4th Grade Math. Sample Lessons/Activities Unit 1: Factors, Multiples, and Arrays. Investigation 1: Representing Multiplications with Arrays

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1 Unit 1: Factors, Multiples, and Arrays Investigation 1: Representing Multiplications with Arrays 1.1 How can students demonstrate the use arrays to model multiplication find multiples of a number?+b How can students use arrays to model multiplication problems and find factors of a 2 digit number using arrays? 1.3 How can students use arrays to model multiplication problems and identify features of a prime, composite, and square numbers? 4.OA.3 4.OA.4 4.OA.3 4.OA.4 4.OA.3 4.OA.4 7: Look for and make Teacher Observation (TO)- Do students generate examples of arrays of familiar objects and find the products represented by these arrays? Today's Number TO- Do students use what they know about Today's Number multiplication to find all the arrays for a given number and label the dimensions of each array? TO- Teacher's discretion Today's Number *multiplication *array *dimension *factor *prime number *composite number *square number Resource Masters (M) Things That Come in Arrays (M1), One- Centimeter Grid paper (M2) Family Letter (M4,6,and 8) One-Centimeter Grid paper (M2) One-Centimeter Grid paper (M2) *Addition *Multiplication combinations with products to 50 *Skip counting *Recognize arrays 1.4 How can students use know multiplication combinations to solve more difficult combinations? 4.OA.3 4.OA.4 7: Look for and make TO- Can students use Array Cards to find the products of pairs of numbers from 1 x 2 to 12 x 12? Today's Number *multiplication combination Array Cards in TK (M9- M29) Factor Pairs (M30) Unit 1 1

2 Unit 1: Factors, Multiples, and Arrays 1.5 How can students manipulate large arrays into smaller arrays? 1.6A Can students solve word problems that involve multiplicative comparisons? 4.OA.3 4.OA.4 4.OA.1 4.OA.2 4.OA.3 7: Look for and make TO- Can students determine the product represented by incomplete or partially covered arrays? Assessment: Representing 8 x 6 (M31) TO- Can students solve multiplicative comparison problems using either multiplication or division equations? Today's Number Using Arrays to Multiply 1A: Array Picture Problems 1B: Factor Pairs 1C: Assessment: Representing 8 X 6 Today's Number M2 (as needed) Assessment Checklist (M32) Thinking: SAB p Multiplicative Comparison Problems M (C2) More Multiplicative Comparison Problems M (C3) *Addition *Multiplication combinations with products to 50 *Skip counting *Recognize arrays Investigation 2: Multiplication Combinations 2.1 Can students use known multiplication combinations to identify multiplications not yet known fluently? 4.OA.4 7: Look for and make TO-Can students use knowledge of multiplication combinations they know to find ones they do no know? Quick Images *product Quick Images: Seeing Numbers (M33) 2.2 Can students use known multiplication combinations to determine the products of more difficult combinations? 2.3 Can students identify whether one number is a factor or a multiple of another? 4.OA.4 4.OA.4 7: Look for and make 7: Look for and make TO- Are students to use multiplication combinations they know to help them solve and commit to memory the ones they do not know fluently? TO- Can students identify whether a number is multiple of a given factor? Quick Images Quick Images *multiple *factor Multiplication cards (M35-40 and TK) As needed: Blank Multiplication cards (M41), Practicing with Multiplication Cards explanation (M42) Multiple Cards (M46-49 and TK) Multiple Turn Over (M45) Multiple Turn Over Recording Sheet *Addition *Multiplication combinations with products to 50 *Skip counting Unit 1 2

3 Unit 1: Factors, Multiples, and Arrays 2.4 Can students use known multiplication combinations to determine the products of more difficult combinations? 2.5 Can students solve multiplication combinations using one or more strategies? 4.OA.4 4.OA.4 7: Look for and make 7: Look for and make TO-At teacher's discretion TO- Are students demonstrating fluency with multiplication combinations? Assessment: Multiplication Combinations (M51) Quick Images Multiplication Combinations 2A: Multiplication Cards 2B: Factor Pairs 2C: multiple Turn Over Quick Images Multiplication Combinations 2A: Multiplication Cards 2B: Factor Pairs 2C: multiple Turn Over Multiplication cards (M35-40 and TK) Array Cards (M9-M29 and TK) Multiple Cards (M46-49 and TK) Multiple Turn Over (M45) Multiple Turn Over Recording Sheet Multiplication Combinations (M51) As optional: M52 *Addition *Multiplication combinations with products to 50 *Skip counting Investigation 3: Finding Factors 3.1 Can students identify the factors of 100? How can students use skip counting to help them identify multiples of a number. 7: Look for and make TO- Are students able to use knowledge of multiplication combinations and reasoning to generate factors of 100/200/300? Quick Images One-Centimeter Grid paper (M2) Four 100 Charts (M53) 300 Chart (M54) Unit 1 3

4 Unit 1: Factors, Multiples, and Arrays 3.2 How were students able to use their knowledge of the factors of 100 to find factors of multiples of 100. Can students use known multiplication combinations to find related multiplication combinations for a given product? 7: Look for and make TO- Are students able to use knowledge of multiplication combinations and reasoning to generate factors of 100/200/300? Counting Around the Class One-Centimeter Grid paper (M2) Four 100 Charts (M53) 300 Chart (M54) 3.3 How can students determine the factors of a number? 4.OA.1 4.OA.2 4.OA.4 3: Construct viable arguments and critique the reasoning of others. 7: Look for and make TO- Can students identify, represent, and explain why the factors of 16 are the same as 48? Counting Around the Class One-Centimeter Grid paper (M2) Thinking: SAB p *Addition *Multiplication combinations with products to 50 *Skip counting 3.4 How can students determine the factors of a number? How will students use representations to show that a factor of a number is also a factor of its multiples? 4.OA.4 7: Look for and make End Of Unit Assessment: M55-M56 Counting Around the Class Unit 1 4

5 4th Grade Math Unit 2: Describing the Shape of the Data Investigation 1: Representing Multiplications with Arrays 1.1 Can students record and organize data in a box and describe the shape of the data distribution? 6: Attend to precision. Teacher Observation (TO)- Can students organize the data? Can students describe the shape of the data? Broken Calculator data bar graph line plot Resource Masters (M) 1.2 Can students measure heights and use the data to describe the heights? 1.3 Can students collect heights and create a representation comparing 2 data sets? 1.4 Can students collect heights and create a representation comparing 2 data sets? 1.5 Are students able to find and compare the medians of the heights? 4.MD.2 4.MD.2 4.OA.3 4.OA.4 4.MD.2 6: Attend to precision 6: Attend to precision 3: Construct viable arguments and critique the reasoning of others. 6: Attend to precision 3: Construct viable arguments and critique the reasoning of others. 6: Attend to precision TO- Can students measure carefully, trying to be as accurate as possible? TO- Do students organize and represent the data clearly? Do students create graphs that make the data sets easy to compare? To-Do students create graphs that show the data clearly and make it easy to compare the two sets of data? Do students draw some conclusions about how much taller a fourth grader is than a first grader? TO- Can students choose a method that makes sense for finding the median? Assessment: Comparing Numbers of Cavities (M7-8) Broken Calculator Broken Calculator Quick Survey Quick Survey outlier range data representation median Height Data from a First-Grade Class (M5) Centimeter Grid Paper (M6) Cavity Data from a Fourth-Grade Class (M9) Thinking: SAB p. 7 Label a graph. How to measure in inches. How to use the measuring tool to measure something longer than the measuring tool. How to set/label two graphs on one sheet of paper to compare the data. What is typical and atypical in a data set. Unit 2 5

6 4th Grade Math Unit 2: Describing the Shape of the Data 2.1 Are students able to create a survey question to compare 2 groups? 2.2 Are students able to collect data for their survey question with 2 groups? 2.3 Can students discuss how to create representations to easily compare 2 sets of data? 2.4 Are students able to use their representations to develop conclusions about their data? 2.5 Can students describe and construct theories about 3 sets of data? 4.MD.2 4.MD.2 3: Construct viable arguments and critique the reasoning of others. 6: Attend to precision. 3: Construct viable arguments and critique the reasoning of others. 6: Attend to precision. 3: Construct viable arguments and critique the reasoning of others. 3: Construct viable arguments and critique the reasoning of others. 6: Attend to precision. 7: Look for and make Investigation 2: Using Data to Compare TO- Is the survey question clear? Will it give students the information they are interested in? How will they record and keep track of whom they asked? TO- Are students able to come up with and use an organized system for recording and keeping track of responses? Do students work together to collect the data? TO- Do students create a representation or representations that allow for an easy comparison of the data sets? TO- Can students draw conclusions from their data? TO- Can students find the median for Mystery Data B? Are students supporting their theories with plausible reasons, using what they already know about the height of living objects and the characteristics of the data set? Broken Calculator Broken Calculator Quick Survey Broken Calculator Broken Calculator survey numerical data line plot bar graph conclusion Assessment Worksheet (M10) Thinking: SAB p Thinking: SAB p Looking at Mystery Data C (M15) Mystery Data C Table Thinking: SAB p. 20 and Line Plot (M16) Label a graph. How to measure in inches. How to use the measuring tool to measure something longer than the measuring tool. How to set/label two graphs on one sheet of paper to compare the data. What is typical and atypical in a data set. Unit 2 6

7 4th Grade Math Unit 2: Describing the Shape of the Data 2.6 Can students examine different possibilities for what data sets with the same median and highest and lowest values could look like? 2.7 Can students use the data as evidence to answer questions that require them to make decisions based on the data? 3.5 Can students create and use data to answer questions? 3: Construct viable arguments and critique the reasoning of others. 6: Attend to precision. 7: Look for and make 3: Construct viable arguments and critique the reasoning of others. 6: Attend to precision. TO-Can students make an accurate line plot? Broken Calculator Do students compare different aspects of the shape of the data? (ex. Highest and lowest values, outliers, median, how is the data concentrated, etc.) 3: Construct viable End Of Unit arguments and Assessment: M18- critique the M21 reasoning of others. 6: Attend to precision. TO-Are students able to Quick gather information from Survey the line lots in order to draw conclusions about the data? Investigation 3: Finding and Comparing Probabilities Broken Calculator value Label a graph. How to measure in inches. How to use the measuring tool to measure something longer than the measuring tool. How to set/label two graphs on one sheet of paper to compare the data. What is typical and atypical in a data set. Unit 2 7

8 4th Grade Math Unit 3: Multiple Towers and Division Stories 1.1 Can students represent a multiplication problem with pictures, diagrams, or models? 4.OA.3 Investigation 1: Representing Multiplications with Arrays Teacher Observation (TO)- How are students solving 14 X 12? Are they breaking apart one of the factors and multiplying both parts by the other factor? Seeing Numbers multiplication Resource Masters (M) Multiplication cards (M9-M14) 1.2 Can students use arrays to model multiplication? Are students using/developing strategies for multiplying that involve breaking apart numbers? 1.3 Can students use arrays to model multiplication? Are students using/developing strategies for multiplying that involve breaking apart numbers? 1.4 Can students use arrays to model multiplication? Are students using/developing strategies for multiplying that involve breaking apart numbers? 4.OA.3 4.OA.4 TO- Do students notice that in order to make a rectangle by combining two arrays, one of the dimensions must be the same on both? Are students considering either factor as a starting place for combining arrays? Seeing Numbers TO- When part of an array is covered, can students visualize what other arrays will Seeing Numbers Using Arrays to Model equation complete a match? Can Multiplication students record their matches correctly with an equation? 1A: Small Array/Big Array 1B: Breaking Up arrays TO- Can students 1C: Solving Multiplication equation identify the larger array Seeing Numbers that is created when the Using two smaller ones are Arrays to Model combined? Can Multiplication students break a larger 1A: Small Array/Big array into two smaller Array arrays, maintain on one 1B: Breaking Up arrays of the dimensions? 1C: Solving Multiplication Array cards (Tool kit) Printable array cards (M17-M37) Small Array/Big Array game directions (M38- M39) Small Array/Big Array Recording Sheet (M40) Array cards (Tool kit) Printable array cards (M17-M37) Small Array/Big Array game directions (M38- M39) Small Array/Big Array Recording Sheet (M40) Array cards (Tool kit) Printable array cards (M17-M37) addition basic X facts 0-12 dividend quotient divisor Unit 3 8

9 4th Grade Math Unit 3: Multiple Towers and Division Stories 1.5 Can students use arrays to model multiplication? Are students using/developing strategies for multiplying that involve breaking apart numbers? 4.OA.4 Assessment: Solving 18 X 7 (M43) Investigation 2: Division equation Seeing Numbers Using Arrays to Model Multiplication 1A: Small Array/Big Array 1B: Breaking Up arrays 1C: Solving Multiplication Problems Small Array/Big Array game directions (M38- M39) Small Array/Big Array Recording Sheet (M40) Array cards (Tool kit) Printable array cards (M17-M37) addition 2.1 How will students solve division story problems? 2.2 How are dividends, divisors, quotients, and remainders related? How can a remainder affect the answer in a division word problem? 4.OA.4 4.NBT.6 4.OA.3 4.OA.4 4.NBT.6 TO- What known multiplication or division Counting Around the relationships do Class students use to solve these division problems? Are students able to solve division story problems by acting out the situation, showing either the grouping or the number being divided? TO- Are students able to solve 44 8 by using number relationships that they know, such as 8 X 5 and 8 X 6? Are students able to determine what to do with remainders in the context of the problem situation? Counting Around the Class division remainder basic X facts 0-12 dividend quotient divisor Unit 3 9

10 4th Grade Math Unit 3: Multiple Towers and Division Stories 2.3 How can a remainder affect the answer in a division word problem? Can students represent a division problem with pictures, diagrams, or models? 2.4 Can students use known multiplication combinations to solve division problems? How can a remainder affect the answer in a division word problem? 4.OA.3 4.NBT.6 4.OA.3 4.NBT.6 3. Construct viable arguments and critique the reasoning of others. 3. Construct viable arguments and critique the reasoning of others. use of structure TO- Are students using known multiplication relationship in solving division problems? Do students recognize that the answer to the question posed in the problem may be different from the answer as expressed in a division equation do to the remainder? TO- How do students find the missing factor? (By using known multiplications, skip counting, repeated addition) Are students able to write multiplication equations that represent the problem accurately? Counting Around the Class Division Stories 2A: Small Array/Big Array 2B: More Division Stories Seeing Numbers Strategies for Division 2A: Missing Factors 2B:Small Array/Big Array 2C: More Division Stories factor Array cards (Tool kit) Printable array cards (M17-M37) Thinking: SAB p. 28 Thinking: SAB p. 31 addition basic X facts 0-12 dividend quotient divisor 2.5 Can students use known multiplication combinations to solve division word problems? 4.NBT.6 TO- Are students recognizing and using Seeing Numbers the relationship between the numbers in Strategies for Division each pair of problems? 2A: Missing Factors 2B: Related Multiplication and Division Problems Array cards (Tool kit) Printable array cards (M17-M37) Unit 3 10

11 4th Grade Math Unit 3: Multiple Towers and Division Stories 2.6 Are students able to create a story problem to represent a division expression? Can students use known multiplication combinations to solve division problems? 4.NBT.6 Assessment: Writing and Solving a Division Problem, M46 Seeing Numbers Investigation 3: Multiplying 10s addition 3.1 Can students understand the effect of multiplying by a multiple of 10? Can students find multiples of 2-digit numbers? 4.NBT.6 TO- Are students able to generate sequences of Counting Around the the multiples of 2-digit Class numbers? Do students easily calculate the 10th multiple in the sequence and use it to find other multiples? multiple factor Thinking: SAB p. 39 basic X facts 0-12 dividend quotient 3.2 Can students understand the effect of multiplying by a multiple of 10? Are students able to represent a multiplication problem with pictures, diagrams, or models? 4.OA.1 4.OA.2 4.OA.4 TO- Can students use one of the available tools to create a visual representation of the factors? Are students able to use their representation to explain the mathematical relationship between the two problems? Counting Around the Class Multiplying Groups of 10 2A: Multiplying by Multiples of 10: What Happens? 2B: Multiple Towers Thinking: SAB p. 46 divisor Unit 3 11

12 4th Grade Math Unit 3: Multiple Towers and Division Stories 3.3 Can students understand the effect of multiplying by a multiple of 10? 3.4 Can students understand the effect of multiplying by a multiple of 10? Are students able to use diverse strategies to answer multiplication combinations to 12 X 12? 4.OA.1 4.OA.2 4.OA.4 4.OA.4 8: Look for and express regularity in repeated reasoning. 8: Look for and express regularity in repeated reasoning. TO- Do students solve the second problem in each pair by relating it to the first? Can students create a story problem that represents one of the pairs of the problems? Assessment: Multiplication Combinations (M50) Counting Around the Class Multiplying Groups of 10 2A: Multiples of 10: Related Problems 2B: Story Problems About 10s 2C: Multiplying by Multilples of 10: What Happens? Counting Around the Class Multiplying Groups of 10 2A: Multiples of 10: Related Problems 2B: Story Problems About 10s Thinking: SAB p. 47 addition basic X facts 0-12 dividend quotient Investigation 4: Strategies for Multiplication divisor 4.1 Can students determine the effect on the product when a factor is doubled or halved? Are students able to represent a multiplication or division problem with pictures, diagrams, or models? 4.OA.1 4.OA.2 4.NBT.6 8: Look for and express regularity in repeated reasoning. TO- Are students recognizing that in each problem, one or two factors have been doubled? Can students make representations that show the doubling or double/half relationship? Seeing Numbers doubled halved Thinking: SAB p Unit 3 12

13 4th Grade Math Unit 3: Multiple Towers and Division Stories 4.2 Are students developing strategies for multiplying that involve breaking apart numbers? Can students use arrays to model multiplication? 4.3 Are students developing strategies for multiplying that involve breaking apart numbers? Can students determine the effect on the product when a factor is doubled or halved? 4.4 Are students developing strategies for multiplying that involve breaking apart numbers? Can students determine the effect on the product when a factor is doubled or halved? 4.OA.1 4.OA.2 8: Look for and express regularity in repeated reasoning. 6: Attend to precision. 8: Look for and express regularity in repeated reasoning. 6: Attend to precision. 8: Look for and express regularity in repeated reasoning. TO- Are students able to break the numbers of the final problem into more manageable parts? Are students recognizing the relationship between the problems in the set and the final problem to be solved? TO- How are students breaking apart these 2- digit numbers to make the problems easier to solve. Do students accurately recombine all parts of the problem to get the final product? Are students using doubling and halving to create an equivalent problem? TO- How are students breaking apart these 2- digit numbers to make the problems easier to solve. Do students accurately recombine all parts of the problem to get the final product? Are students using doubling and halving to create an equivalent problem? Seeing Numbers Seeing Numbers Strategies for Multiplication 2A: Multiplication Cluster Problems 2B: More Multiplication Problems 2C: Array Card Games Seeing Numbers Strategies for Multiplication 2A: Multiplication Cluster Problems 2B: More Multiplication Problems 2C: Array Card Games addition basic X facts 0-12 dividend quotient divisor Unit 3 13

14 4th Grade Math Unit 3: Multiple Towers and Division Stories 4.5 Are students able to solve division problems by making groups of the divisor? Are students using known multiplication combinations to solve division problems? Did students developed strategies for multiplying that involve breaking apart numbers? End Of Unit Assessment: M51-M52 6: Attend to precision. Counting Around the Class addition basic X facts 0-12 dividend quotient Unit 3 14

15 Unit 4: Size, Shape, and Symmetry Investigation 1: Representing Multiplications with Arrays 1.1 Can students use units of measurement to lengths in cm, in, ft, yd, m? 4.MD.1 4.MD.3 Teacher Observation (TO)- Are students able to measure lengths appropriately? Are students able to estimate lengths using benchmarks? Today's Number Area Volume Perimeter Linear - Measurement Inch Foot Yard Centimeter Meter Benchmark Resource Masters (M) *Linear Measurement *Perimeter *2-D shapes 1.2 Are students able to determine when to estimate or us exact measurements when needed? 4.MD.1 TO- Can students find relationships among Today's Number measurement tools? Can students use and read measurement tools accurately? Millimeter Standard System Metric System Kilometer Estimate *Attributes of Triangles and Quadrilaterals *Right Angles 1.3 Can students find the perimeter using standard units? 4.MD.1 4.MD.2 4.MD.3 TO- Can student identify and measure the perimeter of objects? Can students position measurement tool correctly? Perimeter Today's Number Measuring Length 1A: Perimeter Problems 1B: LogoPaths Activity: Missing Measures (optional) 1C: Assessment: How Long Is Our Classroom? Thinking: SAB p. 8 *Area of rectangles and other shapes through decomposition Unit 4 15

16 Unit 4: Size, Shape, and Symmetry 1.4 Can students find the perimeter using standard units and identify possible causes of measurement errors? 1.5 Can students find the perimeter using standard units and identify possible causes of measurement errors? 4.OA.3 4.OA.4 4.MD.1 4.MD.2 4.MD.3 6: Attend to precision. TO- Do students have a sense of how long the path of 100 feet long will be? Do students position the measuring tool to get the most accurate measurements? Can students accurately keep track of the length and calculate the total measurement? Today's Number Measuring Length 1A: Perimeter Problems 1B: LogoPaths Activity: Missing Measures Today's Number Measuring Length 1A: Perimeter Problems 1B: LogoPaths Activity: Missing Measures (optional) 1C: Assessment: How Long Is Our Classroom? 1D: Mapping 100 Feet Investigation 2: Polygons of Many Types Thinking: SAB p *Linear Measurement *Perimeter *2-D shapes *Attributes of Triangles and Quadrilaterals *Right Angles 2.1 Can students define a polygon by their attributes? 4.G.1 4.G.2 6: Attend to precision. TO- Are students articulating properties such as: it has to be closed, it has to have line segments for sides, the sides cannot cross? Are students identifying shapes that are less familiar as polygons? What attributes do students pay attention to as they make their rules? Quick Images Polygon Line Segment Endpoint Vertex (Vertices) Orientation *Area of rectangles and other shapes through decomposition Unit 4 16

17 Unit 4: Size, Shape, and Symmetry 2.2 Are students able to make new polygons by combining polygons? Can students identify the number of sides for various polygons? 4.G.1 6: Attend to precision. TO- Can students combine two or more Quick Images polygons to make a new shape that is a closed figure? Do students trace around the outside edge of the polygonal shapes and correctly count the number of sides? Trapezoid Equilateral Triangle Parallelogram Hexagon *Linear Measurement 2.3A Are students able to identify lines (parallel, perpendicular), angles (right, acute, obtuse) and right triangles? 2.3 Are students able to make new polygons by combining polygons? Can students identify the number of sides for various polygons by their attributes? 4.G.1 4.G.2 4.MD.3 4.G.1 4.G.2 4.MD.3 4.G.1 4.G.2 TO- Do students understand that an Quick Images 6: Attend to precision. angle that turns through n one-degree angles is said to have an angle measure of n degrees? TO- Can students combine two or more 6: Attend to precision. polygons to make a new shape that is a closed figure? Do students trace around the outside edge of the polygonal shapes and correctly count the number of sides? Quick Images Working With Polygons 3A: Guess My Rule with Shape Cards 3B: Making Polygons 3C: LogoPaths Activity: 600 Steps (optional) Point line ray line segment perpendicular lines parallel lines angle right angle acute angle obtuse angle right triangle Side Angle Right Angle Parallel Shape Cards (M19-20) *Perimeter *2-D shapes *Attributes of Triangles and Quadrilaterals *Right Angles *Area of rectangles and other shapes through decomposition Unit 4 17

18 Unit 4: Size, Shape, and Symmetry 2.4 Can students use vocabulary words to describe attributes and properties of quadrilaterals? 2.5 Can students use vocabulary words to describe attributes and properties of quadrilaterals? Can students indentify relationships between squares and rectangles? 4.G.1 4.G.2 4.G.1 4.G.2 3. Construct viable arguments and critique the reasoning of others. 6: Attend to precision. 3. Construct viable arguments and critique the reasoning of others. 6: Attend to precision. TO- What geometric terms do students use to state their rules? Can students combine two or more polygons to make a new shape that fits the given description? Assessment: What is a Quadrilateral? Quick Images Quick Images Quadrilateral Square Rectangle Thinking: SAB p. 29 *Linear Measurement *Perimeter *2-D shapes *Attributes of Triangles and Quadrilaterals *Right Angles 3.1 Can students identifying right angles as 90 degrees? Can students measure acute angles by using 90 degrees? 4.MD.6 4.MD.7 Investigation 3: Measuring Angles TO- Do students easily reognize the shape of a right angle? Can students find combinations of angles that fit into a 90-degree angle exactly? Today's Number Angle Degree Right Angle Equilateral Triangle *Area of rectangles and other shapes through decomposition Unit 4 18

19 Unit 4: Size, Shape, and Symmetry 3.2 Can students measure acute angles by using 90 degrees? Can students use known angles to measure other angles? 4.MD.6 4.MD.7 TO- Are students using what they know about 90-degree to reason about the number of degrees of the angles in the Power Polygon pieces? Today's Number Measuring and Building Angles 2A: How Many Degrees? 2B: Building Angles 2C: LogoPaths Activity: 600 Steps, other Polygons (optional) Acute Obtuse Thinking: SAB p *Linear Measurement 3.3 Can students measure acute angles by using 90 degrees? Can students use known angles to measure other angles? 3.4A Can students draw lines, parts of lines, and angles? Are students able to use the relationship between the degree measure of an angle and circular arcs? Are students able to use a protractor to measure angles? 4.MD.6 4.MD.7 4.MD.5.a 4.MD.5.b 4.MD.6 4.G.1 TO- Are students able to draw polygons containing only 90- degree angles that have more than four sides? Today's Number Measuring and Building Angles 2A: How Many Degrees? 2B: Assessment: Building Angles 2C: LogoPaths Activity: 600 Steps, other Polygons (optional) Quick Images protractor Assessment Checklist (M22) *Perimeter *2-D shapes *Attributes of Triangles and Quadrilaterals *Right Angles *Area of rectangles and other shapes through decomposition Unit 4 19

20 Unit 4: Size, Shape, and Symmetry Investigation 4: Finding Area 4.1 Can students find the area of symmetrical designs? 4.2 Can students find the area of symmetrical designs? Can students identify the large the unit of area, the a smaller the umber of units needed to measure the area? 4.MD.3 4.G.2 4.G.3 4.MD.3 4.G.2 4.G.3 TO- Can students create a symmetrical design? Quick Images Do students understand that area is the measure of the whole surface of the design? How do students find the area? TO- How do students determine area? Quick Images Symmetrical Thinking: SAB p. 52 *Linear Measurement *Perimeter *2-D shapes 4.3 Can students identify the area of polygons by decomposing shapes? 4.4 Can students identify the area of polygons by decomposing shapes? 4.MD.3 4.G.2 4.G.3 4.MD.3 4.G.2 4.G.3 TO- Do students recognize a turn of 90- degrees? Do students use congruence or symmetry in their explanation? TO- How do students find area? Do students decompose shapes into smaller to find area? Quick Images Finding Area 3A: Crazy Cakes 3B: LogoPaths Activity: Mazes (optional) Quick Images Finding Area 2A: Crazy Cakes 2B: LogoPaths Activity: Mazes (optional) 2C: Measuring Area on Geoboards Square Unit Pentagon Thinking: SAB p *Attributes of Triangles and Quadrilaterals *Right Angles *Area of rectangles and other shapes through decomposition Unit 4 20

21 Unit 4: Size, Shape, and Symmetry 4.5 Are students able to find the area of a rectangle? Are students able to find the area of a rectangle using are of a triangle? 4.6 Are students able to find the area of a rectangle? Can students identify the area of polygons by decomposing shapes? 4.7 Can students identifying right angles as 90 degrees? Can students measure acute angles by using 90 degrees? Can students identify the area of polygons by decomposing shapes? 4.MD.3 4.MD.3 4.G.3 4.MD.3 4.G.1 4.G.2 6: Attend to precision. TO- How do students determine area? TO- How do students decompose shapes? How are students finding the area of rectangles? How are students finding the area of triangles? End-of-unitassessment: Today's Number Finding Area 3A: LogoPaths Activity: Mazes (optional) 3B: Measuring Area on Geoboards 3C: Area of Rectangles Today's Number Today's Number Thinking: SAB p *Linear Measurement *Perimeter *2-D shapes *Attributes of Triangles and Quadrilaterals *Right Angles *Area of rectangles and other shapes through decomposition Unit 4 21

22 4th Grade Math Unit 5: Landmarks and Large Numbers 1.1 Can Students read, write, and sequence numbers to 1,000? 1.2 Can Students read, write, and sequence numbers to 1,000? 1.3 Can Students add and subtract multiples of 10, 100, 1,000? Can Students read, write, and sequence numbers to 1,000? 1.4 Can Students use multiples of 10 and 100 to find the difference between any 3-digit number and 1,000? Can Students represent addition and on a number line? 4.NBT.1 4.NBT.2 4.NBT.2 4.NBT.2 4.OA.3 4.OA.4 Investigation 1: Representing Multiplications with Arrays Teacher Observation (TO)- Are students able Broken Calculator to read and write Activity: Making a numbers up to 1,000? 1,000 Book Are students familiar with the structure of the number system in the hundreds? TO- Ares students able to read and write numbers in the hundreds? Do the students use landmark numbers to help them locate other numbers? TO- Can students easily add and subtract multiples of 10 and 100, starting at any number? Broken Calculator Practicing Place Value Activity: Changing Places (M15) TO- If students are either adding up or Practicing Place Value subtracting back, what size are the "chunks" of numbers that they use? Do students make use of landmark numbers at "stopping-off places" (e.g., =600) Place Value Resource Masters (M) Changing Places (M15) Changing Places Recording Sheet (M12) Change Cards for Changing Places (M10-11) Thinking: SAB p. 2 *Solving addition and problems with 2- digit and 3-digit numbers *Composition of numbers to 1,000 *Addition *Variety of situations *Addition and combinations *Addition and relationships 1.5A Can students round numbers to the nearest ten and the nearest hundred? Can students write numbers to 1,000 in expanded form? 4.NBT.2 4.NBT.3 TO- Can students round 2- or 3-digit numbers to the nearest ten or nearest hundred? Practicing Place Value expanded form less than greater than Unit 5 22

23 4th Grade Math Unit 5: Landmarks and Large Numbers 1.5 Can Students add and subtract multiples of 10, 100, and 1,000? Can Students use multiples of 10 and 100 to find the difference between any 3-digit number and 1,000? 1.6 Can Students add and subtract multiples of 10, 100, and 1,000? Can Students use multiples of 10 and 100 to find the difference between any 3-digit number and 1,000? 4.NBT.2 4.MD.2 4.NBT.2 4.MD.2 TO- Are students able to read and write 3-digit Broken Calculator numbers? Do students The recognize the value of Number System to digits in numbers? Can 1,000 students add multiples 1A: Changing Places of 10 mentally? 1B: How Many Miles to 1,000? 1C: Assessment: Numbers to 1,000 TO- Are students able to read and write 3-digit Broken Calculator numbers? Do students The recognize the value of Number System to digits in numbers? Can 1,000 students add multiples 1A: Changing Places of 10 mentally? 1B: How Many Miles to 1,000? 1C: Assessment: Numbers to 1,000 Digit Cards (M16-18) and also in tool kit. Assessment Numbers to 1,000 (M19) Assessment checklist (M20) Digit Cards (M16-18) and also in tool kit. Assessment Numbers to 1,000 (M19) Assessment checklist (M20) *Solving addition and problems with 2- digit and 3-digit numbers *Composition of numbers to 1,000 *Addition *Variety of situations 2.1 Can Students add 3 and 4-digit numbers? Can Students identify, describe, and compare addition strategies by focusing on how each strategy starts? 4.NBT.2 4.MD.2 3: Construct viable arguments and critique the reasoning of others. 6: Attend to precision. 8: Look for and express regularity in repeated reasoning. Investigation 2: Adding it Up TO- Do students have at least one addition strategy that they can use accurately and efficiently? Can students record their strategies and solutions clearly? Practicing Place Value Addition Strategies *Addition and combinations *Addition and relationships Unit 5 23

24 4th Grade Math Unit 5: Landmarks and Large Numbers 2.2 Can Students add 3 and 4-digit numbers? Can Students identify, describe, and compare addition strategies by focusing on how each strategy starts? 2.3 Can Students identify, describe, and compare addition strategies by focusing on how each strategy starts? Can Students develop arguments about why two addition expressions are equivalent? Can Students use story contexts and representations to support explanations about equivalent addition expressions? 2.4 Can Students use clear and concise notation to record addition and strategies? Can Students understand the meaning of the steps and notation of the U.S. algorithm for addition? 4.MD.2 4.MD.2 4.MD.2 3: Construct viable arguments and critique the reasoning of others. 6: Attend to precision. 8: Look for and express regularity in repeated reasoning. 3: Construct viable arguments and critique the reasoning of others. 6: Attend to precision. 8: Look for and express regularity in repeated reasoning. 6: Attend to precision. 8: Look for and express regularity in repeated reasoning. TO- Do students have at least one addition strategy that they can use accurately? Do students use the same strategy for every addition problem, or do they choose a strategy based on the number relationships in the problem? Broken Calculator TO- Can students solve some or all of the starter Broken Calculator problems mentally, or do they need to write them down and break them apart? Can students accurately follow through one of the starts to solve the final problem? TO- Can students explain Solution1, Practicing Place Value adding by place? Can students explain the U.S. algorithm, especially what they "carried" 1 means and where it comes from? Thinking: SAB p. 29 *Solving addition and problems with 2- digit and 3-digit numbers *Composition of numbers to 1,000 *Addition *Variety of situations *Addition and combinations *Addition and relationships Unit 5 24

25 4th Grade Math Unit 5: Landmarks and Large Numbers 2.5 Can Students find combinations of 3-digit numbers that add to 1,000? 2.6 Can Students add 3 and 4-digit numbers? Can Students find combinations of 3-digit numbers that add to 1,000? 3.1 Can Students read, write, and sequence numbers to 10,000? Can Students understand the structure of 10,000 and its equivalence to one thousand 10s, one hundred 100s and ten 1,000s? 3.2 Can Students read, write, and sequence numbers to 10,000? Can Students understand the structure of 10,000 and its equivalence to one thousand 10s, one hundred 100s and ten 1,000s? 4.MD.2 4.MD.2 4.NBT.1 4.NBT.2 4.NBT.1 4.NBT.2 6: Attend to precision. TO- Do students make one 3-digit number and then figure out how much more they need to get to 1,000? Do students use place value, such as focusing on the 100s first as a way of getting close to 1,000, and then filling in the 10s and 1s? Assessment: Solving Addition Problem in Two Ways (M23) TO- Can students identify the first and the last number on each chart? Do students notice and understand the pattern of numbers throughout the 100 chart? Can students identify some numbers in the middle of each chart? Practicing Place Value Broken Calculator Investigation 3: Working with Numbers to 10,000 Broken Calculator TO- Do students use what they know about Broken Calculator the number of 100s in 10,000? Can students keep track of the groups of 10s as they work their way up to 10,000? Close to 1,000 (M21) Close to 1,000 Recording Sheet (M22) Thinking: SAB p. 39 *Solving addition and problems with 2- digit and 3-digit numbers *Composition of numbers to 1,000 *Addition *Variety of situations *Addition and combinations *Addition and relationships Unit 5 25

26 4th Grade Math Unit 5: Landmarks and Large Numbers 3.3 Can Students read, write, and sequence numbers to 10,000? Can Students add and subtract multiples of 10, 100, and 1,000? Can Students recognize the place value of digits in large numbers? 3.4 Can Students add 3 and 4-digit numbers? Can Students add and subtract multiples of 10, 100, and 1,000? Can Students find combinations of 3-digit numbers that add to 1,000? 4.NBT.2 4.NBT.2 4.MD.2 TO- Can students accurately read and write numbers in the thousands? Can students identify the pace values in a 3- or 4- digit number? Do students recognize which digits of their starting number will change as the result of their computation? TO- Can students add numbers in the hundreds and thousands? Do students have at least one addition strategy that they can use accurately? Do students use clear and concise notation? Do students use their chosen strategies efficiently, combining larger "chunks" of numbers and using a minimum number of steps? Broken Calculator Practicing Place Value 2A: Planning a Road Trip 2B: Changing Places on the 10,000 Chart 2C: Close to 1,000 *Solving addition and problems with 2- digit and 3-digit numbers *Composition of numbers to 1,000 *Addition *Variety of situations *Addition and Unit 5 26

27 4th Grade Math Unit 5: Landmarks and Large Numbers 3.5 Can Students add 3 and 4-digit numbers? Can Students add and subtract multiples of 10, 100, and 1,000? Can Students find combinations of 3-digit numbers that add to 1,000? 3.6A Can Students understand placevalue concepts to 1,000,000? Can Students use >, =, and < to compare numbers to 1,000,000? Can Students write numbers to 1,000,000 in expanded form? Can Students round numbers to 1,000,000? 4.1 Can Students understand the action of problems? Can Students represent situations? Can Students represent addition and on a number line? 4.NBT.2 4.MD.2 4.NBT.1 4.NBT.2 4.NBT.3 4.NBT.2 TO- Can students add numbers in the hundreds and thousands? Do students have at least one addition strategy that they can use accurately? Do students use clear and concise notation? Do students use their chosen strategies efficiently, combining larger "chunks" of numbers and using a minimum number of steps? Practicing Place Value 2A: Planning a Road Trip 2B: Changing Places on the 10,000 Chart 2C: Close to 1,000 TO- Do students write the correct value for Practicing Place Value each digit? Do students skip an addend when the digit is 0? Investigation 4: Subtraction TO- Are students able to show the action of the Broken Calculator problem with representation? Do students have at least one efficient strategy for solving these problems? What strategies are students using? combinations *Addition and relationships *Solving addition and problems with 2- digit and 3-digit numbers *Composition of numbers to 1,000 *Addition *Variety of situations *Addition and combinations *Addition and Unit 5 27

28 4th Grade Math Unit 5: Landmarks and Large Numbers 4.2 Can Students solve problems by breaking numbers apart? Can Students represent situations? Can Students find combinations of 3-digit numbers that add to 1,000? 4.3 Can Students solve problems by breaking numbers apart? Can Students represent situations? Can Students find combinations of 3-digit numbers that add to 1,000? 4.NBT.2 4.NBT.2 TO- Do Students interpret the problems correctly; that is, do Broken Calculator Subtraction Strategies they know that they are Subtraction Story finding the difference and not combining two amounts? What strategies do students use? How do students Problems 2A: Solving Subtraction Problems 2B: What's the Story 2C: Close to 1,000 keep track of their strategies as they are showing their solutions? Are students able to write a story problem that represents a solution? TO- Do Students interpret the problems correctly; that is, do they know that they are finding the difference and not combining two amounts? What strategies do students use? How do students keep track of their strategies as they are showing their solutions? Are students able to write a story problem that represents a solution? Subtraction Broken Calculator Strategies Subtraction Story Problems 2A: Solving Subtraction Problems 2B: What's the Story 2C: Close to 1,000 Thinking: SAB p. 57 *Solving addition and problems with 2- digit and 3-digit numbers *Composition of numbers to 1,000 *Addition *Variety of situations *Addition and combinations *Addition and relationships Unit 5 28

29 4th Grade Math Unit 5: Landmarks and Large Numbers 4.4A Can students understand the meaning of the steps and notation of the U.S. algorithm for? Can students use clear and concise notation for recording addition and strategies? 4.4 Can Students understand the action of problems? Can Students develop arguments about how the differences represented by two expressions are related? Can students use story contexts and representations to support explanations about related expressions? 4.NBT.2 4.NBT.2 8: Look for and express regularity in repeated reasoning. TO- Do students understand how the Practicing Place Value numbers are broken apart to show regrouping? Can students use this algorithm to solve problems? Do they understand the shorthand notation of the algorithm? TO- Can students solve the starter problems Practicing Place Value mentally? Which starter problems do student choose to solve the final problem? If the choose the start that changes one of the numbers to a landmark, can they accurately follow through by making an adjustment for the change? *Solving addition and problems with 2- digit and 3-digit numbers *Composition of numbers to 1,000 *Addition *Variety of situations *Addition and combinations *Addition and relationships Unit 5 29

30 4th Grade Math Unit 5: Landmarks and Large Numbers 4.5 Can Students solve problems by breaking numbers apart? Can Students add 3 and 4-digit numbers? 4.6 Can Students solve problems by breaking numbers apart? Can Students add 3 and 4-digit numbers? 4.NBT.2 4.MD.2 4.NBT.2 4.MD.2 TO- Do students have at least one strategy they Practicing Place Value can use efficiently? Do students record their Solving Addition and strategies clearly and Subtraction Problems concisely? Is their 2A: Which Is Farther? computation accurate? How Much Farther? What strategies do 2B: Money Problems students use? Can 2C: Close to 1,000: Plus students write amounts and Minus of money accurately? 2D: Assessment: Do students look for Numbers to 10,000 ways to balance positive score with negative scores? Can students combine positive an negative numbers? TO- Do students have at least one strategy they Practicing Place Value can use efficiently? Do students record their Solving Addition and strategies clearly and Subtraction Problems concisely? Is their 2A: Which Is Farther? computation accurate? How Much Farther? What strategies do 2B: Money Problems students use? Can 2C: Close to 1,000: Plus students write amounts and Minus of money accurately? 2D: Assessment: Do students look for Numbers to 10,000 ways to balance positive score with negative scores? Can students combine positive an negative numbers? *Solving addition and problems with 2- digit and 3-digit numbers *Composition of numbers to 1,000 *Addition *Variety of situations *Addition and combinations *Addition and relationships Unit 5 30

31 4th Grade Math Unit 5: Landmarks and Large Numbers 4.7 Can Students solve problems by breaking numbers apart? Can Students add 3 and 4-digit numbers? Can students use clear and concise notation for recording addition and strategies? 8: Look for and express regularity in repeated reasoning. TO- Can students use strategies efficiently to Broken Calculator solve addition problems? Can students use strategies efficiently to solve problems? End-of-Unit Assessment (M29) Unit 5 31

32 Unit 6: Fraction Cards and Decimal Squares Investigation 1: Representing Multiplications with Arrays 1.1 Can students find the fractional parts of a rectangular area? Can students interpret the meaning of the numerator and the denominator of a fraction? 4.NBT.2 4.NF.1 4.NF.3.a 4.NF.3.b Teacher Observation (TO)-Can students find ¼ Practicing Place Value and ¾ of a rectangle? Can students explain how they know that it is ¼, either by demonstrating that it is composed of 6 out of 24 squares or by showing that it is 1 of 4 equal pieces? Fraction, Denominator Numerator Resource Masters (M) *Fractions *Fraction relationships *Equal shares *Fractions as part of a whole 1.2 Can students find the fractional parts of a rectangular area? Are students able to identify relationships between unit fractions when one denominator is a multiple of the other (e.g., halves and fourths, thirds and sixths) Can students identify equivalent fractions? 1.3 How are fractions used in problem-solving situations? 4.NBT.2 4.NF.3.a 4.NF.3.b 4.NBT.2 4.NF.3.d TO- Can students find and ⅓ and ⅙ of a 4X6 Practicing Place Value rectangle? Can students identify ⅓ as one of three equal parts of a whole (and ⅙ as 1 out of 6 equal parts)? Can students use correct fraction notation for the parts they identify? TO- Can students find fractional parts of 24 Practicing Place Value objects and/or group of objects represented by fractions with numerators greater than 1? Can students use representations to show that they have identified the correct quantity? Thirds Sixths *Numerator and Denominator *Halves, Fourths, Eights *Thirds and Sixths *Simple Equivalent Fractions (Halves and Fourths) *Mixed Numbers *Decimal Fractions as money (0.25, 0.5) Unit 6 32

33 Unit 6: Fraction Cards and Decimal Squares 1.4 Can students find the fractional parts of a rectangular area? Are students finding fractional parts of a group? Are students comparing the same fractional parts of different-sized wholes? 1.5 Can students find the fractional parts of a rectangular area? Are students able to write, read, and apply fraction notation? 4.OA.3 4.OA.4 4.NBT.2 4.NF.1 4.NF.3.a TO- Can students interpret the meaning of Practicing Place Value a fraction in the context of area? Finding Fractions of a Which of the fractional 5X12 Rectangle, M11. parts are students able to find easily? What strategies are students using to find fractional parts of the 5X12 rectangle? TO- Can students divide a rectangle into Practicing Place Value fractional parts and identify each of the fractions that they draw? Can students write an equations that represents the sum of all the fractional parts equaling 1? Assessment: Identifying and Comparing Fractions (M12) Thinking: M12 *Fractions *Fraction relationships *Equal shares *Fractions as part of a whole *Numerator and Denominator *Halves, Fourths, Eights *Thirds and Sixths *Simple Equivalent Fractions (Halves and Fourths) *Mixed Numbers *Decimal Fractions as money (0.25, 0.5) Unit 6 33

34 Unit 6: Fraction Cards and Decimal Squares 1.6 Can students use representations to add fractions that sum to 1? Can students add fractions with the same and related denominators? 4.NBT.2 4.NF.3.a 4.NF.3.b TO- Are students adding fractions by using what they know about representing fractions and reasoning from their knowledge of equivalent fractions and fraction combinations? Can students add fractions with like denominators mentally and explain how they know what the sum is? Can students solve problems with sums greater than 1? Practicing Place Value Fractions 2A: Adding fractions 2B: Combinations That Equal 1 2C: Finding Fractions of a Rectangle 2D: Story Problems About a Class *Fractions *Fraction relationships *Equal shares *Fractions as part of a whole *Numerator and Denominator *Halves, Fourths, Eights 1.7 Can students estimate sums of fractions? Can students use representations to add fractions that sum to 1? Can students add fractions with the same and related denominators? 4.NBT.2 4.NF.2 4.NF.3.a TO- Are students adding fractions by using what they know about representing fractions and reasoning from their knowledge of equivalent fractions and fraction combinations? Can students add fractions with like denominators mentally and explain how they know what the sum is? Can students solve problems with sums greater than 1? Practicing Place Value 2A: Adding fractions 2B: Combinations That Equal 1 2C: Finding Fractions of a Rectangle (5 X 12 and 10 X 10) *Thirds and Sixths *Simple Equivalent Fractions (Halves and Fourths) *Mixed Numbers *Decimal Fractions as money (0.25, 0.5) Unit 6 34