In fifth grade Mathematics, students learn concepts based on the following Strands:
Number Concepts, Theory, Sense
- Explain the relationship (including the use of exponential notation) among place values of numbers up to one billion.
- EXT: Compare and contrast ancient numeration systems and compare with our Hindu-Arabic system.
- Compare, contrast, and define the intent and characteristics of the four operations including associative property, commutative property, properties of 0 and 1, inverse operations, and similarities.
- Explain/show the use of the distributive property to multiply a 1-digit number by a 2- or 3-digit number.
- Choose an appropriate estimation strategy (compatible numbers, rounding, front end, clustering, or using a referent) to fit a given situation.
- EXT: Compare estimation strategies, including rounding and front end estimation, for finding total cost.
- Identify and find multiples, common multiples, composite, and prime numbers. Find the Greatest Common Factor and the Least Common Multiple. Use the rules of divisibility for 2, 3, 5, and 10.
- EXT: Investigate, develop, and use the rules of divisibility for the numbers 4, 6, 8, and 9.
- Estimate, analyze, and find equivalent fractions.
- Compare and order fractions, whole numbers, and mixed numbers.
- Analyze and rename mixed numbers to fractions in the form a/b and do the reverse.
- Read, write, compare, order, and round decimals through the ten thousandths place.
- Understand the relationship between fractions and decimals and convert one to the other through hundredths.
- Investigate positive rational numbers including decimals, ratios, fractions, and percents in problem-solving settings.
- EXT: Convert one to the other.
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Operations
- Add and subtract any whole numbers.
- EXT: Add and subtract money amounts by simulating deposits and withdrawals from a savings account.
- Estimate products. Multiply whole numbers with 2 digits in one factor and 3 digits in the other. Recognize the use of properties.
- Estimate quotients. Divide by 1-digit divisors.
- EXT: Investigate and interpret remainders in problem-solving settings.
- Find an estimated quotient using multiplication and place value to solve problems with 2-digit divisors. Divide by 2-digit divisors. Recognize alternative ways to express remainders. EXT: Find unit prices and determine best buys by using estimation and division.
- Add and subtract fractions and mixed numbers with the same and different denominators.
- Estimate products. Multiply fractions and whole numbers by fractions.
- EXT: Demonstrate with physical materials and record division of whole numbers and fractions by fractions.
- Estimate, add, and subtract decimal numbers through thousandths.
- Estimate products. Multiply a 2-digit decimal by a 2-digit whole number.
- EXT: Estimate products. Multiply a decimal number by a decimal number.
- Estimate products. Mentally multiply a decimal (tenths, hundredths, and thousandths) by 10 and 100.
- EXT: Mentally divide a decimal number by 10 and 100.
- Estimate quotients. Divide a decimal by a whole number less than 10.
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Measurement
- Measure to the nearest eighth of an inch and to the nearest millimeter including objects longer than the measuring tool.
- Estimate and measure mass (ounces, pounds, tons, grams, and kilograms) and capacity (pints, cups, quarts, gallons, liters, milliliters, and cubic centimeters).
- Develop strategies for finding and estimating the perimeter and area of polygons.
- EXT: Develop formulas for perimeter and area.
- Investigate the relationship of diameter to circumference and to radius.
- EXT: Use C = ¼ x d to find circumference.
- Develop the formula for finding the volume of rectangular prisms.
- EXT: Find the volume of irregular solids made of cubes (e.g., staircase).
- Solve problems involving elapsed time in hours, minutes, and seconds.
- Enlarge and/or reduce an image using ratios and a grid.
- Draw and measure angles using a protractor and a straightedge.
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Geometry
- Describe, draw, and label points, lines, line segments, rays, angles, perpendicular lines, parallel lines, and lines of symmetry.
- Classify angles as acute, right, or obtuse, and triangles by angles and/or sides.
- Draw congruent polygons; draw similar figures by using scale.
- Identify parts of a circle including diameter, radius, circumference, arcs, chords, and center.
- Review locating and naming points using coordinates and a grid.
- EXT: Relate using longitude and latitude to locate points on a map or globe to using ordered pairs.
- Classify solids and identify the number of faces, edges, and vertices.
- EXT: Investigate and explain the relationship between faces, edges, and vertices of polyhedrons (e.g., prisms, pyramids, and cylinders).
- Investigate surface area by constructing a variety of prisms.
- Identify slides, flips, and rotations; build tessellations with congruent shapes using slides, flips, and rotations.
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Data Analysis/Statistics/Probability
- Read, collect, and interpret data; make bar graphs, multibar graphs, line plots, and line graphs.
- EXT: Synthesize data from 2 or more kinds of graphs.
- Investigate and construct stem-and-leaf plots and circle graphs.
- Solve real-life problems by applying the skills of data gathering, graphing, and computation. Graph data using computer programs.
- EXT: Investigate the use of spreadsheets to organize data.
- Explain the concept of average; find the mean, median, mode, and range of a set of data.
- Conduct surveys and analyze the data to make predictions.
- EXT: Verify predictions by continued experimenting.
- Determine the probability of multiple, exclusive outcomes within a single event by making tree diagrams; express probabilities as fractions.
- Solve problems by finding possible outcomes and interpreting chance in real-life contexts.
- EXT: Conduct experiments to verify predicted probabilities.
- Investigate and determine elements that affect fairness in game settings.
- EXT: Investigate how probability factors affect strategy games by playing strategy games.
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Patterns/Functions/Algebra
- Solve simple equations for missing addends or missing factors.
- Represent growth patterns by using variables and expressions.
- Identify and extend addition and multiplication patterns including perfect squares, trinumbers, quadrinumbers, and hexinumbers.
- Multiply and divide by tens and multiples of ten by using patterns, multiplication properties, and mental math.
- Choose and write equations with 1 variable to solve real-life problems (e.g., x - 5 = 32).
- EXT: Write a word problem to match a given equation.
- Complete a chart showing input and output when given a function rule.
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Problem Solving/Application
- Pose problems from everyday life situations and from within and outside mathematics.
- EXT: Simplify problem solving by using computer software (e.g., spreadsheet, graphing program).
- Solve problems by using a logical procedure (a plan).
- Identify information that is available but not needed to solve a problem or additional information needed to solve a problem.
- Select and use appropriate materials and tools needed to solve a problem (e.g., calculator, graph paper, manipulatives).
- Develop and apply operations and strategies (e.g., act it out, build a model, draw a picture or diagram, guess and check, make a chart or table, make a list, make a graph, use a pattern, use logical reasoning, solve a simpler problem, work backward) to solve a wide variety of nonroutine and multistep routine problems.
- EXT: Create a poster that defines and explains one of the strategies and includes one or more problems that appropriately exemplify the strategy.
- Solve problems by working collaboratively with peers; entertain others' points of view.
- Share, explain (verbalize/record), and justify (defend) reasoning during and after solving a problem.
- Verify and interpret results with respect to the original problem situation. Compare and analyze solution paths (process used to solve problems).
- Generalize solutions and strategies to new problem situations including problems without numbers (e.g., If I want to know how many miles to the gallon my car gets, what information do I need and then what should I do?).
- Acquire confidence in using mathematics meaningfully to solve problems.
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