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

35 Unit 6: Fraction Cards and Decimal Squares 1.8A Can students use visual representations to subtract fractions with like denominators? Can students subtract fractions with like denominators? 4.NF.3.a 4.NF.3.d TO- Are they using Quick rectangles or making Survey drawings that match the context of the problem? Are they maintaining equal sized parts? Are students continuing to reason about the size of fractions? *Fractions *Fraction relationships *Equal shares *Fractions as part of a whole 2.1 Can students interpret the meaning of the numerator and the denominator of a fraction? Can students represent fractions greater than 1? Can students find fractional parts of a rectangular area? 4.NF.1 4.NF.2 Investigation 2: Ordering Fractions 3: Construct viable arguments and critique the reasoning of others. TO- Can students draw representations of fractions that range from 0/2 to 2½, including improper fractions? Are students recognizing that fractions in which the numerator and the denominator are the same equal 1? Do students recognize some equivalent fractions and use this understanding to create their representations? Quick Survey How to Make Fraction Cards (M19), Blanks for Fraction Cards (M16-18) *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 35

36 Unit 6: Fraction Cards and Decimal Squares 2.2 Can students interpret the meaning of the numerator and the denominator of a fraction? Can students represent fractions greater than 1? Can students find fractional parts of a rectangular area? 4.NF.2 3: Construct viable arguments and critique the reasoning of others. TO- Can students draw representations of fractions that range from 0/2 to 2½, including improper fractions? Are students recognizing that fractions in which the numerator and the denominator are the same equal 1? Do students recognize some equivalent fractions and use this understanding to create their representations? Quick Survey Thinking: SAB p. 31 *Fractions *Fraction relationships *Equal shares *Fractions as part of a whole *Numerator and Denominator *Halves, Fourths, Eights 2.3 Can students interpret the meaning of the numerator and the denominator of a fraction? Can students identify equivalent fractions? Can students order fractions and justify their order through reasoning about fraction equivalencies and relationships? 4.NF.1 4.NF.2 3: Construct viable arguments and critique the reasoning of others. TO- How do students Quick decide which fraction is Survey greater? Are students paying attention to the value and meaning of both the numerator and denominator? Are students recognizing equivalent fractions? Thinking: SAB p. 35 *Thirds and Sixths *Simple Equivalent Fractions (Halves and Fourths) *Mixed Numbers *Decimal Fractions as money (0.25, 0.5) Unit 6 36

37 Unit 6: Fraction Cards and Decimal Squares 2.4 Can students identify equivalent fractions? Can students compare fractions to the landmarks 0, ½, 1, and 2? 2.5 Can students order fractions and justify their order through reasoning about fraction equivalencies and relationships? Can students compare fractions to the landmarks 0, ½, 1, and 2? Can students represent fractions using a number line? 2.6 Can students order fractions and justify their order through reasoning about fraction equivalencies and relationships? Can students compare fractions to the landmarks 0, ½, 1, and 2? Can students represent fractions using a number line? 4.NF.2 4.NF.1 4.NF.2 4.NF.3.a 4.NF.1 4.NF.2 TO- How do students decide whether a fraction is less than ½ or more than ½? Do students recognize fractions that are equivalent to 0, 1, and 2? Can students sort the fractions by reasoning about fraction equivalencies and other fraction relationships they know? Quick Survey TO- How do students Quick order fractions? Survey How do students decide about the order of Comparing Fractions fractions that are close 3A: Making a Fraction in size but have different Number Line denominators? 3B: Capture Fractions TO- How do students Quick order fractions? Survey How do students decide about the order of Comparing Fractions fractions that are close 3A: Making a Fraction in size but have different Number Line denominators? 3B: Capture Fractions Landmarks Capture Fractions (M20-M21) Thinking: M23 *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 37

38 Unit 6: Fraction Cards and Decimal Squares 2.7A Can students make a line plot to display a data set of measurements involving fractions? Can students add and subtract mixed numbers with like denominators using representations and reasoning about fractions and the operations? 4.NF.3.c 4.MD.4 TO- When students use Quick the information from Survey the table to complete the line plot can they correctly plot the data? Are students statements about the data accurate? What strategies are students using to solve addition and problems? Investigation 3: Working With Decimals *Fractions *Fraction relationships *Equal shares *Fractions as part of a whole *Numerator and Denominator 3A.1 Can students multiply a whole number and a fraction? Can students use visual models to solve word problems involving multiplication of a whole number and a fraction? 4.NF.4.a 4.NF.4.b 4.NF.4.c TO- What representations and Practicing Place Value strategies do students use to solve the problems? Can students write a multiplication equation for the problem? Decimal *Halves, Fourths, Eights *Thirds and Sixths *Simple Equivalent Fractions (Halves and Fourths) 3A.2 Can students multiply a fraction and a whole number? Can students use visual models to solve word problems involving multiplication of a fraction and a whole number? 4.NF.4.a 4.NF.4.b 4.NF.4.c TO- What strategies do students use to solve the problems? Can students write a multiplication equation for the problem? Can students decide whether their answers to the problems are reasonable? Practicing Place Value Math Workshop 2A: Multiplying Fractions and Whole Numbers (SAB p. 44F) 2B: More Multiplying Fractions and Whole Numbers (SAB 44G) *Mixed Numbers *Decimal Fractions as money (0.25, 0.5) Unit 6 38

39 Unit 6: Fraction Cards and Decimal Squares 3A.3 Can students multiplying fractions and whole numbers? Are students using visual models to solve word problems involving multiplication of a fraction and a whole number? 4.NF.4.a 4.NF.4.b 4.NF.4.c What strategies do students use to solve the problems? Can students write a multiplication equation for the problem? Can students decide whether their answers to the problems are reasonable? Assessment: Multiplying with Fractions, M41 Practicing Place Value Multiplying with Fractions 2A: Multiplying Fractions and Whole Numbers 2B: More Multiplying Fractions and Whole Numbers 2C: Multiplying with Fractions *Fractions *Fraction relationships *Equal shares *Fractions as part of a whole *Numerator and Denominator 3.1 How will students identify everyday uses of fractions and decimals? Can students read and write tenths and hundredths? 3.2 Can students read and write tenths and hundredths? Can students order decimals and justify their order through reasoning about representations and meaning of the numbers? 4.NF.5 4.NF.6 4.NF.7 4.MD.2 4.NF.6 4.NF.7 6: Attend to precision. TO- Can students represent the numbers on the 10 X 10 square? Do students read and understand the meaning of the decimal numbers? Practicing Place Value 6: Attend to precision. Can students represent tenths and hundredths as part of the square? Can students use the representations and/or reason about the meaning of the decimal numbers to compare them? Can students determine the value of each number? Practicing Place Value *Halves, Fourths, Eights *Thirds and Sixths *Simple Equivalent Fractions (Halves and Fourths) *Mixed Numbers *Decimal Fractions as money (0.25, 0.5) Unit 6 39

40 Unit 6: Fraction Cards and Decimal Squares 3.3 Can students identify decimal and fraction equivalents? 3.4 Can students estimate the sums of decimal numbers? Can students use representations to combine tenths and hundredths? 3.5 Can students read and write tenths and hundredths? Can students order decimals and justify their order through reasoning about representations and meaning of the numbers? 4.NF.5 4.NF.6 4.NF.7 4.NF.7 4.MD.2 4.NF.7 4.MD.2 TO- Can students fill in the 10X 10 square to Practicing Place Value represent the decimal? Fill Two Activity (M28) Are students examining their partially filled squares to choose a decimal card that will fill the square? How are students combining the decimals to show the total? TO- Do students make reasonable estimates? Practicing Place Value Do students keep track of the meaning of each digit (i.e., which digit represents tenths, which represent hundredths, and which represent whole numbers)? TO- Do students notice whether their sum is or Practicing Place Value is not reasonable? Do students keep track of Comparing and the meaning of each Combining Decimals digit (i.e., which digit 1A: Decimal Compare represents tenths, which 1B: Fill Two represent hundredths, 1C: Making Your Own and which represent Running Logs whole numbers)? Are students able to add the numbers accurately? Thinking: SAB p *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 40

41 Unit 6: Fraction Cards and Decimal Squares 3.6 Can students read and write tenths and hundredths? Can students order decimals and justify their order through reasoning about representations and meaning of the numbers? 3.7 Can students identify fractional parts of a group? Can students order fractions with like and unlike denominators? Can students compare decimal numbers? Can students read, write, and interpret decimal fractions in tenths and hundredths? 4.NF.7 4.MD.2 4.NF.2 4.NF.7 Continuation of same assessments from session 3.5 End Of Unit Assessment: M31 Practicing Place Value Comparing and Combining Decimals 1A: Decimal Compare 1B: Fill Two 1C: Making Your Own Running Logs Practicing Place Value Thinking: M31 *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 41

42 4th Grade Math Unit 7: Moving Between Solids and Silhouettes 3.1 Can students find the number of cubes (volume) that will fit into the box made by a given pattern? 4.NF.7 Investigation 1: Representing Multiplications with Arrays persevere in solving 8: Look for and express regularity in repeated reasoning. Teacher Observation (TO)- 10 mintue Math: While students find the Practicing Place Value volume of given boxes, how close are their predictions? Are students able to use the pattern to construct the box? Rectangular Prism Resource Masters (M) 3.2 Can students design patterns for boxes that hold a given number of cubes (volume)? Can students see that cubes filling a rectangular prism can be decomposed into congruent layers? 4.NF.7 persevere in solving 8: Look for and express regularity in repeated reasoning. TO- What strategies are students using to complete the pattern? Are students able to figure out how many layers the box needs? Do students understand the relationship between the actual box and the squares that appear on the pattern? 10 mintue Math: Practicing Place Value *Cube *Rectangular Prism *How many cubes fit in an open box 3.3 Can students see that cubes filling a rectangular prism can be decomposed into congruent layers? Can students develop a strategy for determining the volume of rectangular prisms? persevere in solving 8: Look for and express regularity in repeated reasoning. TO- Are students able to find the volume without building the box? What strategies are students using to make the pattern? Do students see the relationship between the number of layers and the number of squares they need to draw for each side? 10 mintue Math: Quick Images 1A: Finding the Volume of More Boxes 1B: Building Boxes from the Bottom Up 1C: Double the Number of Cubes Thinking: SAB p. 48 Unit 7 42

43 Unit 8: How Many Packages? How Many Groups Investigation 1: Multiplication with2 Digit Numbers 1.1 Are students able to estimate 2 digit multiplication problems? Can students multiply multiples of 10? Teacher Observation (TO)-Are students using multiples of 10 to make their estimates? Closest Estimate estimate multiplication landmark multiple Resource Masters (M) Thinking: SAB p. 1 *Multiplication and Division 1.2 Are students able to estimate 2 digit multiplication problems? Can student break a problem into smaller parts to solve 2 digit multiplication combined sub products? TO- Can students create story problem and solve and 2-digit by 2-digit multiplication problem? Closest Estimate Thinking: SAB p. 5-6, 8 *Multiplication Combinations 12 X 12 *Solve and represent a 2- digit and 1-digit multiplication problem by visualizing or story context 1.3 Can student break a problem into smaller parts to solve 2 digit multiplication combined sub products? Can students multiply multiples of 10? Are students able to represent a multiplication or division problem with picture or diagrams? TO-Are to students able to solve a set of using break apart to solve 2- digit problems? Closest Estimate cluster CM Grid paper (Resource Master (M11) *Arrays *Skip counting *Relationship between multiplication and division *Remainders Unit 8 43

44 Unit 8: How Many Packages? How Many Groups 1.4 Can student break a problem into smaller parts to solve 2 digit multiplication combined sub products? Can students multiply multiples of 10? Are students able to represent a multiplication or division problem with picture or diagrams? 4.OA.3 4.OA.4 TO-Can students identify factor factors of numbers that Counting Around the are multiples of 10? Class Are to students able to solve a set of problems Multiplication Practice and using break apart to 2A: Factor Bingo solve 2-digit problems? 2B: Multiplication Can students estimate Cluster Problems and solve 2-digit 2C: Assessment: multiplication story Solving Multiplication problems? Problems Factor Bingo Gameboards A and B (M14-15) Thinking: SAB p. 14- Number Cards for 15 Factor Bingo (M16) Factor Bingo Game Explanation (M17) Assessment Checklist: Solving Multiplication Problems (M18) *Multiplication and Division *Multiplication Combinations 12 X Can student break a problem into smaller parts to solve 2 digit multiplication combined sub products? Can students multiply multiples of 10? Are students able to represent a multiplication or division problem with picture or diagrams? 2.1 Can student solve multiplication problems by changing one factor to create an easier problem? Are students able to represent a multiplication or division problem with picture or diagrams? 4.OA.3 4.OA.5 4.OA.3 4.MD.2 3. Construct viable arguments and critique the reasoning of others. Teacher discretion Counting Around the Class Multiplication Practice 2A: Factor Bingo 2B: Multiplication Cluster Problems 2C: Assessment: Solving Multiplication Problems Investigation 2: Strategies for Multiplication TO- Can students solve problems in which one Closest Estimate of the factors has been changed to a multiple of 10? *Solve and represent a 2- digit and 1-digit multiplication problem by visualizing or story context *Arrays *Skip counting *Relationship between multiplication and division *Remainders Unit 8 44

45 Unit 8: How Many Packages? How Many Groups 2.2 Can student solve multiplication problems by changing one factor to create an easier problem? Can student break a problem into smaller parts to solve 2 digit multiplication combined sub products? Can students multiply multiples of 10? 4.OA.3 3. Construct viable arguments and critique the reasoning of others. 8: Look for and express regularity in repeated reasoning. TO- Are students able to break apart a 2-digit multiplication problem to solve easily? Are students able to solve story problems with the possibility of rounding up? Closest Estimate Solving Multiplication Problems 2A: more Multiplication Cluster Problems 2B: Problems About Oranges 2C: Factor Bingo *Multiplication and Division *Multiplication Combinations 12 X Can student solve multiplication problems by changing one factor to create an easier problem? Can student break a problem into smaller parts to solve 2 digit multiplication combined sub products? Can students multiply multiples of 10? 3. Construct viable arguments and critique the reasoning of others. 8: Look for and express regularity in repeated reasoning. TO- At teacher's discretion Closest Estimate Solving Multiplication Problems 2A: more Multiplication Cluster Problems 2B: Problems About Oranges 2C: Factor Bingo Thinking: SAB p. 29 *Solve and represent a 2- digit and 1-digit multiplication problem by visualizing or story context *Arrays *Skip counting 2.4A Can students multiplying a 4-digit number by a 1-digit number? 4.OA.3 4.MD.2 3. Construct viable arguments and critique the reasoning of others. 8: Look for and express regularity in repeated reasoning. TO- Can students solve the problems accurately? What strategies do students use to solve the problems? Were they able to keep track of all the parts of the four digit number? Close Estimate with 4-Digit Numbers *Relationship between multiplication and division *Remainders Unit 8 45

46 Unit 8: How Many Packages? How Many Groups 2.4 Can student solve multiplication problems by changing one factor to create an easier problem? Can student break a problem into smaller parts to solve 2 digit multiplication combined sub products? Can students multiply multiples of 10? 2.5 Can student break a problem into smaller parts to solve 2 digit multiplication combined sub products? 3.1 Are students able to solve division problems by breaking the problem into parts or represent using pictures or diagrams? 4.OA.5 4.OA.5 4.NBT.6 4.MD.2 3. Construct viable arguments and critique the reasoning of others. 8: Look for and express regularity in repeated reasoning. 8: Look for and express regularity in repeated reasoning. TO- Can students put multiplication problems into story contexts and solve the problems? Assessment Activity (M19) Counting Around the Class Solving Multiplication Problems 2A: More Multiplication Cluster Problems 2B: Writing Multiplication Story Problems 2C: Factor Bingo Counting Around the Class Solving Multiplication Problems 2A: More Multiplication Cluster Problems 2B: Writing Multiplication Story Problems Investigation 3: Solving Division Problems TO- Can students solve division problems by making groups of the divisor? Counting Around the Class divisor division Assessment Activity (M19) Thinking: SAB p *Multiplication and Division *Multiplication Combinations 12 X 12 *Solve and represent a 2- digit and 1-digit multiplication problem by visualizing or story context *Arrays *Skip counting *Relationship between multiplication and division *Remainders Unit 8 46

47 Unit 8: How Many Packages? How Many Groups 3.2 Are students able to use multiples of 10 or break apart into parts to solve division problems? 4.OA.5 4.NBT.6 TO- Can students Closest accurately identify Estimate landmark multiples (5th, Using 10th, 20th)? Multiples of 10 Are students able to 2A: Problems About solve division problems Multiple Towers 2B: Solving Division with 2-digit and 3-digit Problems numbers? 2C: Factor Bingo remainder 300 Chart (M20) Factor Bingo (M14-15) Number Cards for Factor Bingo (M16) Factor Bingo Instructions (M17) 3.3 Are students able to use multiples of 10 or break apart into parts to solve division problems? 3.4 Are students able to use multiples of 10 or break apart into parts to solve division problems? 3.5A Can students divide a 4-digit number by a 1-digit number? 4.OA.3 4.OA.5 4.NBT.6 4.OA.5,, 4.NBT.6 4.NBT.6 8: Look for and express regularity in repeated reasoning. TO- At teacher's discretion TO- At teacher's discretion TO- Can students solve the problems accurately? What strategies do students use to solve the problems? Can students accurately express any remainders in the context of the problem? Closest Estimate Using Multiples of 10 2A: Problems About Multiple Towers 2B: Solving Division Problems 2C: Factor Bingo Counting Around the Class Using Multiples of 10 2A: Problems About Multiple Towers 2B: Solving Division Problems 2C: Factor Bingo Close Estimate with 4-Digit Numbers Factor Bingo (M14-15) Number Cards for Factor Bingo (M16) Factor Bingo Instructions (M17) Thinking: SAB p. 48 *Multiplication and Division *Multiplication Combinations 12 X 12 *Solve and represent a 2- digit and 1-digit multiplication problem by visualizing or story context *Arrays *Skip counting *Relationship between multiplication and division *Remainders Unit 8 47

48 Unit 8: How Many Packages? How Many Groups 3.5 Are students able to use the relationship between multiplication and division to solve problems? 3.6 Are students able to solve multiplication problems with 2 digit numbers by making groups of the divisor? 4.OA.3 4.OA.5 4.MD.2 4.OA.5 4.NBT.6 3. Construct viable arguments and critique the reasoning of others. TO- Are students able to solve multiplication and Counting Around the division problems with 2- Class digit and 3-digit numbers? TO- Are students able to communicate their thinking clearly? Assessment: End-of-the- Unit Assessment (M21- M22) *Multiplication and Division *Multiplication Combinations 12 X 12 *Solve and represent a 2- digit and 1-digit multiplication problem by visualizing or story context *Arrays *Skip counting *Relationship between multiplication and division Unit 8 48

49 Unit 9: Penny Jars and Plant Growth Investigation 1: Representing Multiplications with Arrays 1.1 Are students able to interpreate the points and shape of a graph in terms of the situation the graph represents? Are students able to find the difference between two values on a line graph? Teacher Observation (TO)- Quick Can students answer Survey questions about features of a 2 topic graph? Can students use the motion graph to answer questions about what the different parts of the graph show? Graph Axis Resource Masters (M) Thinking: SAB p. 6 *Graphing *Temperature *Line graphs *Change over time 1.2 Are students able to interperate the points and shape of a graph in terms of the situation the graph represents? Are students able to identify features of a graph that represents quantity and those that represent changes in quantity? TO- Can students classify words or phrases that describe speed and sketch a graph? Quick Survey *Individual change on a graph *X-axis *Y-axis *Variables *Tables Unit 9 49

50 Unit 9: Penny Jars and Plant Growth Investigation 2: Penny Jars and Towers 2.1 Are students able to find the value of one quantity in a situation of constant change, given the value of the other? Can students create a representation for a situation of constant change? 4.OA.3 4.OA.4 TO- Can students find the Closest number of something within X Estimate amount of rounds given the starting number and the number of pennies added in each round? Can students make representations of jars situations using diagrams, pictures, tables or graphs that show the number of something of each round? Table Representation Penny Jar Situation Cards (M19) Thinking: SAB p. 15 *Graphing *Temperature *Line graphs 2.2 Are students able to find the value of one quantity in a situation of constant change, given the value of the other? Can students use tables to represent the relationship between two quantities of constant change? Are students able to interpret numbers in a table in terms of what they represent? Can students create a representation for a situation of constant change? 4.OA.5 4.NBT.6 TO- Can students determine the number of something for any given round later in the sequence? Closest Estimate Thinking: SAB p. 18 *Change over time *Individual change on a graph *X-axis *Y-axis *Variables *Tables Unit 9 50

51 Unit 9: Penny Jars and Plant Growth 2.3 Are students able to find the value of one quantity in a situation of constant change, given the value of the other? Can students use tables to represent the relationship between two quantities of constant change? Can students write an arithmetic expression for finding the value of one constant? 4.OA.5 TO- Can students use the sequence to determine if the number is doubled in the 20th round or not? Quick Survey Thinking: SAB p *Graphing *Temperature *Line graphs *Change over time *Individual change on a graph 2.4 Are students able to indentify points in a graph with corresponding values in a table? Can students plot points one coordinate grid? 4.OA.5 4.NBT.6 TO- Can students complete a table and graph the results? Closest Estimate Penny Jar Talbes A and B (M23) *X-axis *Y-axis *Variables *Tables Unit 9 51

52 Unit 9: Penny Jars and Plant Growth 2.5 Are students able to find the value of one quantity in a situation of constant change, given the value of the other? Can students write an arithmetic expression for finding the value of one constant? 4.OA.5 4.NBT.6 TO- Can students complete a table to solve for problems? Can students compare tables and graphs from 2 situations? Closest Estimate Assessment Checklist: Penny Jar Compari-sons (M27) Thinking: SAB p. 35 & 37 *Graphing *Temperature *Line graphs *Change over time 2.6 Are students able to find the value of one quantity in a situation of constant change, given the value of the other? Can students write an arithmetic expression for finding the value of one constant? 4.OA.5 4.NBT.6 TO- Can students identify whether single and double towers can ever have a given number of windows? Can students make table and graph to compare 2 situations and answer questions? Closest Estimate *Individual change on a graph *X-axis *Y-axis *Variables *Tables Unit 9 52

53 Unit 9: Penny Jars and Plant Growth 2.7 Can students find the steepness of graphs or parts of graphs in terms of rate of change? Can students make a rule to relate one variable to another in terms of constant change? Can students use symbolic letter notation to represent the value of one variable in terms of another? 4.OA.5 TO- At teacher's discretion Quick Survey *Graphing *Temperature *Line graphs *Change over time *Individual change on a graph 2.8 Can students make a rule to relate one variable to another in terms of constant change? Can students use symbolic letter notation to represent the value of one variable in terms of another? 4.OA.5 4.NBT.6 TO- Can students create rules for a pattern/ Closest Estimate *X-axis *Y-axis *Variables *Tables Unit 9 53

54 Unit 9: Penny Jars and Plant Growth Investigation 3: Collecting and Analyzing Measurements 3.1 Can students identify points in a graph with corresponding values in a table? Can students plot points on a coordinate grid? Can students find the steepness of graphs or parts of graphs in terms of rate of change? 4.OA.5 4.MD.1 4.MD.4 TO- Can students graph a Quick and make prediction for Survey growth? Can students use their graphs to answers questions about slower and faster growth? *Graphing *Temperature *Line graphs 3.2 Can students plot points on a coordinate grid? Can students find the steepness of graphs or parts of graphs in terms of rate of change? Can students find the steepness of graphs or parts of graphs in terms of rate of change? 4.OA.5 4.MD.1 4.MD.4 TO- Can students create a new graph with similar data and then compare the 2? Quick Survey *Change over time *Individual change on a graph *X-axis *Y-axis *Variables 3.3 Can students identify points in a graph with corresponding values in a table? 4.OA.5 4.NBT.6 4.MD.1 Can students create their own story to make a graph? Closest Estimate Matching Numbers, Stories, and Graphs (M36) *Tables Unit 9 54

55 Unit 9: Penny Jars and Plant Growth 3.4 Can students interpret points and shape of a graph in terms of the situation? Can students compare tables, graphs, and situations of constant change and those with out? Can students plot points on a coordinate grid? 3.5 Can students find the steepness of graphs or parts of graphs in terms of rate of change? Can students write an arithmetic expression for finding the value of one constant? Can students write and arithmetic expression for finding the value of one quantity in terms of the constant rate? 4.NBT.6 4.OA.5 4.MD.1 TO- Can students graph a constant rate of change? TO- Can students interpret data to match stories to graphs? Assessment: End-of-the- Unit Assessment (M37- M39) Closest Estimate Quick Survey Decrease *Graphing *Temperature *Line graphs *Change over time *Individual change on a graph *X-axis *Y-axis *Variables *Tables Unit 9 55

56 Unit Author Title Strand G4U1 Tang, Greg The Best of Times: Math Strategies That Multiply Multiplication and Division Investigati on 1: Represent ing Multiplica tions with Arrays Cushman, Jean Do You Wanna Bet?: Your Chance to Find Out about Probability Data Analysis and Probability G4U2 Nagda, Ann Whitehead Tiger Math: Learning to Graph from a Baby Tiger Data Analysis and Probability G4U3 Anno, Masaichiro Anno's Mysterious Multiplying Jar Multiplication and Division G4U3 Tang, Greg 4.OA.3 4.OA.4 Multiplication and Division G4U3 Michelson, Richard Ten Times Better Multiplication and Division G4U4 Adler, David A. Shape Up!: Fun with Triangles and Other Polygons 2D Geometry and Measurement G4U4 Burns, Marilyn The Greedy Triangle 2D Geometry and Measurement G4U4 Burns, Marilyn Spaghetti and Meatballs for All!: A Story 2D Geometry and Measurement G4U4 Friedman, Aileen A Cloak for the Dreamer 2D Geometry and Measurement G4U4 Tompert, Ann Grandfather Tang's Story: A Tale Told with Tangrams 2D Geometry and Measurement G4U5 McKissack, Patricia C. A Million Fish More or Less Addition, Subtraction, and the Number System G4U5 Schwartz, David M. How Much Is a Million? Addition, Subtraction, and the Number System G4U5 Schwartz, David M. On Beyond a Million: An Amazing Math Journey Addition, Subtraction, and the Number System G4U5 Wells, Robert E. Can You Count to a Googol? Addition, Subtraction, and the Number System G4U6 Hutchins, Pat The Doorbell Rang Fractions G4U6 Nagda, Ann Whitehead Polar Bear Math: Learning about Fractions from Klondike and Snow Fractions G4U6 Adler, David A. Fraction Fun Fractions G4U7 Clement, Rod Counting on Frank 3D Geometry and Measurement G4U7 Pluckrose, Henry Arthur Knowabout: Capacity 3D Geometry and G4U7 Schwartz, David M. Millions to Measure 3D Geometry and Measurement G4U7 Macaulay, David Pyramid 3D Geometry and Measurement G4U8 Birch, David The King's Chessboard Multiplication and Division G4U8 Demi, Hitz One Grain of Rice: A Folktale Multiplication and Division G4U9 Schwartz, David M. G Is for Googol: A Math Alphabet Book General Read Alouds 56

57 Read Alouds 57