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Mahomet-Seymour Schools


Mathematics - Grade 5




Representations and Ordering


The learner will:


Represent place values from units through billions using powers of ten and decimals through thousandths.

Order, compare, and solve equations using whole numbers up to a billion and decimals through thousandths.

Represent multiplication as repeated addition.

Recognize, translate between, and model multiple representations of decimals, fractions less than one, and percents.

Solve problems involving descriptions of numbers, including characteristics and relationships.

Identify fractional pieces that have the same value but different shapes.

Compare and order fractions and decimals efficiently and find their approximate position on a number line.

Solve problems involving the commutative, distributive, and identity properties of operations on whole numbers.

Identify prime and composite numbers.

Explore and use divisibility rules.

Determine the least common multiple and the greatest common factor of a set of numbers.

Estimate, demonstrate and model situations involving addition, subtraction and multiplication of fractions, whole numbers and decimals.

Simplify arithmetic expressions with rational numbers using the field properties and the order of operations.

Recognize and use the inverse relationships of addition and subtraction, multiplication and division to simplify computations and solve problems.

Solve multiplication number sentences and word problems with whole numbers, decimals, and fractions.

Compute with 10, 100, 1000, and other powers of 10.








Ratios, Proportions and Percents


The learner will:


Determine 50% and 100% of a given group in context.

Model the concept of percent using manipulative or drawings.

Create and explain a pattern that shows a constant ratio.

Solve problems involving proportional relationships.








Units, Tools, Estimations and Applications


The learner will:


Measure and draw, with a greater degree of accuracy, any angle using a protractor or angle ruler.

Convert US customary and metric measurements into larger or smaller units.

Estimate and measure distance, weight, temperature, and elapsed time using reasonable units with acceptable levels of accuracy.

Estimate and measure the perimeter, area, and volume of regular and irregular shapes.

Describe how precision is affected by choice of units.

Develop, use, and justify appropriate formulas and tools to determine the area of all polygons.

Develop and use formulas for determining the circumference and area of circles.

Select appropriate tools to measure, draw, or construct figures.

Calculate the surface area and volume of a cube, rectangular prism and triangular prism using formulas.

Solve problems involving map interpretation.








Representations, Patterns, and Expressions


The learner will:


Identify, extend, and describe arithmetic and geometric sequences of numbers whether presented in numeric or pictorial form.

Create, describe, and extend patterns.

Evaluate algebraic expressions, word problems and equations for given values.

Express properties of numbers in operations using variables.

Simplify algebraic expressions involving like terms.








Connections Using Tables, Graphs, and Symbols


The learner will:


Represent and analyze patterns and functions using words, tables, and graphs.

Describe verbally, symbolically, and graphically, a simple relationship presented by a set of ordered pairs or numbers.

Demonstrate how the change in one quantity affects the other in a functional relationship involving whole numbers and unit fractions.








Writing, Interpreting, and Solving Equations


The learner will:


Create, model, and solve algebraic equations using concrete materials.








Properties of Single Figures and Coordinate Geometry


The learner will:


Identify, draw, compare, and analyze attributes of two- and three-dimensional shapes and lines and develop vocabulary to describe the attributes.

Perform simple constructions with appropriate tools.

Determine and describe the relationships within a circle. (e.g., pi, the diameter, the radius, and the circumference)

Determine unknown angle measures using angle relationships and properties of a triangle or a quadrilateral.

Classify and identify two- or three-dimensional shapes according to their properties (e.g., regular and irregular, concave and convex, types of quadrilaterals, pyramids, and prisms)

Predict the result of composing or decomposing shapes or figures.









Relationships Between and Among Multiple Figures


The learner will:


Demonstrate congruence and similarity of plane figures using transformations. (translation, rotation, reflection)

Determine the relationships between the number of vertices or sides in a polygon, the number of diagonals, and the sum of its angles.

Match a front, right side, and top view drawing with a three-dimensional model built with cubes.

Identify and describe the five regular polyhedra.

Create regular and semi-regular tessellations using pattern blocks, other manipulative, or technology.

Make, test, and justify conjectures about various quadrilateral and triangle relationships, including the triangle inequality.

Justify that the sum of the angles of a triangle is 180 degrees.






The learner will:


Create double bar graphs, double line graphs, and stem and leaf plots with and without technology, using given data.

Select an appropriate graph format to display given data.

Read and interpret, infer, predict, draw conclusions, and evaluate data from any graph.

Determine mean, median, mode, minimum value, maximum value, and range, and discuss what each does to help interpret a given set of data.

List all possible outcomes of a single event and tell whether an outcome is certain, impossible, likely, or unlikely.

Record probabilities as fractions, decimals, or percents.

Demonstrate that the sum of all probabilities equals one.

List outcomes by a variety of methods (e.g., tree diagram).