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1 Number Properties and Operations Whole number sense and addition and subtraction are key concepts and skills developed in early childhood. Students build on their number sense and counting sense to develop multiplication and division. They move flexibly and fluently through basic number facts, operations and representations. Their understanding of the base-10 number system expands to include decimals. They examine various meanings and models of fractions. They explore data, perform measurements and examine patterns as part of the development process for number and operations, using other mathematics strands to enrich number. Computational fluency with whole numbers, relationships among decimals and fractions and techniques for reasonable estimations represent elementary number. Number Sense MA-EP Students will: apply multiple representations (e.g., drawings, manipulatives, base-10 blocks, number lines, expanded form, symbols) to describe whole numbers (0 to 9,999): apply multiple representations (e.g., drawings, manipulatives, base-10 blocks, number lines, symbols) to describe fractions (halves, thirds, fourths); apply these numbers to represent realworld problems and explain how the base 10 number system relates to place value. Apply multiple representations to describe and compare whole numbers and fractions. Identify a one, two and three digit number. Demonstrate a three digit number using expanded form. List numbers in order from least to greatest using one digit, two digit, or three digit numbers. Discuss the parts of a fraction, then compare and contrast the fraction parts. Cardinal numbers, Ordinal numbers (Place Values) (Numbers and Comparisons) (Add, Subtract, & Manipulate) (Fraction Concepts) Use place value blocks to show a given number. Use base 10 blocks and mats to show regrouping or use dimes & pennies to show regrouping. Hundreds, Tens, One, Place value, Rods, Units Expanded form, Digit, Least to greatest, Fewer, More, Sequence, Regroup, Trading, 1

2 Borrowing Fraction, Halves, Thirds, Fourths, Numerator, Denominator MA-EP Students will read, write, and rename whole numbers (0 to 9,999) and apply to real-world and mathematical problems. MA-EP Students will compare (<, >, =) and order whole numbers to whole numbers, decimals to decimals (as money only) and fractions to fractions (limited to pictorial representations). DOK 1 Estimation MA-EP Students will apply and describe appropriate strategies for estimating quantities of objects and computational results (limited to addition and subtraction). Number Operations MA-EP Students will analyze real-world problems to identify appropriate representations using Read, write, count, and model whole numbers (0 to 1, 000). Order groups of object to quantity. Explore appropriate estimation procedures. Apply and describe appropriate strategies for estimating quantities. Develop part-whole relations using numbers. Demonstrate how to show money amounts using cents and decimals. Compare 2 numbers using less than, greater than, or equal. Comparison Symbols (Greater than, Less than, Equal, Compare) Using estimation strategies, predict the quantity of objects. Record estimations, compute correct amounts, and graph or chart data. Operation, Solution, Solve, Strategies Estimate, Quantities, Rounding Demonstrate adding or subtracting whole numbers of three digits or (Numbers and Comparisons) Number 12 OR Explain three reasons why 12 is an even number. (Estimate Quantities to 999) Math Facts (Lesson) Math Facts (Power Point) (Estimation Skills) (Add, Subtract & Manipulate) 3 3 2

3 mathematical operations, and will apply operations to solve real-world problems with the following constraints: add and subtract whole numbers with three digits or less; multiply whole numbers of 10 or less; add and subtract fractions with like denominators less than or equal to four and add and subtract decimals related to money. Explore and solve towdigit addition and subtraction problems. Explore and develop factor-factor product using manipulatives. Multiply whole numbers by 0, 1, 2, 3,, 5, & 10. Relate division facts to multiplication facts. Solve multi-digit addition and subtraction problems with numerals and symbols. less using manipulatives (pennies, dimes, rods, units). How do you know when to regroup in addition? Regrouping, Carry How do you know when to regroup in subtraction? Regrouping, Borrow, Mental math, Sum, Addend, Product, Difference, Quotient, Remainder, Add, Subtract, Divide How do you construct a number sentence? (Mental Math & Problem Solving) Math Facts (Lesson) Math Facts (Power Point) MA-EP Students will skip-count forward and backward by 2s, 5s, 10s, and 100s. Vertically (count on, count back) Horizontally, Number sentence, Plus, Minus, Take away, Fact families Doubles, Doubles plus one 1 MA-EP

4 Students will divide two digit numbers by single digit divisors (with or without remainders) in real-world and mathematical problems. Ratios and Proportional Reasoning (not assessed at the elementary level) Properties of Numbers and Operations MA-EP Students will identify and provide examples of odd numbers, even numbers, and multiples of number, and will apply these numbers to solve real-world problems. Explore, develop, and use the concepts of multiples. Explore, develop, and use the concepts of odd and even numbers. Identify odd and even numbers on a calendar by marking odd dates with red and even dates with green and compare the number of red days to green days. Odd, Even, Skip count, Multiples, Forward, Backward Number 12 OR Explain three reasons why 12 is an even number. (Numbers & Comparisons) (Counting & Skip-Counting) (Skip Counting) 3 MA-EP Students will use the commutative properties of addition and multiplication, the identity properties of addition and multiplication and the zero property of multiplication in written and mental computation. Explore and use properties of numbers for written and mental computation. Measurement Students progress from measuring using nonstandard units to using standard units of measurement. They identify measurable attributes of objects, estimate and measure weight, length, perimeter, area, angles, temperature, time and money. They convert units within the same measurement system. 1 Measuring Physical Attributes MA-EP Students will apply standard units to measure length (to the nearest half-inch or the nearest centimeter) and to determine: weight (nearest pound); time (nearest quarter hour); to 5 min. money (identify coins and bills by value) Use nonstandard units to measure and compare length, weight, area, and volume. Compare and order objects by shape, size, Identify different combinations of coins that equal one dollar. Round outside temperature to the nearest ten degrees using a Halloween Suncatchers (Geometry and Measurement) Living Math (Adding and Subtracting Numbers) Subtraction

5 and temperature (Fahrenheit). DOK 1 and color. Use standard units of measurement to identify describe, and compare measurable attributes and make estimates. Identify, compare, and order amounts of money using coins and bills and use correct symbols for money. Tell time to the hour, half hour, quarter-hour, five minutes and one minute and determine elapsed time. thermometer. Measure partner s feet to the nearest inch and centimeter. Read time to nearest 5 minutes to tell classmates when lunch is near. Nonstandard, Standard, Weight, Pound, Gram, Ounce, Inch, Foot, Yard, Centimeter, Meter, Liquid, Cup, Pint, Quart, Gallon, Liter Area, Perimeter, Length, Weight, Width, Height, Amount, Unit of measure, \$ sign, Decimal, Penny, Dime, Nickel, Quarter, Half dollar Quarter hour, Quarter till, Quarter after (of) (Flash Cards, Workmats for subtraction facts) (Units & Systems of Weigh/Linear Measure) OR Ruler Measurement Halloween Suncatchers (Geometry and Measurement) Subtraction (Flash Cards, Workmats for subtraction facts) (Units & Systems of Weight/Linear Measure) Living Math (Adding and Subtracting Numbers) Subtraction (Flash Cards, Workmats for subtraction facts) Counting Money Subtraction (Flash Cards, Workmats for subtraction facts) (Money) (Time) Real World Measurement 5

6 (Baking Unit) Use touch five money math strategy. MA-EP Students will use standard units to measure temperature in Fahrenheit and Celsius to the nearest degree. Money bingo MA-EP Students will choose appropriate tools (e.g., thermometer, scales, balances, clock, ruler) for specific measurement tasks. 1 MA-EP-2.1. Students will use nonstandard and standard units of measurement to identify measurable attributes of an object (length in, cm; weight oz, lb) and make an estimate using appropriate units of measurement. MA-EP Students will use units of measurement to describe and compare attributes of objects to include length (in, cm), width, height, money (cost), temperature (F), and weight (oz, lb), and sort objects and compare attributes by shape, size, and color. MA-EP Students will estimate weight, length, perimeter, area, angles, and time using appropriate units of measurement. Systems of Measurement MA-EP Students will describe, define, give examples of Predict the length of a specific object

7 and use to solve real-world and mathematical problems nonstandard and standard (U.S. Customary, metric) units of measurement to include length (in., cm.), time, money, temperature (Fahrenheit) and weight (oz., lb). MA-EP Students will determine elapsed time by half hours. MA-EP Students will convert units within the same measurement including money (dollars, cents), time (minute, hours, days, weeks, months), weight (ounce, pound), and length (inch, foot). Geometry Students explore and find basic geometric elements and terms, two-dimensional shapes and three-dimensional objects. They find and use symmetry. They move twodimensional figures in a plane and explore congruent and similar figures. Shapes and Relationships MA-EP Students will describe and provide examples of basic geometric elements and terms (sides, edges, faces, vertices, angles), and will apply these elements to solve real-world and mathematical problems. MA-EP Students will describe and provide examples of basic two-dimensional shapes (circles, triangles, squares, rectangles, trapezoids, rhombuses, hexagons), and will apply these shapes to solve real-world and mathematical problems. Identify, describe, model, draw, compare, and classify 2- dimensional figures and 3-dimensional objects using elements, attributes and properties. Investigate and solve real-world problems using the elements, attributes, and properties, of basic 2- dimensional figures. Sides, Edges, Faces, Angles, Vertex Identify, Compare Measure, Label, Construct (Geometric Elements) Halloween Suncatchers (Geometry and Measurement) (Identify & Construct Figures) 7

8 DOK - 2 MA-EP Students will describe and provide examples of basic three-dimensional objects (spheres, cones, cylinders, pyramids, cubes), and will apply the attributes to solve real-world and mathematical problems. DOK 1 Investigate and solve real-world problems using the elements, attributes and properties of 3-dimentional objects. What does it mean if something is threedimensional? Cube, Cone, Sphere, Cylinder, Pyramid, Rectangular prisms, Plane, Three dimensional, Solids (Identify and Construct Figures) MA-EP Students will identify and describe congruent figures in real-world and mathematical problems. Transformations of Shapes MA-EP Students will describe and provide examples of line symmetry in real-world and mathematical problems or will apply one line of symmetry to construct a simple geometric design. Coordinate Geometry Determine if simple shapes are congruent. Determine lines of symmetry in simple shapes and identify and describe symmetrical 2- dimensional figures. Examine examples of line symmetry in realworld situations. Explore flips, slides, and turns. What is a line of symmetry? How do you determine if two objects are congruent? Congruent, Symmetry, Line of symmetry, Geometric design, Manipulatives Alphabet Symmetry Shapes - OR (Congruency & Symmetry) 2,3 8

9 MA-EP Students will locate points on a grid representing a positive coordinate system. Identify, draw, and represent line segments and angles. Locate points and figures on a grid. Data Analysis and Probability Students pose questions, plan and collect data, organize and display data and interpret displays of data. They generate outcomes for simple probability activities, determine fairness of probability games and explore likely and unlikely events. Data Representations MA-EP-.1.1 Students will analyze and make inferences from data displays (drawings, tables/charts, tally tables, pictographs, bar graphs, circle graphs with two or three sectors, line plots, two-circle Venn diagrams). DOK 3 Make a graph using concrete manipulatives and read data displayed on a concrete graph. Display, read and compare data on student-invented graphs and student-collected data (pictograph and bar graph). What is data? What is the most popular color? Bar graph, Data, Pictograph, Interpret Collect, Organize How can data be organized? (Create & Interpret Graphs) Cookie Graph Measurements & Graphing (Pumpkin Unit) Construct a bar graph from data collected of the various colors of vehicles in the parking lot. 2 MA-EP-.1.2 Students will collect data. Display data in line plots. MA-EP-.1.3 Students will organize and display data. Characteristics of Data Sets MA-EP-.2.1 Students will determine the mode (of a set of data 9

10 with no more than one mode) and the range of a set of data. Experiments and Samples MA-EP-.3.1 Students will pose questions that can be answered by collecting data. Probability MA-EP-..3 Students will describe and give examples of the probability of an unlikely event (near zero) and a likely event (near one). Explore chance through games and events. Compare likely and unlikely outcomes. Explore basic concepts of probability through simple experiments. Algebraic Thinking Students explore and examine patterns and develop rules to go with patterns. They generate input-output for functions and create tables to analyze functions. They use ordered pairs and plot points in the first quadrant of the Cartesian plane. Students use number sentences with missing values. Patterns, Relations, and Functions MA-EP Students will extend simple patterns (e.g., 2,,6,8, ; ). Identify and describe patterns in real life and in numerical and geometric situations. Reproduce and extend patterns using manipulatives. Recognize and extend simple number patterns. 10

11 MA-EP Students will describe functions (input-output) through pictures and words. MA-EP Students will determine the value of an output given a function rule and an input value. Use calculators to explore how constant addition produces a pattern and can be expressed as a rule for a pattern. Explore input-output machines and solve simple function machine tasks. Variables, Expressions, and Operations Equations and Inequalities 11

12 MA-EP Students will model real-world and mathematical problems with simple number sentences (equations and inequalities) with a missing value (e.g., 2 +? = 7, < 6) and apply simple number sentences to solve mathematical and real-world problems. Solve simple equations. Solve simple inequalities. Solve for unknowns in simple open sentences. Use manipulatives, numbers, and/or symbols to model realworld situations with simple number sentences. Read and create story problems to represent mathematical sentences with missing values. Explore unknowns and open sentences to express relationships. Create stories about mathematical sentences with missing values. 12

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