Topic 1: Understanding Addition and Subtraction

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1 Topic 1: Understanding Addition and Subtraction 1-1: Writing Addition Number Sentences Essential Understanding: Parts of a whole is one representation of addition. Addition number sentences can be used to show parts of a whole. Interactive Learning: Children will show word sentences with cubes and then record them. 1-2: Stories About Joining Essential Understanding: Joining parts to make a whole is one interpretation of addition. Addition number sentences can be used to show joining parts of a whole. Interactive Learning: Children listen to joining stories. They represent the stories with connecting cubes and write corresponding addition number sentences. 1-3: Writing Subtraction Number Sentences Essential Understanding: Subtraction number sentences can be used to show separating parts from a whole or comparison subtraction situations. Interactive Learning: Children use cubes to find the missing part of a whole. Then they record their results as an introduction to writing subtraction sentences. 1-4: Stories about Separating Essential Understanding: Separating parts from a whole and comparison are two interpretations of subtraction. Interactive Learning: Children listen to separating stories, model them with cubes, and write subtraction sentences to solve them. 1-5: Stories About Comparing Essential Understanding: Separating parts from a whole and comparison are two interpretations of subtraction. Interactive Learning: Children listen to comparing stories, show them with cubes, and write number sentences to solve them.

2 1-6: Connecting Addition and Subtraction Essential Understanding: Addition and subtraction have an inverse relationship. The inverse relationship between addition and subtraction can be used to find subtraction facts; every subtraction fact has a related addition fact. Interactive Learning: Children model parts of a whole using counters. Then they write addition and subtraction number sentences. 1-7: Problem Solving: Use Objects Essential Understanding: Some problems can be solved by using objects to act out the actions in the problems. Interactive Learning: Children use counters on a part-part-whole mat to determine whether to add or subtract to solve story problems.

3 Topic 2: Addition Strategies 2-1: Addition: Adding 0, 1, 2 Essential Understanding: The number relationships of 0 more than, 1 more than, and 2 more than are the basis for addition facts with 0, 1, and 2. Interactive Learning: Children identify 0, 1, and 2 counters and solve addition exercises with 0, 1, and : Addition: Doubles Essential Understanding: Doubles facts can be associated with memorable real-world situations. Interactive Learning: Children use counters and make drawings to represent doubles facts and use the representations to complete doubles facts. 2-3: Addition: Near Doubles Essential Understanding: Basic addition facts that are near doubles can be found using a related doubles fact. Interactive Learning: Children will use connecting cubes to model doubles and near doubles facts. 2-4: Addition: Adding in Any Order Essential Understanding: Two numbers can be added in any order. Interactive Learning: Children will use two-color connecting cube trains to learn about changing the order of addends in addition facts. 2-5: Addition: Adding Three Numbers Essential Understanding: Three or more whole numbers can be grouped and added in any order. Interactive Learning: Children will draw connecting cubes from a bag in order to get three numbers to add. Then they will choose an order to add the numbers.

4 2-6: Addition: Making 10 to Add 9 Essential Understanding: Addition facts involving 9 can be changed to an equivalent fact with 10. Interactive Learning: Children use counters and ten-frames to explore strategies to add with : Addition: Making 10 to Add 8 Essential Understanding: Addition facts involving 8 can be changed to an equivalent fact with 10. Interactive Learning: Children will make 10 to help them add : Problem Solving: Draw a Picture and Write a Number Sentence Essential Understanding: Information in a problem can often be shown using a picture or diagram and used to understand and solve the problem. Interactive Learning: Children will draw pictures and write number sentences to solve story problems.

5 Topic 3: Subtraction Strategies 3-1: Subtraction: Subtracting 0, 1, 2 Essential Understanding: The number relationships of 0 less than, 1, and 2 from a number by applying the concepts of 0 less than, 1 less than, and 2 less than a number. Interactive Learning: Children apply the concepts of 0 less than, 1 less than, and 2 less than to write and solve subtraction sentences. 3-2: Subtraction: Thinking Addition to Subtract Doubles Essential Understanding: Addition and subtraction have an inverse relationship. The inverse relationship between addition and subtraction can be used to find subtraction facts; every subtraction fact has a related addition fact. Interactive Learning: Children will use doubles facts to subtract. 3-3: Subtraction: Thinking Addition to 10 to Subtract Essential Understanding: Addition and subtraction have an inverse relationship. The inverse relationship between addition and subtraction can be used to find subtraction facts; every subtraction fact has a related addition fact. Interactive Learning: Children use addition facts to solve related subtraction facts. 3-4: Subtraction: Thinking Addition to 18 to Subtract Essential Understanding: Addition and subtraction have an inverse relationship. The inverse relationship between addition and subtraction can be used to find subtraction facts; every subtraction fact has a related addition fact. Interactive Learning: Children use counters and subtraction cards to model related addition and subtraction. 3-5: Subtraction: Finding the Missing Part Essential Understanding: A missing part or addend in an addition number sentence can be found by thinking about a related subtraction fact. Some missing parts/addends in an addition number sentence can be found by counting up from the given addend to the sum. Interactive Learning: Children will use a part-part-whole model to find a missing part.

6 3-6: Problem Solving: Two-Question Problems Essential Understanding: Sometimes the answer to one problem or question is needed to find the answer to another problem or question. Interactive Learning: Children will use the answer to one question to answer the second question in story problems.

7 Topic 4: Place Value: Numbers to : Number: Models of Tens Essential Understanding: Numbers can be used to tell how many. The decade numbers are built on groups of ten. The oral names are similar, but not the same as the number of tens counted. Interactive Learning: Children form groups of tens using connecting cubes. They count the tens and write how many tens they have and how many ones they used. 4-2: Number: Models for Tens and Ones Essential Understanding: Numbers can be used to tell how many. In a two-digit number, the tens digit tells how many groups of tens and the ones digit tells the number of ones. Interactive Learning: Children will form groups of tens and ones using concrete materials. They will count the tens and ones and write the number. 4-3: Number: Reading and Writing Numbers Essential Understanding: The numbers 21 to 99 are written by joining two number words that describe the number of tens and the number of ones. Numbers through 20 are each represented by a unique number word. Interactive Learning: Children will read and write number words for 0 to : Number: Using Models to Compare Numbers Essential Understanding: For 2 two-digit numbers, the number with more tens is the greater number. If the two numbers have an equal number of tens, then the number with more ones is greater. Interactive Learning: Children will learn how to compare two-digit numbers using concrete materials. 4-5: Number: Using Symbols to Compare Numbers Essential Understanding: Place value can be used to compare and order numbers. Interactive Learning: Children will learn how to use the >, <, and = symbols to compare two-digit numbers.

8 4-6: Number: Before, After, and Between Essential Understanding: The position words before, after, and between can be used to explain number relationships. Interactive Learning: Children will use a hundred chart identify the number that s before or after a given number or the number between two numbers. 4-7: Number: Order Numbers Essential Understanding: Ordering 3 or more numbers is similar to comparing 2 numbers because each number must be compared to each of the other numbers. Interactive Learning: Children order 3 two-digit numbers from least to greatest. 4-8: Patterns: Number Patterns on a Hundred Chart Essential Understanding: Counting and place-value patterns can be seen on a hundred chart. Interactive Learning: Children identify and extend number patterns on a hundred chart. 4-9: Patterns: Even and Odd Numbers Essential Understanding: Some numbers can be divided into two equal groups (even numbers) and some cannot (odd numbers). Interactive Learning: Children will use cubes to determine which numbers, from 1 through 20, are even and which are odd. 4-10: Problem Solving: Use Data from a Chart Essential Understanding: In order to solve problems, data needs to be selected from a source outside the statement of the problem like a chart. Interactive Learning: Children will use a chart to solve problems.

9 Topic 5: Counting Money 5-1: Money: Dime, Nickel, and Penny Essential Understanding: Specific coins each have a unique value. The size of a coin does not indicate its value. Interactive Learning: Children will identify the value of a group of dimes, nickels, and pennies. Supplementary lesson: 3-Minute Coin Grab; Pattern Block Activity 5-2: Money: Quarter and Half-Dollar Essential Understanding: Specific coins each have a unique value. The size of a coin does not indicate its value. Interactive Learning: Children will take three coins from a collection and find the value. 5-3: Money: Counting Collections of Coins **Supplement with Math Center: Problem Solving: Tricky-Triangle Money Puzzle Essential Understanding: Money amounts can usually be counted in different ways. When counting money, it is usually easier to start with the coin or bill with the greatest value. Interactive Learning: Children will explore how to count on to find the total amount of a set of mixed coins. 5-4: Money: Ways to Show the Same Amount Essential Understanding: The same amount of money can often be represented using different combinations of coins and bills. Interactive Learning: Children will use different combinations of coins to show 1 dollar. 5-5: Money: One Dollar Essential Understanding: Specific coins or bills each have a unique value. The size of a coin does not indicate its value. Interactive Learning: Children count combinations of dollar bills and coins.

10 5-6: Money: Problem Solving: Make an Organized List Essential Understanding: Some problems can be solved be generating a list of outcomes and organizing that list in a systematic way so all outcomes are accounted for. Interactive Learning: Children will make an organized list using tallies to show combinations of coins to make a given amount of money. Supplementary lesson: Illuminations: Making Change

11 Topic 6: Mental Addition 6-1: Addition: Adding Tens Essential Understanding: Adding tens is like adding ones. Interactive Learning: Children use tens rods and unit cubes to model addition of a multiple of ten to a two-digit number. 6-2: Addition: Adding Ones Essential Understanding: When adding a number less than ten to a two-digit number using the traditional algorithm, it may be necessary to rename 10 ones as 1 ten. Interactive Learning: Children use the make-ten strategy to mentally add a one-digit number to a two-digit number. 6-3: Addition: Adding Tens and Ones Essential Understanding: Two-digit numbers can be broken apart using tens and ones and added in different ways. Interactive Learning: Children model mental math strategies to add two-digit numbers using ten-frame cards. 6-4: Addition: Adding on a Hundred Chart Essential Understanding: Patterns on a hundred chart can be used to add numbers and to develop mental math strategies and number sense. Interactive Learning: Children will use the patterns on a hundred chart to add 2 twodigit numbers. Supplementary Lesson: Counting Puzzle 6-5: Problem Solving: Look for a Pattern Essential Understanding: Some problems can be solved by identifying elements that repeat in a predictable way. Interactive Learning: Children will use connecting cubes to look for a pattern to solve problems.

12 Topic 7: Mental Subtraction 7-1: Subtraction: Subtracting Tens Essential Understanding: Subtracting tens is like subtracting ones. Interactive Learning: Children use little ten-frames to subtract multiples of ten from a two-digit number. 7-2: Subtraction: Finding parts of 100 Essential Understanding: When the total is 100 and one part is known, the other part can be found using different counting strategies. Interactive Learning: Children use little ten-frames to model a known part of 100 to find the missing part. 7-3: Subtraction: Subtracting on a Hundred Chart Essential Understanding: Patterns in a hundred chart can be used to subtract numbers and to develop mental math strategies and number sense. Interactive Learning: Children will use a hundred chart to find the difference between 2 two-digit numbers. 7-4: Subtraction: Adding On to Subtract Essential Understanding: The difference between two numbers can be found by adding up from the smaller number to the larger number. Interactive Learning: Children use models to find the difference between 2 two-digit numbers. 7-5: Problem Solving: Missing or Extra Information Essential Understanding: Some problems have data missing needed to find the answer, and some problems have extra data not needed to solve the problem. Interactive Learning: Children identify extra information and missing information in a problem.

13 Topic 8: Adding Two Digit Numbers 8-1: Addition: Regrouping 10 Ones for 1 Ten Essential Understanding: 10 ones can be regrouped for 1 ten. Interactive Learning: Children will use connecting cubes to model the addition of onedigit numbers to two-digit numbers. They will decide if regrouping is needed. 8-2: Addition: Models to Add Two- and One-Digit Numbers Essential Understanding: The standard addition algorithm for two-digit and one-digit numbers breaks the calculations into simpler calculations using place value, starting with the ones and then the tens. Answers to the simpler calculations are used to give the final sum. Interactive Learning: Children will model adding a one-digit number to a two-digit number and record their work. They will decide if regrouping is needed. Supplementary Lesson: Cover a Flat 8-3: Addition: Adding Two- and One-Digit Numbers Essential Understanding: The standard addition algorithm for two-digit and one-digit numbers breaks the calculation into simpler calculations using place value, starting with the ones and then the tens. Answers to the simpler calculations are used to give the final sum. Interactive Learning: Children will use paper and pencil to add one-digit numbers to two-digit numbers with and without regrouping. 8-4: Addition: Models to Add Two-Digit Numbers Essential Understanding: The standard algorithm for adding two-digit and two-digit numbers is just an extension of the algorithm for adding two-digit and one-digit numbers. The ones are added first and then the tens. Interactive Learning: Children use connecting cubes to model adding 2 two-digit numbers and then record the sum. They will decide if regrouping is needed.

14 8-5: Addition: Adding Two-Digit Numbers **Supplement with Math Center Problem Solving: Target Sum Essential Understanding: The standard algorithm for adding two-digit and two-digit numbers is just an extension of the algorithm for adding two-digit and one-digit numbers. The ones are added first and then the tens. Interactive Learning: Children will use paper and pencil to add two-digit numbers to other two-digit numbers, with and without regrouping. 8-6: Addition: Adding Three Numbers Essential Understanding: Three numbers can be grouped and added in any order. Interactive Learning: Children will add 3 two-digit numbers using strategies such as doubles, counting on, and making 10 when appropriate. 8-7: Problem Solving: Draw a Picture and Write a Number Sentence Essential Understanding: Information in a problem can often be shown using a diagram and used to solve the problem. Interactive Learning: Children draw pictures and write number sentences to solve story problems.

15 Topic 9: Subtracting Two-Digit Numbers 9-1: Subtraction: Regrouping 1 Ten for 10 Ones Essential Understanding: 1 ten can be regrouped for 10 ones. Interactive Learning: Children will use connecting cubes to represent numbers and complete subtraction problems. 9-2: Subtraction: Models to Subtract Two- and One-Digit Numbers Essential Understanding: The standard algorithm breaks the calculation into simpler calculations starting with the ones and then the tens. Interactive Learning: Children will model subtracting a one-digit number from a twodigit number and record their work. Supplementary Lesson: Math Center: Pick-a-Pattern 9-3: Subtraction: Subtracting Two- and One-Digit Numbers Essential Understanding: The standard subtraction algorithm breaks the calculation into simpler calculations starting with the ones and then the tens. Interactive Learning: Children will use paper and pencil to subtract one-digit numbers from two-digit numbers, with and without regrouping. 9-4: Subtraction: Models to Subtract Two-Digit Numbers Essential Understanding: The standard algorithm for subtracting two-digit and twodigit numbers is just an extension of the algorithm for subtracting two-digit and one-digit numbers. Interactive Learning: Children will use models to subtract a two-digit number from a two-digit number. 9-5: Subtraction: Subtracting Two-Digit Numbers Essential Understanding: The standard algorithm for subtracting two-digit and twodigit numbers is just an extension of the algorithm for subtracting two-digit and one-digit numbers. Interactive Learning: Children will use paper and pencil to subtract two-digit numbers from other two-digit numbers, with and without regrouping.

16 9-6: Subtraction: Using Addition to Check Subtraction Essential Understanding: The inverse relationship between addition and subtraction can be used to check subtraction. Interactive Learning: Children will subtract two-digit numbers and check their answers by writing the related addition problem. 9-7: Problem-Solving: Two-Question Problems Essential Understanding: Sometimes the answer to one problem/question is needed to find the answer to another problem/question. Interactive Learning: Children will solve two-question problems by first answering one question and then using that result to answer a second question.

17 Topic 10: Using Addition and Subtraction 10-1: Addition: Adding Money Essential Understanding: The process for adding money written using cent notation is the same as adding whole numbers. Interactive Learning: Children will learn how to complete and record addition problems using two-digit coin amounts. 10-2: Addition: Estimating Sums Essential Understanding: Rounding is a process for finding a multiple of 10 or 100 closest to a given number. Rounding can be used to estimate sums as can place value and number relationships. Interactive Learning: Children will estimate the sum of two-digit numbers. 10-3: Addition: Ways to Add Essential Understanding: All sums and differences can be found using models (cubes). Some calculations are done easily using mental math or paper and pencil. More complex calculations can be done using a calculator. Interactive Learning: Children will use different methods to help them solve addition problems. 10-4: Subtraction: Subtracting Money Essential Understanding: The process for subtracting money written using cent notation is the same as subtracting whole numbers. Interactive Learning: Children will learn how to subtract two-digit coin amounts. 10-5: Subtraction: Estimating Differences Essential Understanding: Rounding can be used to estimate differences as can place value and number relationships. Interactive Learning: Children will estimate differences by finding the number of dimes they have left after buying toys.

18 10-6: Subtractions: Ways to Subtract Essential Understanding: All sums and differences can be found using models (cubes). Some calculations are done easily using mental math or paper and pencil. More complex calculations can be done using a calculator. Interactive Learning: Children will use different methods to solve subtraction. 10-7: Problem Solving: Try, Check, and Revise Essential Understanding: Some problems can be solved by making a reasoned first try for what the answer might be and then through additional reasoning arrive at the correct answer. Interactive Learning: Children will solve problems involving adding and subtracting money by using the try, check, and revise strategy.

19 Topic 11: Geometry 11-1: Geometry: Flat Surfaces, Vertices, and Edges Essential Understanding: Three-dimensional or solid figures have length, width, and height. Many can be described, classified, and analyzed by their faces, edges, and vertices. Interactive Learning: Children describe the number of faces, vertices, and edges of solid figures. 11-2: Geometry: Relating Plane Shapes to Solid Figures Essential Understanding: Three-dimensional or solid figures have length, width, and height. Many can be described, classified, and analyzed by their faces, edges, and vertices. Many everyday objects closely approximate standard geometric solids. Interactive Learning: Children identify the plane shapes that are made by tracing the flat surfaces of solid figures. 11-3: Geometry: Making New Shapes Essential Understanding: Many everyday objects closely approximate standard geometric solids. Some shapes can be combined to make new shapes. Interactive Learning: Children use pattern blocks to make and trace larger shapes. Then they count the number of sides and vertices. 11-4: Geometry: Cutting Shapes Apart Essential Understanding: Some shapes can be decomposed into other shapes. Interactive Learning: Children draw lines on large shapes to form two or more smaller shapes. 11-5: Geometry: Congruence Essential Understanding: Shapes in the plane can be the same size and shape. Interactive Learning: Children will identify and create congruent shapes.

20 11-6: Geometry: Ways to Move Shapes Essential Understanding: Shapes in the plane can be translated (slid), rotated (turned), or reflected across a line (flipped). Interactive Learning: Children will show translations, rotations, and reflections with pattern blocks. 11-7: Geometry: Symmetry Essential Understanding: Some shapes can be reflected across one or more lines passing through the shape so the shape folds onto itself exactly. Interactive Learning: Children will cut out shapes that have symmetry and shapes that do not have symmetry. 11-8: Problem Solving: Use Reasoning Essential Understanding: Some problems can be solved by reasoning about the conditions in the problem. Interactive Learning: Children will use clues to solve riddles about plane shapes and solid figures.

21 Topic 12: Fractions 12-1: Fractions: Wholes and Equal Parts Essential Understanding: A region can be divided into equal-sized parts in different ways. Equal-sized parts of a region have the same area but not necessarily the same shape. Interactive Learning: Children fold paper to show 2 and 4 equal parts. 12-2: Fractions: Unit Fractions and Regions Essential Understanding: A fraction describes the division of a whole (region, set) into equal part. A unit fraction names one of the equal parts. Interactive Learning: Children will use pattern blocks to identify and show unit fractions of a region. 12-3: Fractions: Non-Unit Fractions and Regions Essential Understanding: A fraction describes the division of a whole (region, set) into equal parts. The bottom number in a fraction tells how many equal parts the whole is divided into. The top number tells how many equal parts are indicated. Interactive Learning: Children use pattern blocks to show and name non-unit fractions of a region. 12-4: Fractions: Estimating Fractional Parts of a Whole Essential Understanding: Benchmark fractions can be used to estimate fractional amounts. Interactive Learning: Children use the benchmark 0, ½, and 1 to estimate fractional parts of a whole. 12-5: Fractions: Fractions of a Set Essential Understanding: A fraction describes the division of a whole (region, set) into equal parts. A unit fraction names one of the equal parts. Interactive Learning: Children name and how fractions of a set.

22 12-6: Problem Solving: Use Objects Essential Understanding: Some problems can be solved by using object to act out actions in the problem. Interactive Learning: Children will use objects to model and solve problems involving fractions of a group.

23 Topic 13: Measurement: Length and Area 13-1: Measurement: Thinking About Attributes Essential Understanding: Objects have different attributes and some attributes are measurable. Interactive Learning: Children will explore the attributes of a cup and how those attributes can be measured. 13-2: Measurement: Exploring Length Essential Understanding: The length of some attributes is measurable. Interactive Learning: Children will estimate and measure classroom objects using nonstandard units. 13-3: Measurement: Measuring Length Using Nonstandard Units Essential Understanding: Measurement is a process of comparing a unit to the object being measured. The length of any object can be used as a measurement unit for length. Interactive Learning: Children will measure the length and height of classroom objects using two nonstandard units, connecting cubes and paper clips. 13-4: Measurement: Inches, Feet, and Yards Essential Understanding: The length of any object can be used as a measurement unit for length, but a standard unit is always the same length. Interactive Learning: Children will identify and draw items that are about an inch, about a foot, and about a yard. 13-5: Measurement: Centimeters and Meters Essential Understanding: The length of any object can be used as a measurement unit for length, but a standard unit is always the same length. Interactive Learning: Children will find and measure classroom objects that are about 1 centimeter and 1 meter long.

24 13-6: Measurement: Exploring Perimeter Essential Understanding: The distance around a figure is the perimeter. To find the perimeter of a polygon, add the length of the sides. Interactive Learning: Children will draw shapes on dot paper and find the perimeter of the shapes. 13-7: Measurement: Exploring Area Essential Understanding: The amount of space inside a shape is its area and area can be estimated and measure using square units. Interactive Learning: Children will use a square pattern block to find the area of two figures. 13-8: Problem Solving: Use Objects Essential Understanding: Some problems can be solved by using objects to act out the actions in the problem. Interactive Learning: Children use objects to measure the area of shapes and to find the distance around the shapes.

25 Topic 14: Measurement: Capacity and Weight 14-1: Measurement: Exploring Capacity **Supplement with Capacity worksheet (has picture of pitchers, spoons, cups.) Essential Understanding: Capacity is a measure of the amount of liquid a container can hold. Different units can be used to measure capacity. Interactive Learning: Children will use a nonstandard unit to compare the capacities of containers. 14-2: Measurement: Measuring Capacity Using Nonstandard Units Essential Understanding: Capacity is a measure of the amount of liquid a container can hold. Different units can be used to measure capacity. Interactive Learning: Children will estimate the capacity of a container and then measure the capacity using a nonstandard unit. 14-3: Measurement: Cups, Pints, and Quarts Essential Understanding: Capacity is a measure of the amount of liquid a container can hold. Different units can be used to measure capacity. Interactive Learning: Children will explore the relationship among cups, pints, and quarts, and identify containers that approximate those units. Supplementary Lesson: Gallon Man (7 sheets) 14-4: Measurement: Liters Essential Understanding: Capacity is a measure of the amount of liquid a container can hold. Different units can be used to measure capacity. Interactive Learning: Children will explore the relationship of various containers that are more than, less than, and about 1 liter. 14-5: Measurement: Exploring Weight Essential Understanding: The weight of an object is a measure of how heavy an object is. Different units can be used to measure weight and they are related to each other. Interactive Learning: Children compare the weight of objects by holding objects in each hand and then placing them on a balance scale.

26 14-6: Measurement: Ounces and Pounds Essential Understanding: The weight of an object is a measure of how heavy an object is. Different units can be used to measure weight and they are related to each other. Interactive Learning: Children identify objects that weigh about the same as, more than, and less than 1 ounce and 1 pound. 14-7: Measurement: Grams and Kilograms Essential Understanding: Mass is a measure of the quantity of matter in an object. Different units can be used to measure mass. Interactive Learning: Children identify objects that measure about the same as, more than, and less than 1 gram and 1 kilogram. 14-8: Problem Solving: Use Objects Essential Understanding: Some problems can be solved by using objects to act out actions in the problem. Interactive Learning: Children use nonstandard units to measure objects in different ways.

27 Topic 15: Measurement: Time and Temperature 15-1: Time: Telling Time to Five Minutes Essential Understanding: Time can be given to the nearest five minutes. Time can be expressed using different units that are related to each other. Interactive Learning: Children tell time to five minutes on analog clocks. 15-2: Time: Telling Time Before and After the Hour Essential Understanding: Time can be expressed before or after the hour. Interactive Learning: Children tell time using minutes before and after the hour. 15-3: Time: Estimating Time Essential Understanding: The amount of time an event lasts can be estimated. Interactive Learning: Children identify activities that take about one second, one minute, one hour, and one day. 15-4: Time: Using a Calendar Essential Understanding: A calendar shows days, weeks, and months. Interactive Learning: Children complete, read, and use a calendar to answer questions. 15-5: Temperature: Fahrenheit and Celsius Essential Understanding: Temperature can be expressed using degrees Fahrenheit or Celsius. Interactive Learning: Children will read and show temperatures on a thermometer in degrees Fahrenheit and Celsius. 15-6: Problem Solving: Multiple-Step Problems Essential Understanding: Some problems can be solved by first finding and solving a sub-problem(s) and then using that answer(s) to solve the original problem. Interactive Learning: Children find and answer hidden questions to solve story problems.

28 Topic 16: Graphs and Probability 16-1: Graphs: Organizing Data Essential Understanding: Data can be organized in different ways. Interactive Learning: Children will use the results of a survey to make a bar graph. Children will then answer questions using the data shown by the bar graph. 16-2: Graphs: Pictographs Essential Understanding: Each type of graph is most appropriate for certain kinds of data. Pictographs and bar graphs make it easy to compare data. Interactive Learning: Children will represent data using a tally chart and a pictograph. 16-3: Graphs: Bar Graphs Essential Understanding: Each type of graph is most appropriate for certain kinds of data. Pictographs and bar graphs make it easy to compare data. Interactive Learning: Children will use the results of a survey to make a tally chart and a bar graph. Then children will answer questions using the data shown by the bar graph. 16-4: Graphs: Coordinate Graphs Essential Understanding: There is a scheme (called the Cartesian Coordinate System) that uses perpendicular number lines intersecting at zero on each to name the location of the points in the plane. Interactive Learning: Children will use ordered pairs to describe the location of cubes on a coordinate grid. 16-5: Graphs: Likely and Unlikely Essential Understanding: The likelihood of an event occurring can be described using the words likely and unlikely. Interactive Learning: Children use two different-colored groups of connecting cubes and predict which color they will more likely pick.

29 16-6: Graphs: Certain, Probable, and Impossible Essential Understanding: The likelihood of an event occurring can be described using the words certain, probable, and impossible. Interactive Learning: Children will spin a two-colored spinner ten times and analyze the results to determine what colors are certain, probable, and impossible to spin. 16-7: Problem Solving: Use a Graph Essential Understanding: Some problems can be solved by making, reading, and analyzing a graph. Interactive Learning: Children sort manipulatives, make both a picture and bar graph to show the results, and then solve the problem using the graphs.

30 Topic 17: Numbers and Patterns to : Number: Building 1,000 Essential Understanding: Numbers can be used to tell how many. Interactive Learning: Children will draw 1,000 Xs on hundred charts, and then count to 1, : Number: Counting Hundreds, Tens, and Ones Essential Understanding: Numbers can be used to tell how many. Our number system is based on groups of ten. Whenever we get 10 in one place value, we move to the next greater place value. Interactive Learning: Children will use place-value models to represent numbers up to 1, : Number: Reading and Writing Numbers to 1,000 Essential Understanding: Our number system is based on groups of ten. Whenever you get 10 in one place value, you move to the next greatest place value. Interactive Learning: Children identify and record numbers up to 1,000 in expanded form, standard form, and number word form. 17-4: Number: Changing Numbers by Hundreds and Tens Essential Understanding: Adding or subtracting hundreds or tens is similar to adding or subtracting single-digit numbers. Interactive Learning: Children use models, drawings, or mental math to find 10 more, 10 less, 100 more, and 100 less than a three-digit number. 17-5: Patterns: Patterns with Numbers on Hundreds Charts Essential Understanding: Counting and place-value patterns can be seen on hundreds charts. Interactive Learning: Children identify patterns of numbers increasing by ones, tens, and hundreds. 17-6: Number: Comparing Numbers Essential Understanding: Place value can be used to compare and order numbers. Interactive Learning: Children will compare 2 three-digit numbers.

31 17-7: Number: Before, After, and Between Essential Understanding: The position words before, after, and between can be used to explain number relationships. Interactive Learning: Children will use a number chart to identify three-digit numbers that are before, after, and between other three-digit numbers. 17-8: Number: Ordering Numbers Essential Understanding: Ordering 3 or more numbers is similar to comparing 2 numbers because each number must be compared to each of the other numbers. Interactive Learning: Children will order 3 three-digit numbers from least to greatest and greatest to least. 17-9: Problem Solving: Look for a Pattern Essential Understanding: Some problems can be solved by identifying elements that repeat in a predictable way. Interactive Learning: Children solve problems by finding number patterns.

32 Topic 18: Three-Digit Addition and Subtraction 18-1: Addition: Mental Math Essential Understanding: There is more than one way to do a mental calculation. Techniques for doing addition or subtraction calculations mentally involve changing the numbers or the expressions so the calculation is easy to do mentally. Interactive Learning: Children will use mental math to add multiples of 100 to threedigit numbers. 18-2: Addition: Estimating Sums Essential Understanding: There is more than one way to estimate a sum. Rounding gives one way to estimate sums. Interactive Learning: Children will estimate the sum of 2 three-digit numbers as either greater than or less than a multiple of a hundred. 18-3: Addition: Models for Adding with Three-Digit Numbers Essential Understanding: The standard addition algorithm for three-digit numbers breaks the calculation into simpler calculations using place value starting with the ones, then the tens and then the hundreds. Interactive Learning: Children will use place-value blocks to add three-digit numbers. 18-4: Addition: Adding Three-Digit Numbers Essential Understanding: The standard addition algorithm for three-digit numbers break the calculation into simpler calculations using place value starting with the ones, then the tens and then the hundreds. Interactive Learning: Children will use paper and pencil to find the sum of 2 three-digit numbers. 18-5: Addition: Mental Math: Ways to Find the Missing Parts Essential Understanding: There is more than one way to do a mental calculation. Interactive Learning: Children will count on or count back from the whole to the known part to find a missing part.

33 18-6: Subtraction: Estimating Differences Essential Understanding: There is more than one way to estimate a difference. Rounding is one way to estimate differences. Interactive Learning: Children will find the nearest hundred of 2 three-digit numbers to estimate their differences. 18-7: Subtraction: Models for Subtracting with Three-Digit Numbers Essential Understanding: The standard subtraction algorithm for three-digit numbers breaks the calculation into simpler calculations using place values starting with the ones, then the tens, and then the hundreds. Interactive Learning: Children will use place-value blocks to subtract three-digit numbers. 18-8: Subtraction: Subtracting Three-Digit Numbers Essential Understanding: The standard subtraction algorithm for three-digit numbers breaks the calculation into simpler calculations using place values starting with the ones, then the tens, and then the hundreds. Interactive Learning: Children will use paper and pencil to subtract three-digit numbers. 18-9: Problem Solving: Make a Graph Essential Understanding: Some problems can be solved by making, reading, and analyzing a graph. Interactive Learning: Children will use data from a table to make a bar graph.

34 Topic 19: Multiplication Concepts 19-1: Multiplication: Repeated Addition and Multiplication Essential Understanding: Repeated addition involves joining equal groups and is one way to think about multiplication. Interactive Learning: Children model multiplication using repeated addition to write number sentences and solve problems. 19-2: Multiplication: Building Arrays Essential Understanding: An array involves joining equal groups and is one way to think about multiplication. Interactive Learning: Children will use counters to build arrays and then use the arrays to help write multiplication sentences. 19-3: Multiplication: Writing Multiplication Stories Essential Understanding: Some real-world situations involve repeated addition or arrays and can be solved using multiplication. Interactive Learning: Children will draw pictures and write multiplication stories to find products. 19-4: Multiplication: Vertical Form Essential Understanding: Multiplication expressions can be represented horizontally or vertically. Interactive Learning: Children use equal groups of counters to write multiplication in horizontal and vertical forms. 19-5: Multiplication: Multiplying in Any Order Essential Understanding: Two numbers can be multiplied in any order. Interactive Learning: Children rotate arrays to see that numbers can be multiplied. 19-6: Problem Solving: Draw a Picture and Write a Number Sentence Essential Understanding: Information in a problem can often be shown using a diagram and used to solve the problem. Some problems can be solved by writing and completing a number sentence or equation. Interactive Learning: Children draw pictures as a way to solve problems.

35 Topic 20: Division Concepts and Facts 20-1: Division: Division as Sharing Essential Understanding: Sharing involves separating equal groups and is one way to think about division. Interactive Learning: Children will use counters to divide a set of objects into equal groups. 20-2: Division: Division as Repeated Subtraction Essential Understanding: Repeated subtraction involves separating equal groups and is one way to think about division. Interactive Learning: Children will use counters and repeated subtraction to find the number of equal groups into which a set of objects can be divided. 20-3: Division: Writing Division Stories Essential Understanding: Some real-world situations involve repeated subtraction or sharing and can be solved using division. Interactive Learning: Children will draw a picture and write a story for a division sentence. 20-4: Division: Relating Multiplication and Division Essential Understanding: Multiplication and division have an inverse relationship. Interactive Learning: Children will make arrays using counters and write a multiplication and related division sentence for them. 20-5: Problem Solving: Make a table and Look for a Pattern Essential Understanding: Some problems can be solved by recording and organizing data in a table and by finding and using numerical patterns in the table. Interactive Learning: Children make input/output tables to solve problems.

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