Course: Mathematics MSD CURRICULUM MAP Grade Level: 4 Number and Numerical Operations Time Frame: Content/Topic Observable Proficiencies/Skills How do we use numbers through the millions? Write and read large numbers. Identify places in whole numbers and the values of the digits in those places. 4:NBT1 4:NBT2 Refer to pacing guide for individual grade level How do we use decimals in our daily lives? Complete a place value chart. Compare large numbers recognizing that 700/ 70 =10 by applying concepts of place value and divisions Expand Numbers through millions. Play “Name that Number.” Play ‘Number Top It.” Play “High Number Toss.” Create a bank account statement. Role play a business exchange of money. Complete metric and standard conversion tables. Count money and make change using all US coins and bills. Keep a bank balance. Convert measurements using both standard and metric systems. 4:NBT4 Form numbers and place them on a place value grid through hundred millions. Write and read large BASE 10 numbers. Ability to play number recognition games with large numbers. Identify places in whole numbers and the values of the digits in those places. Determine magnitude estimates for calculations 4:NBT1 4:NBT2 4:NF 4:NBT3 Ongoing self-assessment of the reasonableness of solutions. How do we use counting in our everyday life? Identify even and odd numbers. Count tally marks. 4:MD4 Read table data to create a graph. Conduct a survey. How do we use measuring in our everyday Use a ruler to measure objects (mm, cm, nearest part 4:MD1 Complete a conversion chart for metric and Ongoing Can you identify the value of a digit within a number? Ongoing Is your response reasonable? Gr. 4 Performance Benchmarks & Fluency Goals SMP1 SMP4 SMP5 Number and Operations in Base 10 Daily Routines. National Standards 4:NF6 Fluently add and subtract multi-digit whole numbers using the standard algorithm. Complete grids with dictated numbers through the hundred millions. Orally read numbers through the hundred millions from print. 1 Course: Mathematics life and what tools do we use? How do we use numbers to locate things in our everyday life? How can we show numbers less than zero? Gr. 4 MSD CURRICULUM MAP of an inch). Use half circle and full circle protractor to measure angles. Use dry and liquid standard and metric. Uses vocabulary such as: longitude, latitude, over, under. Compass directions (cardinal and intermediate directions). Use ordered pairs to plot points. Use a scale to convert a map or globe measure to actual distance. Calculate a balance using debits/credits. Read positive and negative numbers on a thermometer Grade Level: 4 standard measurements. SMP3 4:MD4 Discover locations in the world from longitude and latitude clues. Take part in a scavenger hunt using compass direction clues. 4:MD1 Keep a record of a bank balance using credits and debits. Submit a record of daily temperatures for an extended period of time. Record the drop in daily temperatures as a negative. Fill in missing numbers on number lines from less than zero, whole numbers, fractions, and decimals How do you read a number line using negative and positive numbers? Read positive and negative numbers on a number line. 4NBT2 Which key words determine whether you should use addition or subtraction? Identify key words in addition and subtraction Recognize the inverse relationship between addition and subtraction. Complete addition and subtraction algorithms. Use mental computation in addition and subtraction problems. 4:OA3 In what ways can you show and describe multiplication and division? Identify key words in multiplication and division. Recognize the inverse relationship between multiplication and division. Complete multiplication algorithms. Use mental computation in problems. Explore the relationship between division addition and multiplication. 4:OA1 4:OA2 4:OA3 4:OA5 Play “Subtraction Target Practice.” Solve, using paper and pencil, single and multistep word problems in which a choice must be made whether to add or subtract. Observe students using manipulative to indicate addition or subtraction. Take timed test of addition and subtraction. Solve, using paper and pencil, single and multistep word problems in which a choice must be made whether to multiply. Take a timed test for multiplication and division facts. Complete multiplication fact tables. Utilize the HSCE protocol for open ended responses. 2 Course: Mathematics MSD CURRICULUM MAP Grade Level: 4 What are the different ways you can practice multiplication and division? Demonstrate use of flash cards. Develop fact family triangles in range 1-100 Complete multiplication table. Explore internet for appropriate practice websites. Develop proficiency with basic multiplication and division number facts using a variety of fact strategies (such as “skip counting” and “repeated subtraction”) and then commit them to memory. 4:OA4 Complete timed tests. List multiples and factors of numbers in range 1100 Observation of game playing (“Baseball Multiplication,” “Beat the Calculator,” “Multiplication/Division Top-It,” etc. Ongoing When and how is it more efficient to use paper and pencil to solve whole number calculations? Demonstrate use of various algorithms including the traditional algorithm. Perform multi-step problems and open-ended questions. 4OA3 Ongoing When and how is it more efficient to use mental math to solve whole number calculations? Mentally estimate for all operations. Choose appropriate functions for solutions to multistep and open-ended problems. Visualize realistic solutions. 4OA3 When and how is it more efficient to use a calculator to solve whole number calculations? Demonstrate use of a calculator to solve complex problems (i.e., large numbers and multi-digit) SMP5 What written procedures are used to computer 3-digit addition/subtraction problems? Demonstrate use of various algorithms in 4-digit addition/subtraction Compute solutions to word problems and open ended questions. 4:NBT3 Fluently add and subtract multi-digit whole numbers using the standard algorithm. Develop a problem solving situation using multiple steps and written explanations. . Utilize the HSCE protocol for open ended responses Ask questions that require an estimated response. Complete paper and pencil quiz utilizing different operations. Orally ask, “Does the answer make sense? “ And “Explain why.” Utilize the HSCE protocol for open ended responses. Play “Beat the Calculator.” Find unit rates. Paper and Pencil vs “Beat the Calculator” game. Calculate unit prices to determine the “better buy.” Use a calculator to solve complex problems Complete Paper and Pencil quiz involving 4-digit addition/subtraction algorithms. Develop a problem solving situation using multiple steps and written explanations (time, distance). Solve mental math problems. Utilize the HSCE protocol for open ended responses. Gr. 4 3 Course: Mathematics What written procedures are used to compute 2-digit multiplication problems? Gr. 4 Demonstrate use of various algorithms in 4-digit multiplication. Compute solutions to word problems and openended questions. What written procedures are used to compute 4 digit numbers divided by 1 digit Demonstrate use of various algorithms in division of 4 digit numbers divided by 1-digit. Compute solutions to word problems and openended questions. How would you add and subtract using decimals? Demonstrate ability to properly align decimal problems in addition and subtraction. How do you solve simple computations using U.S. money? Demonstrate ability to properly align decimal problems in addition and subtraction of money. Correctly count combinations of coins and bills. Successfully compute change in various word problems and open-ended questions. Utilize a calculator to compute amounts of U.S. money. Record withdrawals and deposits for a bank account. Demonstrate ability to accurately multiply and divide decimals. How do you multiply and divide using decimals? Ongoing MSD CURRICULUM MAP Does your answer make sense? Estimate the reasonableness of your response using inverse operations. 4:NBT5 4:NBT6 4:NF7 4:NF7 4:NF7 4OA1 Grade Level: 4 Multiply a whole number of up to four digits by a one-digit whole number, and multiply two twodigit numbers Develop a problem solving situation using multiple steps and written explanations. Solve mental math problems to be solved using dry erase boards. Utilize the HSCE protocol for open ended responses. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors. Develop a problem solving situation using multiple steps and written explanations. Solve mental math problems. Utilize the HSCE protocol for open ended responses. Solve problems involving addition and subtraction of decimals.. Solve mental math problems. Utilize the HSCE protocol for open ended responses Maintain a bank balance using credits and debits. Play Credit/Debit game. Respond to word problems involving money and making change. Utilize the HSCE protocol for open ended responses. Compare two decimals to hundredths record results using <,>,= Interpret a multiplication equation as a comparison e.g. 35=7 * 5 as a statement that 35 is 5 times as many as 7 4 Course: Mathematics MSD CURRICULUM MAP Grade Level: 4 Number and Operations - Fractions Where and when do we use fractions? Determine greater fractions within a given set. Identify part of a whole using pattern blocks. List equivalent fractions. Relate everyday items to fractions (example: clock fractions, etc.). Locate fractions on number lines. 4:NF2 4OA5 Use pattern blocks to illustrate fractions of a whole. Solve clock fraction problems. Compose a rule for finding equivalent fractions. Label sections of a number line. How do we show whole numbers, equivalent fractions, and decimals through pictures? Understand vocabulary-numerator, denominator, whole, mixed number. Illustrate whole numbers, fractions, and decimals. Represent equivalent forms of the same number. 4:NF1 4:NF5 Use pattern blocks and base ten blocks to visually identify fractional and decimal parts. Identify fractional parts of a number line. Solve “fraction of” problems using money. Rename fractions as decimals and decimals as fractions. Complete equivalent fraction models. How are numbers similar or different? Order numbers within a given set using symbols in algebraic equations. 4:NF3 4:NBT List whole, fractional, and decimal numbers in order from least to greatest and greatest to least. Solve equations using greater than, less than, and equal to. What can we use to help visualize addition and subtraction of fractions? Utilize diagrams expressing addition and subtraction of fractions. Demonstrate ability to express addition and subtraction of fractions. How do you multiply fractions by whole numbers? Gr. 4 Solve problems using a mixed number set which includes whole numbers and simple fractions. 4:NF3 Solve “fraction of” number stories. Add and subtract fractions. Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. 4:NF4 Solve word problems involving multiplication of a fraction ( with denominators 2,3,4,5,6, 8, 10, 12 &100) by a whole number. 5 Course: Mathematics MSD CURRICULUM MAP Grade Level: 4 Estimation How do you use estimation to compare objects? What are different strategies you can use for estimation? When is it useful to estimate? Distinguish between greater than, less than, and equal to symbols. State orally how numbers compare to each other. Demonstrate ability to round numbers. Demonstrate the ability to use a variety of estimation strategies. Check reasonableness of estimate. Display estimate and exact responses. 4:NBT2 Compare two sets of objects (greater than, less than, equal to) 4:NBT3 Estimate quantities using a variety of strategies such as mental math and rounding 4:NBT3 Determine reasonable and unreasonable estimates. Geometry and Measurement Geometric Properties Time Frame: Content/Topic How do you compare objects according to shapes and sizes? What are the properties of 2D figures? Can you identify the vertex, edge, face, side, and angle of a shape? How do you identify different 2D figures? What makes 2 shapes congruent? How many lines of symmetry does a shape have? Gr. 4 Observable Proficiencies/Skills National Standards Recognize congruity. Classify objects according to size and shape. Classify 2D figures based on the presence or absence of parallel or perpendicular lines, angles of a specific size and type e.g right angles Define vertex, edge, face, side, and angle. Complete a label, a diagram to identify vertex, edge, face, side, and angle of a shape Recognize and label diagrams of 2D shapes. Construct various 2D figures. List properties of various 2D figures. 4MD1 Define congruent. Recognize when shapes are congruent. Find lines of reflection. Identify lines of symmetry in a variety of shapes. Recognize that regular shapes have the same number of lines of symmetry as their sides and angles. 4G2 Performance Benchmarks Make a scale drawing of a room. Read and create maps to scale. 4G2 4MD Complete a diagram of a shape labeling vertex, edge, face, side, angle 4G2 Construct various 2D figures. Draw inscribed polygons Identify 2D shapes by their sides and angles. Create Venn Diagrams to compare and contrast. Indicate shapes in pictures and around room. Match congruent shapes. 4G3 Use a ruler to indicate the lines of symmetry in a variety of 2D shapes. Fold papers to create lines of symmetry. Use pattern blocks to create shapes with various lines of symmetry. 6 Course: Mathematics MSD CURRICULUM MAP Grade Level: 4 What are the parts of a line? Label parts of a line. Define point, line, line segment, rays, angle types, and end point. 4G1 How do we classify angles as acute, right, straight, or reflex? Know the definition of acute, right, obtuse, reflex and straight angles. Measure angles to label. Categorize angles by name. Define diameter, radius, and center of a circle. Label parts of a circle. 4G1 4MD5 Display ability to draw and measure angles using a protractor. Solve addition and subtraction problems to find unknown angles. 4MD6 4MD7 What are the parts of a circle? How do you measure angles and then classify them? 4MD5 Construct lines using line segments, rays, and form points, using rulers. Label the parts of the line using letters, property name, line segments, lines, angles and rays. Use a compass to construct a line segment. Use geoboards to construct a variety of lines. Use a compass to create acute, right, obtuse, reflex and straight angles. Use a compass to measure the amount of degrees in various angles. Draw concentric circles. Use a compass to construct a circle. Label diameter, radius and center utilizing a straight edge. Define diameter, radius, center of a circle. Solve addition and subtraction problems to find unknown angles Coordinate Geometry Gr. 4 How do we plot points on a coordinate grid? Read an ordered pair. Recognize the x -axis and y axis on a coordinate graph. 4:MD2 How do we plot and connect points on a coordinate grid/graph? 4:MD2 Read an ordered pair. Recognize the x axis and y axis on a coordinate graph. Follow specific directions for connecting one point to another using a straight edge. Identify points using an ordered pair to specify location. Locate a point using an ordered pair for direction. Label points on a grid based on location. Plot a series of points using ordered pairs to establish location. Use a straight edge to connect points on a coordinate grid. 7 Course: Mathematics MSD CURRICULUM MAP 4:MD Units of Measurement Ongoing How do you explain and measure various objects in different ways? How do we measure objects to the nearest part of a whole? Use a ruler (metric and standard), scale, measuring cups, tape measure, liquid measuring tools, etc. Read a number line indicating parts of a whole measure. Use a scale to represent fractions of various lengths. Use a yard/metric stick to measure fractions of lengths or distances. 4:MD1 How do we calculate the area of an object? Use proper formula for measuring the area of an object. Use a scale to measure the weight of an object in ounces. Use standard liquid measurement devices 4MD3 Read time accurately. Determine the amount of hours and minutes that have passed between two given times. Learn formula for area and perimeter. Evaluate word problem to determine appropriate formula. 4MD2 How do we measure the weight of an object in ounces? How do we determine the capacity of a given amount of liquid? How do we know how much time has past? When do we use area and when do we use perimeter? Gr. 4 Grade Level: 4 4:MD1 4MD2 4MD2 4MD2 4MD3 Identify all the attributes of a given object. Measure objects appropriately. Measure distance between two points on a map and determine actual distance using a scale. Use ruler or tape measure to measure objects to the nearest fraction of a unit. Determine the area of various 2-dimensional given object Determine the weight of an object to the nearest ounce Determine the capacity of various amounts of liquid Calculate the amount of time that has passed to the nearest minute. Plan a trip from one place to another. Decide appropriate application and solve. Utilize the HSCE protocol for open ended responses. 8 Course: Mathematics MSD CURRICULUM MAP Algebraic Thinking 4:OA 4:OA5 Ongoing How can we explain patterns in different ways? Ongoing Can you tell if a pattern will continue or end? Explain. Can you describe how the pattern was created? Recognize patterns. Describe what you see through words or pictures. Extend patterns. Predict and check whether a pattern will continue or end. Recognize pattern and apply rule to continue pattern. Can you describe two or more ways the pattern was created? Identify various patterns and apply rules to continue patterns. 4:OA5 How can we show change through a graph? (e.g., temp., height) Create and label a graph given data. Read a graph. 4:OA5 How do you solve this problem? Add, subtract, multiply, and divide 4:OA3 Recognize and use symbols for greater than, less than, and equal to Understand Commutative property 4:OA2 4:NBT2 4:OA1 Understand the Associative property 4:OA1 Ongoing Ongoing 4:OA5 4:OA5 Grade Level: 4 Describe patterns through a variety of fashions. Create a graph to show some growth over time. Distinguish between patterns that end and ones that continue infinitely. Determine pattern and properly extend. Create a pattern that can be explained. Whole number patterns that grow or shrink as a result of repeatedly adding, subtracting, multiplying by, or dividing by a fixed number (e.g., 5, 8, 11….Or 800, 400, 200 Determine pattern and properly extend. Create a pattern that can be explained. Create a pattern with more than one extension. Sequences can often be extended in more than one way (e.g., the next term after 1,2,4,…could be 8why?) Modeling Create a graph given data. Interpret data from a graph (student height, week of temperature, etc.) Utilize the HSCE protocol for open ended responses. Solve multi-step open word problems. Decide if number sentence is true, false, or can’t tell. Procedures How do we compare numbers? Ongoing Ongoing Ongoing Gr. 4 Can you give an example of the commutative property? Can you change the order of multiplying factors without changing the product? Correctly read and write number sentences using greater than, less than, or equal to signs. Show examples of the Commutative property using different operations. Multiply sets of numbers associatively 9 Course: Mathematics MSD CURRICULUM MAP Grade Level: 4 Data Analysis Time Frame Content/Topic Observable Proficiencies/Skills National Standards Performance Benchmarks Data Analysis Ongoing What can we do with information collected from the school environment? Collect data, display and organize information gathered (tallies, etc.) 4MD4 How can we show the data we collected? What information can we get from our display? Create and read a pictograph, bar graph, line plot, line graph, and table from data. Understand the meaning of the terms mean, mode, and median. Determine the mean, mode, and median for a set of data. Interpret the results. Average (mean), most frequent (mode), middle term (median) 4MD4 4MD4 Find the mean, mode, and median for a given set of numbers. Draw inferences from given data. Create a class project to interpret data. Create line plots using tallies. Analyze data in various ways. Use data to determine probability. Place data into a Venn diagram. Explain the meaning of the diagram. Know how to complete a list, a chart and a tree diagram. Know the appropriate form for displaying a given set of information. 4MD4 Name a variety of categories. Sort information into subcategories. 4MD4 Discuss various interpretations of data for probability. Complete a Venn diagram comparing attributes. Explain results. Complete a list, a chart or a tree diagram depending on which is appropriate. Create a tree diagram and an organized list to find all possible combinations. Correctly sort data into subcategories. Collect, organize, and display data in fractions of a unit (1/2, ¼, 1/8) (E.g Form a line plot and interpret the different lengths of an insect collection) Create and interpret various displays of data. Systematic Learning and Counting How many ways can we interpret our results? What does a Venn diagram show us? Ongoing How can we display information in an organized fashion? Ongoing How can we subdivide information into categories? Gr. 4 4MD4 4MD4 10 Course: Mathematics MSD CURRICULUM MAP Grade Level: 4 Mathematical Practices Time Frame Content/Topic Observable Proficiencies/Skills SMP1 SMP2 SMP4 Problem Solving Ongoing Ongoing Ongoing Ongoing Gr. 4 SMB5 SMB6 SMB7 Identify and discuss problems involving inquiry/discovery 4OA3 Solve and write explanations of open-ended problems. 4OA3 Solve problems that do not have routines (e.g. inferring and interpreting questions) Solve problems with different solutions. 4OA3 Solve problems in various ways (e.g., tree diagrams, charts, using manipulatives, drawing pictures, and label short words). 4OA3 What are some different problem solving strategies? How are problems alike? What could a checklist of the problem solving process look like? Create problems and model how to solve them. 4OA3 Self-assessment of their answer to the open-ended question. Find similarities between number stories. Check and monitor the process used to solve number stories. 4OA3 4OA3 Verbal explanation of comparisons. Self-assessment using checklists including steps to problem solve. Utilize the HSCE protocol for open ended responses. 4OA3 Observational notes during classroom interest-based investigations. NJ State Math Open-ended Rubric Utilize the HSCE protocol for open ended responses. Completion of number story using population census data. Completion of number stories by generating multiple solutions. Completion of number story using multiple methods. Utilize the HSCE protocol for open ended responses. SMP3 What are some key words that can help us better understand number stories? Why do we need to describe explanations of problems? When do we need to explain our answers? How do people think differently? Read and write number stories along with solutions. SMP3 Oral and written questioning. Discuss, listen, and question problems. SMP3 Observations during classroom discussions. Explain cognitive steps involved in solving problems. Solve peer generated problems. SMP3 SMP3 Why is it important that we all use the same mathematical language? Identify mathematical vocabulary. SMP3 Written and oral explanations of problem solutions. Solutions and monitoring of peer generated problems. Utilize the HSCE protocol for open ended responses. Class generated vocabulary chart. Connections Ongoing Performance Benchmarks/Assessments What are some problems in everyday life? What makes an open-ended problem different? What strategies can you use if a problem confuses you? Why are there different solutions to problems? How can you find the strategy that works for you? Communication Ongoing National Standards Where is the Math in everyday life? Recognize recurrent themes across mathematical domains (e.g., patterns in numbers, algebra, and geometry). SMP2 SMP4 SMP4 Create a Where’s the Math Bulletin board with pictures, drawings and cut outs. Recognize recurring themes across mathematical domains (e.g., patterns in numbers, algebra, and geometry). 11 Course: Mathematics Ongoing How does what I know about math help me solve this problem? Ongoing How does math help us in our daily lives? Ongoing How does math help us in our other subject areas? How do mathematical ideas build on each other? Ongoing MSD CURRICULUM MAP Use connections among mathematical ideas to explain concepts (e.g., 2 linear equations have a unique solution because the lines they represent intersect at a single point). Recognize that mathematics is used in a variety of contexts outside of mathematics. Apply mathematics in practical situations and in other disciplines. Understand how mathematical ideas interconnect and build on one another to produce a coherent whole. SMP4 Oral questioning. SMP4 Tell about ways that we use math. SMP4 Point out mathematical connections in other subjects. SMP2 SMP4 SMP8 Understand how mathematical ideas interconnect and build on one another to produce a coherent whole. Why do we need to explain and justify our answers? Understand that we have to explain and justify our answers. SMP8 Solve an open ended math problem. Utilize the HSCE protocol for open ended responses. How do we support our answers and explain our mathematical thinking? How can you prove your answer in more than 1 way? How do we determine if our answer makes sense? How can we probe that an answer is unreasonable? What are the ways that we can use to explain our reasoning? How can we determine if an answer is correct and well supported Support answers and explain mathematical thinking. SMP8 Explain your answers in variety of ways. SMP8 Can students use HSCE (Highlight/Solve/Circle; Check/Explain strategy? Show more than one way to solve the problem. Estimate to determine reasonableness of an answer. SMP8 Ask student to determine if answers make sense. Provide examples that show that an answer is not reasonable. SMP8 Have student explain why something is incorrect. Explain reasoning using words, pictures, and number sentences. Evaluate a response to an open-ended question and decide whether the answer is correct and well-supported. SMP8 Solve an open ended math problem using words, pictures and number sentences. Uses a rubric to self assess open ended tasks. Reasoning Ongoing Ongoing Ongoing Gr. 4 SMP8 SMP4 Representations Ongoing Grade Level: 4 How can we use manipulatives to communicate ideas? How can we use pictures, diagrams, charts and tables to communicate ideas? Use manipulatives to organize, record, and communicate mathematical ideas. Use pictures, diagrams, charts, and tables to organize, record, and communicate mathematical ideas. How can we use number model and other symbols to communicate ideas? How do we choose the tools we need to solve a problem? Use number models and other symbols to organize, record, and communicate mathematical ideas. Choose and apply the appropriate representation to solve a problem. SMP4 SMP4 SMP3 SMP4 Have students demonstrate problems with base ten blocks, pattern blocks, etc. Have students solve an open ended math problem using pictures, diagrams, charts and tables to communicate their ideas. Use number models for daily routines. Ask students what strategies they would use to solve a problem. Select, apply, and translate among mathematical representations to solve problems. 12 Course: Mathematics MSD CURRICULUM MAP SMP5 Technology Ongoing Gr. 4 How do you use technology to gather, analyze, and communicate mathematical information? How do you use technology to organize and display information? How do you create a graph using technology? How do you use a calculator to solve a math problem? How do you use computer software to explore geometric properties? How do you use computer software to explore mathematical concepts with science applications? Grade Level: 4 Use technology to gather, analyze, and communicate mathematical information. SMP5 Use software to gather, analyze and communicate findings from a data set. Use computer spreadsheets, software, and graphing utilities to organize and display quantitative information. Create graphs using graphing calculators and computer software. Solve problems using calculators. SMP5 Use Excel to create a graph or table displaying class data. SMP5 Use Excel to create a graph or table displaying class data. SMP5 Have students explain the calculator keys. Use computer software to explore the properties or geometric objects. Use computer software to explore mathematical concepts with science applications. SMP5 Use computer software to explore the properties of geometric objects. Use computer software to explore mathematical concepts with science applications. SMP5 13
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