# Math 5th grade. Create your own number and explain how to use expanded form to show place value to the ten millions place.

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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 Students will: Apply multiple representations (e.g., drawings, manipulatives, base-10 blocks, number lines, expanded form, symbols) to represent whole numbers (0 to 99,999,999); Apply multiple representations e.g., drawings, manipulatives, base-10 blocks, number lines, expanded form, symbols) to describe commonly-used fractions, mixed numbers, and decimals through thousandths; Apply these numbers to represent realworld problems and Explain how the base-10 number system relates to place value. Create your own number and explain how to use expanded form to show place value to the ten millions place. Justify the placement of a decimal point in a given whole number. <, >, =, <, >, Tenths; Hundredths; Thousandths Intervals Positive/Negative, Integers Unit segment Denominator Numerator Reduce; simplify; lowest terms Of -> multiplication Is -> equal Place Value Construct a drawing representing the following: ¾, 1 /, 1 /, 6 / 8 (Number Line) Math Vocabulary (Fractions) Dicey Decimals (Number Systems) Fractions (The Number Line) 1 Construct a number line from -10 to 10 including whole numbers and fractions. Describe patterns used in our number system. 1

2 MA Students will read, write, and rename whole numbers, fractions, and decimals, and apply to realworld and mathematical problems. MA Students will compare (<, >, =) and order whole numbers), fractions and decimals, and explain the relationships (equivalence, order) between and among them. Joey went to the store with a certain amount of money and he spent a fraction of it, how would you determine how much money he had left? Express answer in fraction & decimal form. Given any number, what is the place value of each digit? Explain the process of listing fractions and decimals in a particular order. (least to greatest, greatest to least) Dicey Decimals (Number Line) Fractions Math Vocabulary (Fractions) Submarine Sandwich OR 4, 4 Equivalent <, >, =, <, >, Pizza OR Shaded Circles OR Fraction Pie OR Fraction Pizza OR Fractions Estimation MA Students will apply and describe appropriate strategies for estimating quantities of objects and computational results in real-world problems. Given a set of data, estimate to the nearest amount. Given the same data, calculate the exact amount. Assess when estimation and exact amounts would be appropriate in real life situations. (Multiply/Divide) Mowing OR, 4 Round, Approximate, Estimate Tenths; Hundredths; Thousandths Exact

3 Number Operations MA Students will analyze real-world problems to identify appropriate representations using mathematical operations, and will apply operations to solve real-world problems with the following constraints: add, subtract, multiply, and divide whole numbers (less than 100,000,000), using technology where appropriate; add and subtract fractions with like denominators through 16, with sums less than or equal to one and add and subtract decimals through hundredths. Justify where to put the decimals in your answers when you add & subtract decimal numbers? The bus could carry students. The students from Room & the students from Room 15 got on the bus. How many more students can the bus carry? Sum Difference Dividend; divisor; quotient; Groups of; equal groups; array Numerator; denominator, reciprocal; invert Addend + addend = sum Factor x factor = product Bracelet OR 1,,,4 MA Students will skip-count forwards and backwards. MA Students will multiply decimals through tenths. Multiples, Patterns, Terms, Sequence Justify where to put the decimal in the answer when multiplying decimal numbers? Guessing Game OR Sit-Ups OR 1, Ratios and Proportional Reasoning Properties of Numbers and Operations MA Students will identify and determine composite numbers, prime numbers, multiples of a number, factors of numbers, and least common multiples (LCM), and will apply these numbers to solve real-world problems. Choose a number between 50 and 100, identify its factors, and explain if it is prime or composite. Composite, Prime, Factors, LCM and GCF Odd; even; prime; composite; multiples; exponent base; powers; square root Factors/Multiples Fractions & Decimals Let s Eat

4 MA Students will use the commutative properties of addition and multiplication, the associative properties of addition and multiplication, the identity properties of addition and multiplication and the zero property of multiplication in written and mental computation. Commutative properties, associative properties, identity properties, zero property Fractions 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. Measuring Physical Attributes MA Students will apply standard units to measure length (to the nearest eighth-inch or the nearest centimeter) and to determine: weight (ounce, pound; gram, kilogram); perimeter; area (figures that can be divided into rectangular shapes); time (nearest minute); temperature (Fahrenheit and Celsius) and angle measures (nearest degree). MA Students will choose appropriate tools (e.g., protractor, meter stick, ruler) for specific tasks and apply skills to solve real-world and mathematical problems. MA Students will use measurements to identify, describe, sort, and compare attributes of objects Weight (ounce, pound; gram, kilogram); Length (nearest eighth-of-an-inch or nearest centimeter); Perimeter; Circumference of Circle Area (figures that can be divided into rectangular shapes) A = L x W;Square Time (nearest minute); Temperature (Fahrenheit and Celsius); and Angles (nearest degree) o degree symbol Choose a unit of measurement and design a playground including fencing & mulch. Explain the process of determining the area and perimeter of your playground. Explain which measurement tool would be used to measure the length of the room, distance to town, degree of an angle, etc. Faces, Edges, Vertices - D figures Sides, Vertices, Angles D figures (Prop of Lines) Temperature Perimeter Art Place Mat Perimeter Measurement Measurement 4 1,,,4, 4, 4

5 and apply these to solve real-world and mathematical problems. MA Students will measure volume of rectangular prisms, liquid capacity, and money using standard units and apply these skills to solve real-world and mathematical problems MA Students will estimate weight, length, perimeter, area, angle measures and time using appropriate units of measurement. Given a rectangular solid explain how many cubes would it take to build it without counting? US Standard & Metric Units Volume = Length x Width x Height Cubic Choose an object and describe each by estimating the units of measurement. Justify how to estimate the weight, length, perimeter, area, and angle measures, of objects in your everyday life. (Geometric Figures), 4 Systems of Measurement MA Students will determine elapsed time. DOK MA Students will describe, define, give examples of and use to solve real-world and mathematical problems nonstandard and standard (U.S. Customary, metric) units of measurement. MA Students will convert units within the same measurement system [U.S. customary (inches, feet, yards, miles; ounces, pounds, tons), metric (millimeters, centimeters, meters, kilometers; grams, kilograms), money, or time] and use the units to solve problems. Create a field trip schedule and determine the elapsed time for each activity. US Customary & Metric Standard & Non-standard measurements (paper clips, candy, etc.) Explain how to convert units of measurement within the same system. U.S. customary (inches, feet, yards, miles; ounces, pounds, tons), metric (millimeters, centimeters, meters, kilometers; grams, kilograms), money, or time (seconds, minutes, hours) Elapsed time (Geometric Figures) Measurement (Measurement) Measurement, 4 5

6 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 Students will describe and provide examples of basic geometric elements and terms [points, segments, lines (perpendicular, parallel, intersecting), rays, angles (acute, right, obtuse), sides, edges, faces, bases, vertices, radius, diameter] and will apply these elements to solve real-world and mathematical problems. MA Students will describe and provide examples of basic two-dimensional shapes [circles, triangles (right, equilateral), all quadrilaterals, pentagons, hexagons, octagons], and will apply these shapes to solve real-world and mathematical problems. MA Students will describe and provide examples of basic three-dimensional objects (spheres, cones, cylinders, pyramids, cubes, triangular and rectangular prisms), will identify three-dimensional objects from two-dimensional representations (nets) and will apply the attributes to solve realworld and mathematical problems. MA Students will identify and describe congruent and similar figures in real-world or Classify the angles in your classroom by describing their attributes. Points, segments, lines (perpendicular, parallel, intersecting), rays, angles (acute, right, obtuse), sides, edges, faces, vertices, radius, diameter Identify real-world objects using attributes of two-dimensional shapes. Circles, triangles (right, obtuse, acute, equilateral, scalene, isosceles), all quadrilaterals (trapezoid, rectangle, square, parallelogram, rhombus, trapezium), pentagons, hexagons, octagons radius, diameter Create a net that would form the -D shape. Create/construct net for a D models such as cylinders or cubes. Classify plane and D figures by their attributes. Net Draw a figure then draw a figure that is congruent and a figure that is similar to the first figure. Label each and explain for each. Math Vocabulary (Geometric Figures) (Probability of Events) Attributes of Polygons (Probability of Events) (Symmetry, Similarity, Congruence) 1,,,4 4, 6

7 mathematical problems. Congruent, Similar Transformations of Shapes MA Students will describe and provide examples of line symmetry in real-world and mathematical problems or will apply line symmetry to construct a geometric design. DOK MA Students will identify or draw 90º rotations, reflections or translations of basic shapes within a plane. DOK 1 Create a portion of a design, complete the symmetrical portion. Line of Symmetry, Symmetrical Draw and identify 90º rotations, reflections, and translations of basic shapes within a plane. Transformations, Rotations (turn), Reflections (flip), Translations (slide) (Data Analysis) Alphabet Symmetry (Graphs) Coordinate MA Students will identify and graph ordered pairs on a positive coordinate system scaled by ones, twos, threes, fives, or tens; locate points on a grid; and apply graphing in the coordinate system to solve real-world problems. When could the coordinate system be applied to a real-world situation? (latitude/longitude, GPS, grid maps) Ordered pairs, Point of origin, Quadrants, Units (Graphs) The Game Battleship 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. 7

8 Data Representations MA Students will analyze and make inferences from data displays (drawings, tables/charts, tally tables, pictographs, bar graphs, circle graphs, line plots, Venn diagrams, line graphs). DOK MA Students will collect data (e.g., tallies, surveys) and explain how the skills apply in real-world and mathematical problems. What data is represented by the x-axis? What data is represented by the y-axis? What categories are represented by the Venn Diagram? Which data is common to both categories in the Venn Diagram? Predict future trends based on the graph. Give possible reasons for the trend shown by the data. Survey, Legend, Icon Function Table, input/output, drawings, tables/charts, frequency tables, pictographs, bar graphs, circle graphs, line plots, Venn diagrams, line graphs Explain the process used to conduct the survey. When is estimation appropriate? (Functions) (Graphs) (Graph/Coordinate Plane) Insect Information (Functions) When are exact tabulations appropriate? MA Students will construct data displays (pictographs, bar graphs, line plots, line graphs, Venn diagrams, tables). Combination, Frequency chart Which type of data is appropriate for each type of graph? Do a survey and create a graph and label appropriately with titles & correct intervals? (Functions) Candy Sales X axis, Y axis Characteristics of Data Sets MA Students will determine and apply the mean, median, mode and range of a set of data. Given the average (mean) what could be the student s 10 possible math grades? Calculator Patterns 1 8

9 Average, Measure of Central Tendencies, Mean, Median, Mode, Range (# Rules/Patterns) Probability Math Vocabulary (Central Tendency) Passing the Test OR Experiments and Samples MA Students will describe and give examples of the process of using data to answer questions (e.g., pose a question, plan, collect data, organize and display data, interpret data to answer questions). List the data you would need to collect & the experimental steps you would take to conduct a particular investigation. Problem-solving (Sequence/Series) (Graphs) 1 Probability (Graphs) MA Students will determine all possible outcomes of an activity/event with up to 1 possible outcomes. MA Students will determine the likelihood of an event and the probability of an event (expressed as a fraction). Given an event determine all possible outcomes. Probability (fractions), Chance (Percent), Combinations, Favorable Outcomes Name an event that would produce the same outcome. Certain = 1 Impossible = 0 Unlikely = fraction < 1/ Likely = fraction > ½ (Data Analysis) Chips in a Hat OR Chris Sandwich Shop OR (Probability of Events) Probability 9

10 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 Students will extend patterns, find the missing term(s) in a pattern or describe rules for patterns (numbers, pictures, tables, words) from realworld and mathematical problems. DOK Create a pattern, determine its rule, and describe it. Sequence, Tessellations, Patterns (# Rules/Patterns) Calculator Patterns (# Rules/Patterns) 1 (Sequence/Series) MA Students will describe functions (input-output) through pictures, tables, or words, and will construct tables to analyze functions based on real-world or mathematical problems. MA Students will determine an output value or an input value for a function rule given the other value. Design an Input/Output table and describe its function. Number changing machine, Input/Output, Function Machine Given a function rule determine the output value. (Functions) 10

11 Variables, Expressions, and Operations MA Students will model verbal descriptions of realworld and mathematical problems using a variable or a missing value in an expression. Write a story problem with a missing value. Create an expression using a variable to model the problem. Story problems, Variable (Basic Equations) 4 Equations and Inequalities MA Students will model real-world and mathematical problems with simple number sentences (equations and inequalities) with a variable or missing value (e.g., 4 = x N, + 5 > 14) and apply simple number sentences to solve mathematical and real-world problems. Explain the process to determine the missing variable in an equation. Equation, Inequalities, Variable (Basic Equations) 4 11

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