be written in different ways (quarter past, half past, a.m., p.m.). 

• Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and cents symbols appropriately. Example: If you have 2 dimes and 3 pennies, how many cents do you have? 
• Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m.

Modules 7 and 8

• Explore the relationship between place value and coins (dimes and pennies). 
• Identify and find the total value of combinations of quarters, nickels, and pennies. 
• Order combinations of coins by value and then find the total value.
• Identify and apply the relative values of different coins to each other. 

Module 9

• Tell and write time from analog and digital clocks to the nearest 5 minutes. 
• Read digital and analog clocks, and use phrases to describe times to five minutes. 
• Practice telling and writing time to the nearest five minutes. 
• Practice telling and writing time, using a.m. and p.m. 

Module 7

• How can I use coins and bills to represent different amounts of money?
• What strategies can I use to solve problems involving money and making change?
• Why is it important to use correct symbols when working with money?

Module 8

• How do I determine the correct amount of money needed to make a purchase or give change?
• In what ways can money problems be solved using real-world examples?
• How does understanding the value of coins and bills help in making financial decisions?

Module 9

• How can I accurately tell and write time to the nearest five minutes?
• What are the similarities and differences between reading analog and digital clocks?
• Why is understanding time important in daily life? 
   

• L7.1 How can you show and write money using 10s and 1s?
• L7.2 How can you identify and find the total value of a group of coins?
• L7.3 How can you order coins to find the total value of a group of coins?
• L7.4 How can you use different coins to show the same money amount in different ways?
• L8.1 How can you solve word problems involving coins and bills? 
• L8.2 How can you find the total value of a combination of dollar bills?
• L8.3 How can you solve word problems involving coins and bills? 
• L9.1 How can you draw hands on a clock and write time on a clock to the nearest 5 minutes?
• L9.2 How can you use different ways to write and say the time shown on a clock?
• L9.3 How can you show and write time to the nearest 5 minutes in three different ways? 
• L9.4 How can you tell time to the nearest five minutes, and is it a.m. or p.m.?
   

• Into Math 2nd Grade Modules 7--9
• Base ten blocks
• Play coins
• Math board
• Paper bag
• Play dollars
• Analog clocks with movable hands
   

• Ones
• Tens
• Cent sign 
• Dime
• Penny
• Nickel
• Quarter
• Greatest Value
• Least Value
• Quarter
• Dollar
• Dollar Sign
• Decimal point
• Hour Hand
• Minute Hand
• Hour
• Midnight
• noon
• Minute
• Half Past
• Quarter Past
• A.M.
• P.M.

• Are you ready? (For All Modules)
• Module Test form A (For All Modules)
  • If needed Reassess Test form B (For All Modules)
     

PA Core Mathematics Standards
Module 10, 11, 12, 13

•  CC.2.1.2.B.3 Students acquire the knowledge and skills needed to: Use place-value understanding and properties of operations to add and subtract within 1000.

Module 14

•  CC.2.2.2.A.1 Students acquire the knowledge and skills needed to: Represent and solve problems involving addition and subtraction within 100.
• Module 15 
• CC.2.2.2.A.1 Students acquire the knowledge and skills needed to: Represent and solve problems involving addition and subtraction within 100.

• Hundred charts and number lines are tools for addition and subtraction problems. 
• Numbers can be represented in expanded form. 
• Ten ones is equivalent to one ten. 
• Ten tens is equivalent to one hundred.
• Concrete and/or visual models represent two-digit numbers. 
• Different strategies are used in addition and subtraction problems.
• Equations can have more than two addends.  
• Multi Step problems are solved using addition and/or subtraction. 

• Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. 
• Add up to four two-digit numbers using strategies based on place value and properties of operations. 
• Explain why addition and subtraction strategies work, using place value and the properties of operations. 
• Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. 
• Understanding that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds. 
• Use addition and subtraction within 100 to solve one-and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, unknown in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. 

Module 10

• Use a hundred chart and number line as a tool for two-digit addition and subtraction. 

Module 11

• Find a sum by decomposing a one-digit addend to make a two-digit addend a multiple of 10. 
• Find a difference by decomposing a one-digit subtrahend to subtract it from a two-digit number.
• Use decomposing a number as a strategy to add two-digit numbers. 
• Apply place-value understanding when decomposing numbers to solve two-digit addition and subtraction. 

Module 12

• Represent two-digit subtraction with regrouping 1 ten as 10 ones. 
• Use place-value charts to represent and record two-digit addition. 
• Use concrete models to represent two-digit subtraction and connect the concrete model to subtraction algorithms. 
• Understand how to record two-digit addition and subtraction with and without regrouping. 

Module 13

• Rewrite addition and subtraction problems given in horizontal form as a vertical addition and subtraction algorithm and find the sum and difference. 
• Use the relationship between addition and subtraction to find the difference. 
• Use strategies of addition to find the sum of 3 two-digit numbers and 4 two-digit numbers. 

Module 14

• Use bar models, equations, and drawings to represent and solve addition and subtraction situations. 

Module 15

• Represent addition and subtraction situations with equations using a symbol for the unknown. 
• Evaluate word problems to decide what operations to use to solve multistep problems. 

Modules 10 - 13

• How does place-value understanding support addition and subtraction within 1000?
• What strategies and properties of operations can I use to solve multi-digit addition and subtraction problems accurately?
• In what ways can I model and explain my thinking when solving problems involving numbers up to 1000?

Module 14

• How can I use different strategies to solve addition and subtraction problems within 100?
• What models or representations can help me understand and explain my solutions?
• How do I determine which operation to use when solving a word problem?

Module 15

• How do real-world situations help us apply addition and subtraction within 100?
• What strategies can I use to check the reasonableness of my answers?
• How can understanding part–part–whole relationships help me solve problems?
   

• L10.1 How can you use a hundreds chart to add a subtract?
• L10.2 How can you use a number line to add a subtract?
• L10.3 How can you rewrite addition problems and find the sum?
• L11.1 How can you break apart an addend to make a new group to help you add?
• L11.2 How can you break apart a ten to help you subtract?
• L11.3 How can you draw a model to help you write an equation?
• L11.4 How can you break about addends into tens and ones?
• L11.5 How can you break apart a number into tens and ones to help you subtract? 
• L12.1 How can you regroup to represent an addition problem? 
• L12.2 How can you regroup to represent a subtraction problem?
• L12.3 How can you regroup to represent a two digit addition problem?
• L12.4 How can you regroup to represent a two digit subtraction problem?
• L12.5 What are the steps to solving double-digit addition problems?
• L12.6 What are the steps to solving double-digit subtraction problems?
• L13.1 How can you rewrite addition problems to find the sum?
• L13.2 How can you rewrite subtraction problems to find the difference? 
• L13.3 How can you use addition to find the difference between numbers on a number line? 
• L13.4 How can you find the sum of 3 two-digit numbers by using addition strategies? 
• L13.5 How can you find the sum of 4 two-digit numbers by using addition strategies?
• L14.1 How can you represent addition and subtraction word problems with bar models and equations?
• L14.2 How can you use equations to represent and solve addition and subtraction word problems?
• L14.3 How can you use bar models and equations to represent and solve two-digit addition word problems?
• L14.4 How can you use bar models and equations to represent and solve two-digit subtraction word problems?
• L15.1 How can you write an equation and use it to solve an addition word problem?
• L15.2 How can you write an equation and use it to solve a subtraction word problem?
• L15.3 How can you solve multi-step addition and subtraction word problems?
   

• Into math grade 2- module 10-15
• Math board
• Base-ten blocks
• Crayons
• Open number line
• Two-color counters
• Connecting cubes
• Number cube
• Number cards 1-100
• Place value chart
• Index cards
• Plus and minus cards
   

• Ones
• Tens
• Add
• Addend
• subtract
• Regrouping
• Addition equation
• Subtraction equation
• Equation
• operation

• Are you ready? (For All Modules)
• Module Test form A (For All Modules)
  • If needed Reassess Test form B (For All Modules)

PA Core Mathematics Standards
Module 16 

•  CC.2.1.2.B.3 Students acquire the knowledge and skills needed to: Use place-value understanding and properties of operations to add and subtract within 1000.

Module 17 

•  CC.2.1.2.B.3 Students acquire the knowledge and skills needed to: Use place-value understanding and properties of operations to add and subtract within 1000.

• Pictures represent three-digit numbers. 
• Numbers can be represented in expanded form. 
• Ten ones is equivalent to one ten.
• Ten tens is equivalent to one hundred. 
• Concrete and/or visual models represent three-digit numbers. 
• Zeros can hold a place in a number. 
• Different strategies are used in addition and subtraction problems.

• Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to the written method. 
• Understand that in adding and subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds. 
• Explain why addition and subtraction strategies work, using place value and the properties of operations. 
   

Module 16

• Draw quick pictures to represent a three-digit addition. 
• Apply place-value concepts when decomposing numbers to solve three-digit addition problems. 
• Record three-digit addition using the standard algorithm with possible regrouping ones or tens. 

Module 17

• Solve problems involving three-digit subtraction by building concrete and visual models. 
• Record three-digit subtraction using the standard algorithm with possible regrouping of hundreds and tens. 
• Show regrouping for subtraction with three-digit numbers with zeros. 
• Record three-digit subtraction using the standard algorithm when there are zeros in the minuend. 
• Record three-digit addition and three-digit subtraction using the standard algorithm with possible regrouping in all place-value positions. 

Modules 16 and 17

• How does understanding place value help us solve addition and subtraction problems within 1000?
• What strategies and properties of operations can I use to solve multi-digit problems efficiently and accurately?
• How can I explain my thinking when solving problems that involve regrouping or decomposing numbers?

• L16.1 How can you draw pictures to add three digit numbers?
• L16.2 How can you break apart addends to add hundreds, tens, and ones?
• L16.3 How can you solve three-digit addition problems with regrouping?
• L16.4 How can you regroup ones and tens to find sums of three-digit numbers? 
• L17.1 How can you use place value to represent three digit subtraction?
• L17.2 How can you subtract a three digit number with regrouping using a concrete model or a visual model?
• L17.3 How can you subtract a three digit number without regrouping using a concrete model or a visual model?
• L17.4 How can you solve three digit subtraction problems when there are zeros in the number?
• L17.5 How can you regroup three digit subtraction problems with zeroes?
• L17.6  How can you use regrouping to solve addition and subtraction problems with three-digit numbers?
   

• HMH math grade 2- Modules 16-17
• Mathboard
• Base-ten blocks
• Place value chart (hundreds, tens, ones)
• Crayon
   

• Hundreds
• Tens
• Ones
• regrouping

• Are you ready? (For All Modules)
• Module Test form A (For All Modules)
  • If needed Reassess Test form B (For All Modules)
     

PA Core Mathematics Standards
Module 18 

•  CC.2.4.2.A.1 Students acquire the knowledge and skills needed to: Measure and  estimate lengths in standard units using appropriate tools.

Module 19 

•   CC.2.4.2.A.1 Students acquire the knowledge and skills needed to: Measure and  estimate lengths in standard units using appropriate tools.

Module 20 

• CC.2.4.2.A.6 Students acquire the knowledge and skills needed to: Extend the  concepts of addition and subtraction to problems involving length.

• Objects have lengths that can be estimated into inches, feet, centimeters, meters and yards. 
• Rulers measure to the nearest inches, feet, centimeters, meters and yards. 
• Data can be represented by different types of graphs.
• Different tools can be used for measurement. 
• Inches are smaller than feet.
• Feet are smaller than yards. 
• Centimeters are smaller than meters. 
• Yardsticks and meter sticks are number lines. 

• Estimate lengths using units of inches, feet, centimeters, and meters. 
• Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes. 
• Generate measurement data by measuring lengths of several objects to the nearest whole unit, or by making repeated measurements of the same object. Show the measurements by making a line plot, where the horizontal scale is marked off in whole-number units. 
• Measure the length of an object twice, using length units of different lengths for the two measurements, and describe how the two measurements relate to the size of the unit chosen. 
• Represent whole numbers as lengths from 0 on a number line diagram with equally spaced points corresponding to the numbers 0,1,2,..., and represent whole number sums and differences within 100 on a number line diagram. 
• Use addition and subtraction within 100 to solve word problems involving lengths that are given in the same units, e.g., by using drawings (such as drawings of rulers) and equations with a symbol for the unknown numbers to represent the problem. 
• Measure and determine how much longer one object is than another, expressing the length difference in terms of standard length unit. 

Module 18

• Estimate the lengths of objects by mentally partitioning the lengths into inches. 
• Generate and use a paper ruler without and with numbers by using 1-inch tiles.
• Measure the lengths of objects to the nearest inch using an inch ruler. 
• Measure the lengths of objects and use a line plot to display the measurement data. 
• Estimate the lengths of objects by mentally partitioning the lengths into feet and 3 foot sections (yards). 
• Measure the lengths of objects in both inches and feet to explore the inverse relationship between 
• size and number of units. 
• Select appropriate tools for measuring different lengths. 

Module 19

• Estimate the length of objects in centimeters by comparing them to known lengths. 
• Measure lengths of objects to the nearest centimeter using a centimeter ruler. 
• Estimate the lengths of objects in meters. 
• Measure the lengths of objects in both centimeters and meters to explore the inverse relationship between size and number of units. 

Module 20

• Explore the relationship between inch units on an inch ruler or a yardstick and units on a number line and use an inch ruler or a yardstick to solve addition and subtraction problems. 
• Solve addition and subtraction problems involving the lengths of objects in inches by using a visual model. 
• Explore the relationship between units on a centimeter ruler or a meter stick and units on a number line and use a centimeter ruler or a meter stick to solve addition and subtraction problems. 
• Solve addition and subtraction problems involving the lengths of objects in centimeters by using a number line diagram. 
• Measure and then find the difference in the centimeter lengths of two objects. 

Module 18

• How do I choose the appropriate tool and unit when measuring the length of an object?
• What strategies help me estimate and measure lengths accurately?
• Why is it important to understand and use standard units of measurement?

Module 19

• How can measurement be used to solve real-world problems?
• What is the difference between estimating and measuring length?
• How do different measurement tools affect the accuracy of a measurement?

Module 20

• How can I use addition and subtraction to solve problems involving length?
• What strategies can I use to solve multi-step word problems that include measurements?
• How does understanding measurement support my ability to solve real-world math problems?
   

• L18.1 How can you use 1-inch tiles to estimate lengths?
• L18.2 How can you use 1-inch tiles to make a ruler to measure objects?
• L18.3 How can you use a ruler to measure the length of an object to the nearest inch? 
• L18.4 How can you measure the length of objects in inches and show the data on a line plot?
• L18.5 How can you use a 12-inch ruler to estimate the length of an object in feet? 
• L18.6.1 How can you measure objects to the nearest inch and the nearest foot?
• L18.6.2 How is measuring in feet different from measuring in inches? 
• L18.7 How can you estimate and measure length to the nearest yard? 
• L18.8 How can you decide which measuring tool to use to measure lengths of different objects?
• L19.1 How can you use an object with a known length to estimate the length of another object? 
• L19.2 How can you measure length to the nearest centimeter using a centimeter ruler? 
• L19.3 How can you estimate the length of an object in meters? 
• L19.4.1 How can you measure objects to the nearest centimeter and the nearest meter?
• L19.4.2 How is measuring in meters different from measuring in centimeters?
• L20.1 How can you solve two-digit addition and subtraction problems using an inch ruler or a yardstick as a number line? 
• L20.2 How can you use a number line to represent and solve addition and subtraction problems about length in inches?
• L20.3 How can you solve two-digit addition and subtraction problems using a centimeter ruler or a meter stick as a number line?
• L20.4 How can you use a number line to represent and solve addition and subtraction problems about length in centimeters?
• L20.5  How can you measure and then find the difference in the lengths of two objects?
   

• HMH grade 2- Modules 18-20
• MathBoard
• 1 inch Square tiles
• 1- inch graph paper
• Crayon
• Chenille sticks
• Inch ruler
• Marker
• Yardstick
• Measuring tape
• String
• Centimeter ruler
• Meter stick
• Base-ten blocks
• Standard pocket folders

• Estimate
• Inch
• ruler
• Inch ruler
• Line plot
• Foot
• Yard
• Yardstick
• Measuring tape
• Centimeter
• Centimeter ruler
• Meter
• Meter stick

• Are you ready? (For All Modules)
• Module Test form A (For All Modules)
  • If needed Reassess Test form B (For All Modules)

PA Core Mathematics Standards
Module 21 

•  CC.2.3.2.A.1 Students acquire the knowledge and skills needed to: Analyze and  draw two- and three-dimensional shapes having specified attributes.

Module 22 

•   CC.2.2.2.A.3 Students acquire the knowledge and skills needed to: Work with  equal groups of objects to gain foundations for multiplication.
• CC.2.3.2.A.2 Students acquire the knowledge and skills needed to: Use the  understanding of fractions to partition shapes into halves, quarters, and thirds.

• Three-dimensional shapes have faces, edges, and vertices. 
• Shapes have different names based on their different attributes. 
• Fractions have equal shares. 
• Shapes can be divided into halves, thirds, or fourths. 
• Shapes can look different but still be the same size.

• Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces. Identify triangles, quadrilaterals, pentagons, hexagons, and cubes. 
• Partition a rectangle into rows and columns of same-size squares and count to find the total number of them.
• Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends.
• Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half of, a third of, etc., and describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape.

Module 21

• Identify and describe three-dimensional shapes according to the number of faces, edges, and vertices.
• Name three-, four-, five-, and six-sided shapes according to the number of sides and vertices.
• Identify angles in two-dimensional shapes.
• Sort two-dimensional shapes according to their attributes.

Module 22

• Partition rectangles into same-sized squares and find the total number of these squares.
• Identify and name equal shares of circles and rectangles as halves, thirds, or fourths.
• Partition circles and rectangles to show halves, thirds, or fourths
• Identify and describe one equal share as a half of, a third of, or a fourth of a whole.
• Use visual models to show that equal shares of the same wholes do not need to have the same shape.

Module 21

• How can I identify and describe the attributes of two- and three-dimensional shapes?
• What strategies can I use to draw shapes that meet specific criteria?
• How do shapes and their attributes help us understand and describe the world around us?

Module 22

• How can I use equal groups to build an understanding of multiplication?
• What does it mean to divide a shape into equal parts, and how do those parts relate to fractions?
• How are multiplication and partitioning similar in the way they group and divide objects or shapes?
• How can visual models help me understand equal groups and fractions?
   

• L21.1 How can you describe and compare the attributes of a three-dimensional shape?
• L21.2 How can you describe and compare the attributes of a two-dimensional shape?
• L21.3 How can you find and count angles in two-dimensional shape? 
• L21.4 How can you compare two-dimensional shapes by the number of sides  and angles? 
• L22.1 How can you use colored tiles to help you find how many rows and columns are in a rectangle?
• L23.2 How can you identify and name shares of shapes as halves, thirds, and fourths?
• L24.3 How can you draw to show halves, thirds, and fourths of a shape?
• L25.4 How can you draw and color to show a half of, a third of, or a fourth of a shape? 
• L25.5 How can you draw to show the same wholes as equal shares in two different ways? 
   

• Boxes
• Markers
• MathBoards
• Two and Three-dimensional shapes
• Dot paper
• Index cards
• Color tiles
• Crayons
   

• Angle
• Edge
• Face
• Hexagon
• Pentagon
• Quadrilateral
• Side
• Vertex
• Vertices 
• Whole
• Halves
• Thirds
• Fourths
• Half of
• columns
• Third of 
• Fourth of 
• Quarter of
• Equal shares
• Rows

• Are you ready? (For All Modules)
• Module Test form A (For All Modules)
  • If needed Reassess Test form B (For All Modules)