Unit: 1.1 Title: Place Value Days : 20 25 days Essential Questions How does estimation and rounding help you work with large numbers? How do you know whether to round up or down to the nearest 10 or hundreds? What strategies and algorithms can you use to help you add and subtract large numbers? How would you use an equation to solve a word problem? How do number patterns and skip counting help you to solve number problems? Content to be Learned Unit Summary: Place value provides the concepts and the foundation for all aspects and use of whole-number understanding and computation. Understanding the value and ordering of numbers along with computational flexibility will help students address real world situations. Skills Students will be able to determine the place value of digits in a number within the 1,000 s place. Students will be able to read, write, compare and order numbers within the 1,000 s place. Students will be able to add and subtract within the 1,000 s place. Students will be able to solve two step word problems using the four operations. Students will be able to write and solve simple number sentences. Student will be able to estimate and round numbers (using mental math when appropriate) within the 1,000 s place. Students will be able to identify and apply patterns within numbers to solve number problems. Assessments Formative Assessments: Daily Work Quizzes Unit Test Standards Domain: Number and Operation in Base Ten 3.NBT Cluster: Understand Place Value and properties of operations to perform multi digit arithmetic 3.NBT.1: Use place value understanding to round whole numbers to the nearest 10 or 100 3.NBT.2: Fluently add and subtract within 1,000 using strategies and algorithms based on place value, properties of operations, and or the relationship between addition and subtraction.
Sample Instructional Activities Topic #1: Understand the place value of a number within the 1,000 s place. Lab: Place Your Number Value Topic #2: Standard, Numeric and Expanded forms of numbers within the 1,000 s place. Lab: Carpet Square Math Topic #3: Comparing and Ordering Numbers Topic #4: Estimating and Rounding numbers within the 1,000 s place. Topic #5: Adding numbers within the 1,000 s place. Lab: RAFT- 1000 Wins Topic #6: Subtracting numbers within the 1,000 s place. Topic #7: Solve and write two step word problems using all four operations with estimating and rounding, mental math. Topic #8: Review and Unit Test Domain: Operations in Algebraic Thinking 3.OA Cluster: Solve problems involving the four operations, and identify and explain patterns in arithmetic 3.OA.8: Solve two step word problems using the four operations. Represent these problems using equations with the letter standing for the unknown quantity. Assess the reasonableness of answers using mental computations and estimation strategies including rounding. 3.OA.9: Identify arithmetic patterns and (including patterns in the addition table and multiplication table), and explain them using properties of operations. Resources http://www.raftbayarea.org/ideas/place%20your%20number%20value.pdf http://www.raftbayarea.org/ideas/carpet%20square%20math.pdf http://www.raftbayarea.org/ideas/1000%20wins.pdf OnCore Math Lessons 42,43,44 Investigations Math Snap-In Units Investigations Number Lines Other Resources????
Unit: 1.2 Title: Multiplication and Division Days : 20 25 days Essential Questions What is Multiplication and Division? How does skip counting and number patterns relate to multiplication? How can arrays, grouping numbers and picture models help to understand multiplication and division problems? How can a multiplication fact table help you to learn and memorize multiplication and division facts to 10? What are some strategies you can use to help solve multi-step multiplication and division word problems? How does finding the area of a rectangle relate to multiplication and division? Content to be Learned Recognize the total as the number of objects in a number of groups. Solve multiplication word problems involving equal groups and arrays. Relate the area of a rectangle to multiplying the side lengths. Represent the Distributive Property of Multiplication using arrays. Assessments Formative Assessments: Daily Work Quizzes Unit Test Oncore Assessment Investigations Games Skills Students will be able to use arrays, number groupings and picture models to understand multiplication and division properties. Students will be able to use a multiplication fact table and fact families to learn and memorize multiplication and division facts to 10. Students will be able to write and solve simple number sentences and word problems involving multiplication and division. Students will apply multiplication and division facts to finding the area of rectangles. Standards Understand properties of multiplication and the relationship between multiplication and division. 1 CCSS.Math.Content.3.OA.A.1 Interpret products of whole numbers, e.g., interpret 5 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 7. CCSS.Math.Content.3.OA.A.2 Interpret whole-number quotients of whole numbers, e.g., interpret 56 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are 1 Limited to factors of 2 5 and 10 and the corresponding dividends in this module.
partitioned into equal shares of 8 objects each. For example, describe a context in which a number of shares or a number of groups can be expressed as 56 8. CCSS.Math.Content.3.OA.A.3 Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. 1 CCSS.Math.Content.3.OA.A.4 Determine the unknown whole number in a multiplication or division equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8? = 48, 5 = _ 3, 6 6 =? Understand properties of multiplication and the relationship between multiplication and division. CCSS.Math.Content.3.OA.B.5 Apply properties of operations as strategies to multiply and divide. 2 Examples: If 6 4 = 24 is known, then 4 6 = 24 is also known. (Commutative property of multiplication.) 3 5 2 can be found by 3 5 = 15, then 15 2 = 30, or by 5 2 = 10, then 3 10 = 30. (Associative property of multiplication.) Knowing that 8 5 = 40 and 8 2 = 16, one can find 8 7 as 8 (5 + 2) = (8 5) + (8 2) = 40 + 16 = 56. (Distributive property.) CCSS.Math.Content.3.OA.B.6 Understand division as an unknown-factor problem. For example, find 32 8 by finding the number that makes 32 when multiplied by 8. Multiply and divide within 100. CCSS.Math.Content.3.OA.C.7 Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 5 = 40, one knows 40 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers. Solve problems involving the four operations, and identify and explain patterns in arithmetic. CCSS.Math.Content.3.OA.D.8 Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. 3 CCSS.Math.Content.3.OA.D.9 Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. For example, observe that 4 times a number is always even, and explain why 4 times a number can be decomposed into two equal addends. CCSS.Math.Content.3.MD.C.7 Relate area to the operations of multiplication and addition. CCSS.Math.Content.3.MD.C.7.a
Find the area of a rectangle with whole-number side lengths by tiling it, and show that the area is the same as would be found by multiplying the side lengths.
Sample Instructional Activities Topic #1: Introduce arrays and picture models to demonstrate multiplication and division properties Topic #2: Properties of Multiplication and division: Property of One (Multiplicative Identity) and Property of Zero when multiplying and dividing numbers Topic #3: Introduce Multiplication and Division Fact Families 2-10 Topic #4: Measure area by counting unit squares and by tiling and apply multiplication to finding the area of rectangles Topic #5: Write and Draw multiplication and division number sentences to solve multiplication problems Topic #6: Solve and write multiplication and divisions word problems Topic #7: Review and Unit Test Resources Oncore Lessons 1-10, 16-27, 52-54, 89-91 Investigations Unit 5 Investigations Snap-ins 3.1a Student Pages C22-C29 Sumdog
Unit: 2.1 Fractions Days : 30 days Essential Questions What are equal parts of a whole? Why do you need to know how to make equal shares? What do the top and bottom numbers of a fraction tell you? How can you tell if a fraction is equal to another fraction? What strategies can you use to compare two fractions using <, >, or = symbols? How do you read a ruler? Content to be Learned This unit will develop the use of fractions and fraction notation, and help children develop the understanding of equivalent fractions. Fractions are a part of a whole and are used in measurement. In this unit number line diagrams will be introduced and used to show and demonstrate the value of a fraction. The ruler will also be used to measure lengths and estimate the measurement of various objects and distances to the nearest half and quarter of an inch. Assessments Formative Assessments: Daily Work Quizzes Unit Test Oncore Assessment Investigations Games Skills Recognize that fractions are a part of a whole. Equal parts of a whole are used when writing/drawing a fraction. Using multiplication and division fractions can be equivalent quantities of the same whole group. You can use a number line diagram to locate and compare fractions. A strong understanding of fractions is helpful when a using a ruler. Standards 3.NF.1: Understand a fraction 1 / b as the quantity formed by one part when a whole is partitioned into b equal parts: understand a fraction a / b as the quantity formed by parts of size 1/b. 3.NF.2: Understand a fraction as a number on the number line; represent fractions on a number line diagram a. Represent a fractions 1/ b on a number line diagram by defining the interval from zero to one as the whole and portioning it into b equal parts. Recognize that each part has size 1/b and that the end point of the part based at zero locates the number 1/ b on the number line. Represent a fraction a/b on a number line diagram by marking off lengths 1/b from zero recognize that the resulting interval has size a/b and that its endpoint locates the number a/b on the number line. 3.NF.3: Explain equivalents of fractions in special cases, and compare fractions by reasoning about their size. a. Understand two fractions as equivalent (equal) if they are the
same size, or the same point on the number line. b. Recognize and generate simple equivalent fractions. Explain why the fractions are equivalent. c. Express whole numbers fractions, and recognize fractions that are equivalent to whole numbers. Compare two fractions with the same numerators or the same denominators by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of the comparisons with the symbols <, >, or = and justify the conclusions. 3.MD.4 Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by marking a line plot with a horizontal scale is marked off in appropriate units-whole numbers halves and quart. Sample Instructional Activities Lesson #1: Equal parts of a whole/equal shares Lesson #2: Find a part of a group Lesson #3: Exploring fractions with pattern blocks Lesson #4: Order Fractions using a number line Lesson #5: Compare fractions with the same denominators or the same numerators Lesson #6: Compare fractions using benchmarks Lesson #7: Model equivalent fractions and recognize equivalent fractions Lesson #8: Whole number fractions Lesson #9: Measure a line to the nearest half inch and quarter inch. Review and Unit Test Resources Investigations: Unit 7 Sessions 1.1 and 1.2 Oncore Lessons 55, 56, 57, 58, 59 61, 105,
Unit: 3.1 Geometry: Shapes and Perimeter Days : 28 days Essential Questions How is perimeter used to solve real world application problems? How are lines, rays, and line segments useful when dealing with angles and polygons? Content to be Learned Area and perimeter can be used to solve real world application problems. Lines, rays, and line segments are necessary to form angles and polygons. Parallel and Intersecting lines differ and are relevant when solving problems with angles and polygons. Assessments Quizzes Tests Unit Test Formative Assessmnet Skills Students will be able to compute the area and perimeter of quadrilaterals. Students will distinguish between lines, rays, and line segments. Students will identify different types of angles. Students will draw and recognize parallel and intersecting lines. Students will understand the characteristics of polygons and quadrilaterals. Students will solve real world problems using properties of perimeter and polygons. Standards 3.G.1: Understand that shapes in different categories (e.g. rhombuses, rectangles (and others) may share attributes and that the shared attributes can define a larger category. Recognize rhombuses and rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories. 3.MD.7: Relate area to the operations of multiplication and division. a. Find the area of a rectangle with whole number side lengths by tiling it, and show that the area is the same as would be found by multiplying the side lengths. b. Multiply side lengths to find areas of rectangle with whole number side lengths in the context of solving real world and mathematical problems, and represent whole number products as rectangular areas in mathematical reasoning. c. Use tiling to show in a concrete case that he area of a rectangle with whole number side lengths a and b + c is the sum of a x b and b x c. Use area models to represent the distributive property in mathematical reasoning.
Sample Instructional Activities Topic #1: Area Topic #2: Perimeter Topic #3: Lines, Rays and Line Segments Topic #4: Angles Topic #5: Parallel and Intersecting Lines Topic #6: Polygons Topic #7: Quadrilaterals Recognize area as additive. Find areas of rectilinear figures by decomposing them into non overlapping rectangles and adding the areas of the non overlapping parts, applying this technique to solve real world problems. 3.MD.8: Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters. Resources Oncore Lessons: 87 105
Unit: 3.2 Data: Bar Graphs Days : 21 Days Essential Questions What are some ways you can represent data? How do you read a tally table and frequency chart? What are the steps in reading and making a bar graph? What are the steps in reading and making a pictograph? What are the steps in reading and making a line plot? Content to be Learned Data can be represented in a bar graph, pictograph and line plot. Tally table and frequency tables are useful when collecting and organized data. Bar graphs, pictographs and line plots are used to show data in a more functional way. Measuring with a ruler is an important life skill Assessments Quizzes Tests Unit Test Formative Assessment Skills Students will collect and record data in tally tables and frequency tables. Students will solve problems by using the strategy make a table. Students will read and interpret data in a pictograph. Students will make a pictograph to show data in a table. Students will read and interpret data on a bar graph. Students will make a bar graph to show data in a table or pictograph. Students will use data represented in bar graphs and pictographs to solve problems. Students will read and interpret data in a line plot. Standards 3.MD.3: Draw a scaled pictograph and scaled bar graph to represent a data set with several categories. Solve one-and two-step how many more and how many less problems using information presented in scaled bar graphs. Sample Instructional Activities Topic #1- Tally and Frequency Tables Topic #2 Creating a Tally and Frequency Table Topic #3 Pictographs Topic #4 Creating a pictograph Topic #5- Bar Graphs Topic #6- Creating a Bar Graph Topic #7- Line Plots Resources Oncore Lessons: 79-85
Topic #8- Creating a line plot Topic #9- Problem Solving Using Graphs Unit: 4.1 Time, Mass, Volume Days : 21 Days Essential Questions How can an analog clock help you to determine the time, estimate time and find elapsed time? What are the different units of measurement you can use to classify the capacity, weight and mass of an object? What tools can you use to measure the capacity, weight and mass of an object? Content to be Learned Students will understand that analog and digital clocks help them to determine what time it is and how much time has passed and how to estimate time. Students will understand that there are different units of measurement for the volume and mass of objects. Students will understand that objects have different capacity, weight and mass. Assessments Quizzes Tests Unit Tests Formative Assessments Skills Students will read, write, and tell time on analog and digital clocks to the nearest hour, half hour and quarter hour. Students will divide models to make equal shares Students will read write and tell time on analog and digit clocks to the nearest 5 minute and nearest minute. Students will decide when to use A.M. and P.M. with time. Students will use a number line or an analog clock to find elapsed time. Students will estimate and measure capacity in customary units. Students will change a measure of capacity in customary units from larger to smaller units or from smaller units to larger mixed units. Students will estimate and measure weight in ounces and pounds. Students will change measures of weight in customary units from larger units to smaller units or from smaller units to larger mixed units. Students will estimate and measure capacity and mass in metric units. Standards 3.MD.1: Tell and write time to the nearest minute and measure time intervals in minutes. Solve word problems involving addition and subtraction of time intervals in minutes. 3.MD.2: Measure and estimate liquid volumes and masses of objects using standard units of grams, kilograms and liters. Add, subtract, multiply, or divide to solve one step word problems involving masses or
volumes that are given in the same units.
Sample Instructional Activities Topic #1- Review the parts of an analog clock and tell time to the nearest hour and half hour. Topic #2 - Tell time to the nearest quarter hour, nearest five minutes and nearest minute. Topic #3 - Elapsed time using a number line and an analog clock. Topic #4 - AM & PM Topic #5 - Measure and estimate liquid volumes. Topic #6 - Volume Word Problems Topic #7- Measure and estimate mass Topic #8 - Mass Word Problems Resources Oncore Lessons: 71 78 Lab: RAFT Foam Squeeze Frenzy