BOE APPROVED 2/14/12 REVISED 9/25/12 Subject/Grade Level: MATHEMATICS/GRADE 3 Curriculum Scope & Sequence Unit Duration Common Core Standards/ Unit Numeration 6 Days Standards: Reviewing 2.NBT.1 Reviewing 2.MD.8 3.NBT.1 3.NBT.2 1-1 Hundreds 1-2 Thousands 1-5A Understanding Number Lines 1-5B Counting on the Number Line 1-5 Comparing Numbers 1-6 Ordering Numbers 1-7 Counting Money 1-8 Making Change 1-9 Problem Solving: Make an Organized List develop a facility with numbers that will serve them throughout their study of math concepts. Our number system is based on groups of ten. In our numeration system, the value of a digit is determined by its position. When counting money it is often easiest to start with the bills or coins that have the greatest value. Place value can be used to compare and order numbers. Can counting up be an effective way to make change? Is place value important when comparing and ordering numbers? How can a mastery of place value and counting money help us in life? Adding Whole Numbers 12 Days Standards: 3.OA.8 3.OA.9 3.MD.3 3.NBT.1 3.NBT.2 combine groups of numbers/objects/ money amounts accurately. 2-1 Addition Meaning and true. Properties Relationships can be 2-2 Adding on a Hundred Chart described and 2-3 Using Mental Math to Add generalizations made for 2-4 Rounding mathematical situations that Addition can be used to solve real world problems that involve joining, separating, part-part whole or comparison. There are properties that are used to govern arithmetic and algebra that are always How can addition properties be used to show relationships that always hold true? How can you use patterns on a hundreds chart to add two digit numbers? How can you break apart numbers to help you add 2 digit numbers using mental math?
2-5 Estimating Sums 2-6 Adding 2-Digit Numbers 2-7A Adding with an Expanded Algorithm 2-7 Models for Adding 3-Digit Numbers 2-8 Adding 3-Digit Numbers 2-9 Adding 3 or More Numbers 2-10 Problem Solving: Draw a Picture have numbers or objects that repeat in predictable ways. Algorithms for number operations, for both mental math and pencil and paper, use equivalence to transform calculations into simpler ones. Numbers can be approximated with numbers that are close. Calculations can be approximated by replacing numbers with other numbers that are close and easy to compute mentally. Any number, numerical expression, or equation can be represented in an infinite number of ways that have the same value. Doing Math involves a variety of processes including problem solving, reasoning, communicating, representing. How can you round numbers? How can you estimate sums? How can you use addition to solve problems? Subtraction Number Sense 5 Days Standards: Reviews 2.OA.5 Reviews 2.NBT.5 Prepares for 2.NBT.2 3.NBT.2 3.OA.8 deduct groups of numbers/objects/mo ney accurately from a whole group and Some real-world problems involving joining, separating, part-part-whole, or comparison can be solved using subtraction. Patterns on a hundred chart can be used to subtract When do we subtract? How can you subtract on a hundred chart? How can you subtract using mental math? How can we use
3-1 Subtraction Meanings 3-2 Subtracting on a Hundred Chart 3-3 Using Mental Math to Subtract 3-4 Estimating Differences 3-5 Problem Solving: Reasonableness compare differences. numbers and to develop mental math strategies and number sense. There is more than one way to do a mental calculation. There is more than one way to estimate a difference. Answers to problems should always be checked for reasonableness, and this can be done in different ways. estimation and rounding to check to see if our answers are reasonable? Subtracting Whole Numbers to Solve Problems 10 Days Standards: 3.NBT.1 3.NBT.2 3.OA.8 3.MD.3 4-1A Making Sense of Addition and Subtraction Equations 4-1 Models for Subtracting 2-Digit Numbers 4-2 Subtracting 2-Digit Numbers 4-3B Subtracting with an Expanded Algorithm 4-3 Models for Subtracting 3-Digit Numbers 4-4 Subtracting 3-Digit Numbers 4-5 Subtracting Across Zero 4-6 Problem Solving: Draw a Picture and Write a Number Sentence. their knowledge of place value relationships to be more efficient problem solvers outside of school. Doing mathematics involves a variety of processes including problem solving, reasoning, communicating, connecting, and representing. Sometimes it is necessary to rename 1 tens as 10 ones when solving subtraction problems. Place value relationships can help simplify mathematical operations and equations. Have you ever needed coins for a dollar machine, but only had a dollar bill? What would you do? What operation is used to take apart and away from a whole? Are all numbers easy to subtract in your head?
Multiplicatio 14 Days Standards: n Meaning 3.OA.1 and Facts 3.OA.3 3.OA.4 3.OA.5 3.OA.9 3.MD.7.b 3.OA.8 3.NBT.3 3.OA.7 5-1 Multiplication as Repeated Addition 5-2 Arrays and Multiplication 5-3 Using Multiplication to Compare 5-4 Writing Multiplication Stories 5-5 Problem Solving: Writing to Explain 5-6 2 and 5 as Factors 5-7 10 as a Factor 5-8A Multiplying by Multiples of 10 5-8 9 as a Factor 5-9 Multiplying with 0 and 1 5-10 Problem Solving: Two- Question Problems multiplication and explain their procedures in reallife situations such as comparing quantities, deciding how much of something is needed, and following a recipe. Some real-world problems involving joining or separating equal groups or comparison can be solved using multiplication. Repeated addition involves joining equal groups and is one way to think about multiplication. An array involves joining equal groups and is one way to think about multiplication. A times as many comparison is one way to think about multiplication. Mathematical explanations can be given using words, pictures, numbers, or symbols. A good explanation should be correct, simple, complete, and easy to understand. How can you find the total number of objects in equal groups? What are arrays, and how do they show multiplication? How can you use multiplication to compare? How can you write a story to describe a multiplication fact? How do you write a good mathematical explanation? Multiplicatio n Fact Strategies: Use Known Facts 16 Days Standards: 3.OA.3 3.OA.5 3.OA.8 3.MD.7.c 3.OA.9 3.MD.8 independently use articulate multiplication facts and properties so that in the long run For a given set of numbers, there are relationships that are always true called properties, and these are the rules that govern arithmetic. Can you use an array to solve multiplication problems? When might you need to multiply three numbers?
6-1AThe Distributive Property 6-1 3 as a Factor 6-2 4 as a Factor 6-3 6 and 7 as Factors 6-4 8 as a Factor 6-5 11 and 12 as Factors 6-6 Multiplying with 3 Factors 6-7A Multiplying to Find Combinations 6-7 Problem Solving: Multiple-Step Problems they will be able to quickly and accurately solve multiplication word and computation problems. Division Meanings 8 Days Standards: 3.OA.2 3.OA.3 3.OA.4 3.OA.6 7-1 Division as Sharing 7-2A Finding Missing Numbers in a Multiplication Table 7-2 Understanding Remainders 7-3 Division as Repeated Subtraction 7-4A Problem Solving: Choose an Appropriate Equation 7-4 Writing Division Stories 7-5 Problem Solving: Use Objects and Draw a Picture to identify how addition, subtraction and multiplication relate to division so that in the long run they may more easily solve division problems. Students will understand that some real-world problems involving joining or separating equal groups or comparison can be solved using division. Sharing involves separating equal groups and is one way to think about division. The remainder when dividing must be less than the divisor. When solving a real-world problem that involves division with a remainder, the nature of the question asked determines how to interpret and use the remainder. Repeated subtraction involves separating equal How can you think of division as sharing? How many are left over? How can you think of division as repeated subtraction? What kinds of stories involve division situations? How can you use objects and draw a picture to solve a problem?
Division Facts 14 Days Standards: 3.OA.2 3.OA.3 3.OA.4 3.OA.6 3.OA.7 8-1 Relating Multiplication and Division 8-2 Fact Families with 2, 3, 4, and 5 8-3 Fact Families with 6 and 7 8-4 Fact Families with 8 and 9 8-5A Making Sense of Multiplication and Division Equations 8-5 Dividing with 0 and 1 8-6 Problem Solving: Draw a Picture and Write a Number Sentence to articulate division facts and properties so that in the long run they will be able to quickly and accurately use division in real world scenarios involving the separation of a whole. groups and is one way to think about division. Sharing and repeated subtraction both involve separating equal groups and are 2 ways to think about division. Some problems can be solved by using objects to act out the problem or by drawing a picture to show the actions in the problem. Multiplication and division have inverse relationships. The inverse relationship between multiplication and division can be used to find division facts; every division fact has a related multiplication fact. How are multiplication and division facts related? How can you use multiplication to help you divide?
Patterns and 5 Days Standards: Relationships 3.OA.9 9-1 Repeating Patterns 9-2 Number Sequences 9-3 Extending Tables 9-6 Geometric Patterns recognize and be able to continue patterns that occur mathematically and in everyday life. Some patterns consist of shapes or numbers arranged in a unit that repeats. Some numerical sequences have a rule that tells how to generate more numbers in the sequence. Some real-world quantities have a mathematical relationship; the value of one quantity can be found if you know the value of the other quantity. How can you continue a repeating pattern? What is the pattern? What pairs of numbers fit a pattern? Solids and Shapes 6 Days Standards: Reviews 1.G.2 3.G.1 3.G.2 10-1 Solid Figures 10-2 Relating Solids and Shapes 10-5 Polygons 10-6 Triangles 10-7 Quadrilaterals 10-8A Combining and Separating Shapes 10-8B Making New Shapes 10-8 Problem Solving: Make and Test Generalizations Students will identify, classify, and describe properties of standard two- and three-dimensional shapes independently in order to recognize geometry in the world around them. Three-dimensional figures have length, width, and height. They can be classified and analyzed by their faces, edges, and vertices. Many everyday objects closely approximate standard geometric shapes. Shapes can be used to describe some attributes of some solids. Two-dimensional or plane shapes have many properties that make them different from one another. Polygons can be described and classified by their sides and angles. Commonalities in attributes of objects or situations can be found and used to make What is a solid figure? How can you describe parts of solid figures? What is a polygon? How can you describe triangles? What are some special names for quadrilaterals? How can you use the attributes of two- and three-dimensional shapes to classify them?
and test generalizations about relationships. Understandin g Fractions 18 Days Standards: 3.NF.1 3.G.2 3.NF.2.a 3.NF.3.d 3.NF.3 3.NF.3.a 3.NF.3.b 3.NF.2 3.NF.2.b 3.NF.3.c 3.OA.3 12-1 Dividing Regions into Equal Parts 12-2A Fractions and Regions 12-3 Fractions and Sets 12-4 Benchmark Fractions 12-5A Comparing Fractions Using Benchmarks 12-5 Finding Equivalent Fractions 12-6 Using Models to Compare Fractions 12-7A Using Models to Compare Fractions: Same Numerator 12-7B Comparing Fractions on the Number Line 12-7 Fractions on the Number Line 12-8A Equivalent Fractions and the Number line 12-8B Whole Numbers and represent and interpret real world items as fractional parts. A region can be divided into equal-sized parts in different ways. A fraction describes the division of a whole (region, set, segment) into equal parts. A fraction is relative to the size of a whole. Each fraction can be associated with the unique point on the number line. Fractions can be approximated by other fractions that are close. The same fractional amount can be represented by an infinite set of different but equivalent fractions. To add fractions with like denominators, add the numerators and write the sum over the same denominator. To subtract fractions with like denominators, subtract the numerators and write the difference over the same denominator. How can you divide a region into equal parts? How can you show and name part of a region? How can a fraction name a part of a group? How do you estimate parts? How can different fractions name the same part of a whole? How can you write fractions in simplest form? How can you compare fractions? How can you locate and compare fractions and mixed numbers on a number line? How can you add fractions? How can you subtract fractions?
Fractions 12-10 Problem Solving: Make a Table and Look for a Pattern Customary Measurement 6 Days Standards: Prepares for 3.MD.2 3.MD.2 3.MD.4 14-1 Understanding Measurement 14-2 Fractions of an Inch 14-3 Using Inches, Feet, Yards, and Miles 14-4 Customary Units of Capacity 14-5 Units of Weight 14-6 Problem Solving: Act It Out and Use Reasoning measure and describe attributes of real world objects using quantified unit amounts. Measurement compares a unit to the object being measured. The length of any object can be a measurement unit for length, but a standard unit, such as an inch, is always the same length. The smaller the unit used, the more units are needed to equal a given length. You do not need to start at 0 to use a ruler to measure length. Fractions of an inch give measurements that are closer to the actual lengths of objects than whole inches. Inches, feet, yards and miles are standard units for measuring length and they are related to each other. Capacity is a measure of the amount of liquid a container can hold. The weight of an object is a measure of how heavy an object is. Some problems can be How do you measure an object in inches? How do you measure to a fraction of an inch? How can you estimate and measure length? How can you estimate and measure capacity? What customary units describe how heavy something is? How can you act out and use reasoning to solve problems?
Metric Measurement 4 Days Standards: 3.MD.2 3.OA.9 15-1 Using Centimeters and Decimeters (can be taught in science) 15-2 Using Meters and Kilometers (can be taught in science) 15-3 Metric Units of Capacity (can be taught in science) 15-4 Units of Mass (can be taught in science) 15-5A Problem Solving: Draw a Picture 15-5 Problem Solving: Make a Table and Look for a Pattern measure and describe attributes of real world objects using quantified unit amounts. solved by using objects to act out the actions in the problem. Some problems can be solved by reasoning about the conditions in the problem. Centimeters, decimeters, meters, and kilometers are standard units for measuring length in the Metric System and they are related to each other. Capacity is a measure of the amount of liquid a container can hold. Mass is a measure of the quantity of matter in an object. Weight and mass are different. Some problems can be solved by recording and organizing data in a table and using numerical patterns in a table. How can you estimate and measure length? How can you estimate and measure capacity? How do you differentiate between mass, weight and capacity? How can you use a table and pattern to solve a problem? Perimeter, 14 Days Standards: Area, and 3.MD.8 Volume 3.NBT.2 find 3.MD.5 the area and 3.MD.5.a, perimeter of regular 3.MD.5.b and irregular shapes 3.MD.6 that exists in the real 3.MD.7 world. 3.MD.7.a, 3.MD.7.b units. The distance around a figure is its perimeter which is the sum of the length of the sides. Different shapes can have the same perimeter. The region inside a shape is its area and can be measured using square How do you find perimeter? How do you find the perimeter of common shapes? How do you find the perimeter of shapes? What shapes can you make when you know the perimeter?
3.MD.8 3.MD.7.c 3.MD.7.d 3.G.2 Previews 5.MD.3 16-1 Understanding Perimeter 16-2A Tools and Units for Perimeter 16-2 Perimeter of Common Shapes 16-3 Different Shapes with the Same Perimeter 16-4 Problem Solving: Try, Check, and Revise 16-6A Covering Regions 16-6B Area and Units 16-6 Estimating and Measuring Area 16-7A Area of Squares and Rectangles 16-7B Area and the Distributive Property 16-7C Area and Irregular Shapes 16-7D Equal Areas and Fractions 16-8 Problem Solving: Solve a Simpler Problem Area can be found by adding the square units or by multiplying. Measurements of solid figures can be estimated or approximated. How do you find area? How do you estimate to find the area of an irregular shape? Time and Temperature 6 Days Standards: 3.MD.1 17-1 Time to the Half Hour and Quarter Hour 17-2 Time to the Minute solve real world problems involving elapsed time. Time can be expressed using different units that are related to each other. There are different units for measuring time. Many clock times can be expressed in more than one How can you show time? Is there more than one way to show time? How can you measure how long an event takes from start to finish?
17-3 Units of Time 17-4 Elapsed Time 17-6 Problem Solving: Work Backward way. The duration of an event can be measured if one knows the start and end times for the event. Some problems with the initial data point unknown can be solved by starting with the end result, reversing the steps and processes, and working backward to the initial data point. How do we solve problems when the beginning information is unknown? Multiplying Greater Numbers 12 Days Standards: 3.NBT.3 3.OA.1 3.OA.5 3.OA.3 3.OA.7 18-1 Using Mental Math to Multiply 18-2 Estimating Products 18-4 Breaking Apart to Multiply 18-5 Using an Expanded Algorithm 18-6 Multiplying 2- and 3-Digit by 1-Digit Numbers 18-7 Problem Solving: Draw a Picture and Write a Number Sentence solve problems involving the maintenance of a budget and articulate the reasonability of their answer. Relationships can be described and generalizations made for mathematical situations that have numbers or objects that repeat in predictable ways. Numerical calculations can be approximated by replacing numbers with other numbers that are close and easy to compute with mentally. Most algorithms for operations with rational numbers, both mental math and paper and pencil, use equivalence to transform calculations into simpler ones. Rules of arithmetic and What patterns develop when we multiply by multiples of 10, 100 and 1,000? What rules for multiplying can we write based on these patterns? When might it be better to estimate a product rather than determine a precise answer? How can we use what we know about basic multiplication facts and place value to multiply large numbers? How can partial products be used to simplify multiplication algorithms? How can we use regrouping to simplify
algebra can be used together with notions of equivalence to transform equations and inequalities so solutions can be found. Doing mathematics involves a variety of processes including problem solving, reasoning, communicating, connecting and representing. multiplication algorithms? How can we use bar diagrams to solve realworld multiplication word problems? Dividing with 1-Digit Numbers 8 Days Standards: 3.OA.6 Prepares for 3.OA.7 3.OA.2 3.OA.7 Prepares for 4.OA.3 3.OA.8 19-1 Mental Math 19-2 Estimating Quotients 19-3 Connecting Models and Symbols 19-4 Dividing 2-Digit Numbers 19-5 Dividing with Remainders (only to prepare for 4 th grade) 19-6 Problem Solving: Multiple- Step Problems divide groups that occur in daily life into subgroups, such as creating sports teams for gym class. Basic facts and place-value patterns can help you mentally divide multiples of 10, 100, and 1000. There are different ways to estimate quotients. Most involve replacing numbers with other numbers that are close and that make it easy to compute mentally. The sharing interpretation for division can be used to model the standard division algorithm. When you divide whole numbers, sometimes there is a remainder. The remainder must be less than the divisor. Some problems can be solved by first finding and solving a sub-problem and then using that answer to How can you divide multiples of 10 and 100 easily? How do you estimate with division? How can you model division? What happens when some are left? How can you solve problems that require more than one step?
solve the original problem. Data, Graphs, and Probability 4 Days Standards: 3.MD.3 3.MD.4 Extends 3.MD.4 20-2 Reading Pictographs and Bar Graphs 20-3 Making Pictographs 20-4 Making Bar Graphs 20-9A Problem Solving: Length and Line Plots 20-9 Problem Solving: Use Tables and Graphs to Draw Conclusions make educated decisions based on their ability to read and interpret graphs.. Each type of graph is most appropriate for certain kinds of data. The key for a pictograph determines the number of pictures needed to represent each number in the set. In a bar graph, the scale determines how long the bar needs to be to represent each number in a set of data. Some problems can be solved by making, reading, and analyzing a graph. How can you read graphs? How do you determine how much a symbol in a pictograph represents? How can you choose a scale to make a bar graph? What conclusions can you draw from tables and graphs?