Math Curriculum - Fifth Grade also available as a printable PDF CESAME site - TERC Literature Connection . 1. Number and Operations Essential Skills: 1. Understand numbers, ways of representing numbers, relationships among numbers and number systems 2. Understand meanings of operations and how they relate to one another 3. Compute fluently 4. Make reasonable estimates and relate them to solutions Important to Know: • Demonstrate an understanding of place value by reading, writing, and decomposing whole numbers to the millions place and decimals to the hundredths place • Demonstrate an understanding of composite and prime numbers and identify prime numbers through 50 • Order integers (positive and negative whole numbers and 0 ) given concrete materials from lowest to highest • Compare any 2 whole numbers using <, >,or = through 1,000,000 • Round whole numbers to the nearest millions and decimals to the nearest tenth. • Demonstrate division as repeated subtraction or equal grouping from a set of numbers • Memorize division facts through 100 divided by 10 • Use strategies to estimate the results of division problems with 2-digit divisors • Solve long division problems accurately and efficiently using 2-digit divisors with and without remainders, showing the quotient as a mixed number • Add, subtract, multiply and divide efficiently sets of whole numbers written vertically and horizontally • Demonstrate an understanding of the associative and commutative properties of addition and multiplication to solve problems involving 3 or more whole numbers • Demonstrate an understanding of the distributive property by being able to write at least 2 ways of grouping and solving a multiplication problem such as 12 X 24 as [(6 X 24) + (6 X 24)] or [(10 X 24) + (2 X 24)] • Explain why the commutative property works in addition and multiplication, but not in subtraction and division • Given a model, compare fractions with denominators 2 through 10. • Convert fractions in tenths and hundredths to decimals • Recognize and convert commonly used percents to fractions and decimals (10%, 20%, 25%, 50%, 75%, 100%) • Use strategies to estimate results. Analyze the results to judge the reasonableness of answers . 2. Algebra Essential Skills: 1. Understand patterns, relations, and functions 2. Represent and analyze mathematical situations and structures using algebraic symbols 3. Use mathematical models to represent and understand quantitative relationships 4. Analyze change in various contexts 5. Use paper and pencil to demonstrate skills prior to using technology Important to Know: • Extend a progressive numeric pattern using one operation • Graph ordered pairs and describe their relationship • Communicate/explain strategies for solving computation problems with one variable • Express/solve math equations using + and - with one variable • Demonstrate how to solve a problem using order of operations • Given a partially completed table of 2 columns, recognize the pattern in the table and complete it and explain the rule used in the table . 3. Geometry Essential Skills: 1. Analyze characteristics and properties of two and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships 2. Specify locations and describe spatial relationships using coordinate geometry and other representational systems 3. Apply transformations and use symmetry to analyze mathematical situations 4. Use visualization, spatial reasoning, and geometric modeling to solve problems 5. Use paper and pencil to demonstrate skills prior to using technology Important to Know: • Create 2-D and 3-D models that illustrate intersecting lines, parallel lines, perpendicular lines and right angles • Identify and compare circles and different quadrilaterals including trapezoid, square, parallelogram, rectangle, rhombus (diamond), and kite • Use the terms intersecting, right angle, circle, obtuse angle, and acute angle • Find the distance between points along horizontal and vertical lines of a coordinate system • Make and use coordinate system to specify locations and to describe paths in the first quadrant • Identify and describe line and rotational symmetry in 2-D figures using concrete materials. • Use the terms flip, turn, and slide • Describe a series of motions using the terms slides, flips, and turns to show that two shapes are congruent • Draw triangles, squares, rectangles, circles, cones, cylinders, spheres, cubes, and prisms • Recognize known shapes in the environment • Recognize known shapes from different perspectives • Use known geometric models to solve problems in other areas of mathematics such as number and measurement • Recognize geometric ideas and relationships and apply them to other disciplines and problems that arise in the classroom or everyday life • Classify triangles by their sides and angles (equilateral, scalene, isosceles, acute, right or obtuse) . 4. Measurement Essential Skills: 1. Understand measurable attributes of objects and the units, systems, and processes of measurement 2. Apply appropriate techniques, tools, and formulas to determine measurements 3. Use paper and pencil to demonstrate skills prior to using technology Important to Know: • Understand the attributes of length, weight, area, perimeter, volume and select the appropriate type of unit and tool for measuring each attribute • Use a protractor to measure an angle up to 90 degrees to the nearest degree • Use concrete materials, grid paper, and given formula to find and label the area of a rectangle or a triangle • Measure the diameter and radius of a circle • Find the perimeter of regular and irregular shapes • Using string, measure the circumference of a circle and relate it to the diameter • Explain how the formula for finding the area of a parallelogram is derived • Using concrete materials, demonstrate and explain how the perimeter of an object can change while the area of the object stays the same • Explain why a common unit of measurement is needed when comparing 2 or more attributes • Using concrete materials, find the surface area of rectangular prisms • Demonstrate, using concrete materials how to find the volume of rectangular prisms • Convert within a system of measurement: from inches to feet, feet to yards, centimeters to meters, minutes to hours, hours to days, seconds to minutes, days to weeks, days to years and years to weeks using whole numbers • Measure a line to the nearest 1/8 inch, given a ruler with divisions to the 1/8 inch • Given the measurement of a single object, estimate the measurement of multiples of that object • Compare a precise measurement with their estimate of that object • Determine the best unit of measurement to use when estimating the length, area, perimeter, and weight • Determine the reasonableness of a measurement by using their knowledge of units of length and weight • Determine elapsed time to the nearest minute • Make change from one, five, ten, and twenty dollars . 5. Data Management and Probability Essential Skills: 1. Select and use appropriate statistical methods to analyze data 2. Develop and evaluate inferences and predictions that are based on data 3. Understand and apply basic concepts of probability 4. Use paper and pencil to demonstrate skills prior to using technology Important to Know: • Make a graph with horizontal and vertical axes. Determine what the values along each axis need to be and label the axes accordingly • Demonstrate an understanding that the marks on the horizontal and vertical axes of a graph need to be equidistant and the numbers equally sequenced. • After creating a bar, line, or circle graph, make conclusions about what the graph depicts • Find and describe the range, mean, mode, and median of a set of data • Determine the probability of a given event using concrete materials • Predict the probability of outcomes of simple experiments. Test the predictions with concrete materials . 6. Problem Solving Essential Skills: 1. Work individually and as a member of a group in formulating and solving problems 2. Build new mathematical knowledge through problem solving 3. Identify and solve problems that arise in mathematics and in other contexts 4. Apply and adapt a variety of appropriate strategies, including choosing appropriate computations, to solve problems 5. Monitor and reflect on the process of mathematical problem solving Important to Know: • Identify needed information to solve a problem • Use the following strategies: act it out, make a physical model, draw a diagram, make a chart or table, generalize, look for a pattern, guess/check/revise, work backwards, solve a simple problem • Translate from words to mathematical symbols • Identify relevant and irrelevant information • Judge the reasonableness of solutions • Solve two-step problems • Generalize a problem solving situation to other content areas . 7. Reasoning and Proof K-12 Essential Skills: 1. Recognize reasoning and proof as a fundamental aspect of mathematics 2. Make and investigate mathematical conjectures 3. Develop and evaluate mathematical arguments and proofs 4. Select and use various types of reasoning and methods of proof . 8. Communication Essential Skills: 1. Organize and consolidate mathematical thinking through communication 2. Communicate mathematical thinking coherently and clearly to peers, teachers, and others 3. Analyze and evaluate the mathematical thinking and strategies of others 4. Use the language of mathematics to express mathematical ideas precisely Important to Know: Oral • Explain fluently and sequentially what method was used to get an answer • Validate and generalize solutions to a problem Written • Explain fluently and sequentially what method was used to get an answer • Validate and generalize solutions • Explain mathematical processes • Record observations and investigations using appropriate math symbols and terms • Keep weekly math journal using math concepts Visual • Use concrete materials to model mathematical ideas • Use tables, charts and graphs to make presentations Kinesthetic • Use body language to demonstrate mathematical ideas . 9. Connections K-12 Essential Skills: 1. Recognize and use connections among mathematical ideas 2. Understand how mathematical ideas interconnect and build on one another to produce a coherent whole 3. Recognize and apply mathematics in contexts outside of mathematics . 10. Representation K-12 Essential Skills: 1. Create and use representations to organize, record, and communicate mathematical ideas 2. Select, apply, and translate among mathematical representations to solve problems 3. Use representations to model and interpret physical, social, and mathematical phenomenon
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