Standards
The student will estimate, demonstrate, solve, and justify solutions to problems using operations with fractions and mixed numbers, including those in context.
Generate resourceDemonstrate/model multiplication and division of fractions (proper or improper) and mixed numbers using multiple representations.*
Generate resourceMultiply and divide fractions (proper or improper) and mixed numbers that include denominators of 12 or less. Answers are expressed in simplest form.*
Generate resourceInvestigate and explain the effect of multiplying or dividing a fraction, whole number, or mixed number by a number between zero and one.*
Generate resourceEstimate, determine, and justify the solution to single-step and multistep problems in context that involve addition and subtraction with fractions (proper or improper) and mixed numbers, with and without regrouping, that include like and unlike denominators of 12 or less. Answers are expressed in simplest form.
Generate resourceEstimate, determine, and justify the solution to single-step and multistep problems in context that involve multiplication and division with fractions (proper or improper) and mixed numbers that include denominators of 12 or less. Answers are expressed in simplest form.
Generate resourceThe student will estimate, demonstrate, solve, and justify solutions to problems using operations with integers, including those in context.
Generate resourceDemonstrate/model addition, subtraction, multiplication, and division of integers using pictorial representations or concrete manipulatives.*
Generate resourceSimplify an expression that contains absolute value bars | | and an operation with two integers (e.g., –|5 – 8| or |−12| 8 ) and represent the result on a number line.
Generate resourceEstimate, determine, and justify the solution to one and two-step contextual problems, involving addition, subtraction, multiplication, and division with integers.
Generate resourceThe student will identify the characteristics of circles and solve problems, including those in context, involving circumference and area.
Generate resourceIdentify and describe chord, diameter, radius, circumference, and area of a circle.
Generate resourceInvestigate and describe the relationship between radius and circumference
Generate resourceInvestigate and describe the relationship between diameter and circumference
Generate resourceDevelop an approximation for pi (3.14) by gathering data and comparing the circumference to the diameter of various circles, using concrete manipulatives or technological models.
Generate resourceDevelop the formula for circumference using the relationship between diameter, radius, and pi.
Generate resourceSolve problems, including those in context, involving circumference and area of a circle when given the length of the diameter or radius.
Generate resourceThe student will reason mathematically to solve problems, including those in context, that involve the area and perimeter of triangles and parallelograms.
Generate resourceDevelop the formula for determining the area of parallelograms and triangles using pictorial representations and concrete manipulatives (e.g., two-dimensional diagrams, grid paper).
Generate resourceSolve problems, including those in context, involving the perimeter and area of triangles and parallelograms.
Generate resourceThe student will describe the characteristics of the coordinate plane and graph ordered pairs.
Generate resourceIdentify and describe the location (quadrant or the axis) of a point given as an ordered pair. Ordered pairs will be limited to coordinates expressed as integers.
Generate resourceGraph ordered pairs in the four quadrants and on the axes of a coordinate plane. Ordered pairs will be limited to coordinates expressed as integers.
Generate resourceIdentify ordered pairs represented by points in the four quadrants and on the axes of the coordinate plane. Ordered pairs will be limited to coordinates expressed as integers.
Generate resourceRelate the coordinates of a point to the distance from each axis and relate the coordinates of a single point to another point on the same horizontal or vertical line. Ordered pairs will be limited to coordinates expressed as integers.
Generate resourceDraw polygons in the coordinate plane given coordinates for the vertices; use coordinates to determine the length of a side joining points with the same first coordinate or the same second coordinate. Ordered pairs will be limited to coordinates expressed as integers. Apply these techniques in the context of solving contextual and mathematical problems.
Generate resourceDraw lines of symmetry to divide regular polygons into two congruent parts.
Generate resourceDetermine the congruence of segments, angles, and polygons given their properties.
Generate resourceDetermine whether polygons are congruent or noncongruent according to the measures of their sides and angles.
Generate resourceThe student will reason and use multiple strategies to express equivalency, compare, and order numbers written as fractions, mixed numbers, decimals, and percents.
Generate resourceEstimate and determine the percent represented by a given model (e.g., number line, picture, verbal description), including percents greater than 100% and less than 1%.*
Generate resourceRepresent and determine equivalencies among decimals (through the thousandths place) and percents incorporating the use of number lines, and concrete and pictorial models.*
Generate resourceRepresent and determine equivalencies among fractions (proper or improper) and mixed numbers that have denominators that are 12 or less or factors of 100 and percents incorporating the use of number lines, and concrete and pictorial models.*
Generate resourceRepresent and determine equivalencies among decimals, percents, fractions (proper or improper), and mixed numbers that have denominators that are 12 or less or factors of 100 incorporating the use of number lines, and concrete and pictorial models.*
Generate resourceUse multiple strategies (e.g., benchmarks, number line, equivalency) to compare and order no more than four positive rational numbers expressed as fractions (proper or improper), mixed numbers, decimals, and percents (decimals through thousandths, fractions with denominators of 12 or less or factors of 100) with and without models. Justify solutions orally, in writing or with a model. Ordering may be in ascending or descending order.*
Generate resourceThe student will reason and use multiple strategies to represent, compare, and order integers.
Generate resourceRepresent integers (e.g., number lines, concrete materials, pictorial models), including models derived from contextual situations, and identify an integer represented by a point on a number line.
Generate resourceIdentify and describe the absolute value of an integer as the distance from zero on the number line.
Generate resourceThe student will recognize and represent patterns with whole number exponents and perfect squares.
Generate resourceRecognize and represent patterns with bases and exponents that are whole numbers.
Generate resourceRecognize and represent patterns of perfect squares not to exceed 202 , by using concrete and pictorial models.
Generate resourceJustify if a number between 0 and 400 is a perfect square through modeling or mathematical reasoning.
Generate resourceRecognize and represent powers of 10 with whole number exponents by examining patterns in place value.
Generate resourceThe student will use ratios to represent relationships between quantities, including those in context.
Generate resourceRepresent a relationship in context that makes a comparison by using the notations 𝑎 𝑏 , a:b, and a to b.
Generate resourceRepresent different comparisons within the same quantity or between different quantities (e.g., part to part, part to whole, whole to whole).
Generate resourceCreate a table of equivalent ratios to represent a proportional relationship between two quantities, when given a ratio.
Generate resourceCreate a table of equivalent ratios to represent a proportional relationship between two quantities, when given a contextual situation.
Generate resourceThe student will identify and represent proportional relationships between two quantities, including those in context (unit rates are limited to positive values).
Generate resourceIdentify the unit rate of a proportional relationship represented by a table of values, a contextual situation, or a graph.
Generate resourceDetermine a missing value in a ratio table that represents a proportional relationship between two quantities using a unit rate.
Generate resourceDetermine whether a proportional relationship exists between two quantities, when given a table of values, context, or graph.
Generate resourceWhen given a contextual situation representing a proportional relationship, find the unit rate and create a table of values or a graph.
Generate resourceMake connections between and among multiple representations of the same proportional relationship using verbal descriptions, ratio tables, and graphs.
Generate resourceThe student will write and solve one-step linear equations in one variable, including contextual problems that require the solution of a one-step linear equation in one variable.
Generate resourceIdentify and develop examples of the following algebraic vocabulary: equation, variable, expression, term, and coefficient.
Generate resourceRepresent and solve one-step linear equations in one variable, using a variety of concrete manipulatives and pictorial representations (e.g., colored chips, algebra tiles, weights on a balance scale).
Generate resourceApply properties of real numbers and properties of equality to solve a one-step equation in one variable. Coefficients are limited to integers and unit fractions. Numeric terms are limited to integers.
Generate resourceConfirm solutions to one-step linear equations in one variable using a variety of concrete manipulatives and pictorial representations (e.g., colored chips, algebra tiles, weights on a balance scale).
Generate resourceWrite a one-step linear equation in one variable to represent a verbal situation, including those in context.
Generate resourceCreate a verbal situation in context given a one-step linear equation in one variable.
Generate resourceThe student will represent a contextual situation using a linear inequality in one variable with symbols and graphs on a number line.
Generate resourceGiven the graph of a linear inequality in one variable on a number line, represent the inequality in two equivalent ways (e.g., x < -5 or -5 > x) using symbols. Symbols include <, >, ≤, ≥.
Generate resourceWrite a linear inequality in one variable to represent a given constraint or condition in context or given a graph on a number line.
Generate resourceGiven a linear inequality in one variable, create a corresponding contextual situation or create a number line graph.
Generate resourceUse substitution or a number line graph to justify whether a given number in a specified set makes a linear inequality in one variable true.
Generate resourceIdentify a numerical value(s) that is part of the solution set of a given inequality in one variable.
Generate resourceThe student will apply the data cycle (formulate questions; collect or acquire data; organize and represent data; and analyze data and communicate results) with a focus on circle graphs.
Generate resourceFormulate questions that require the collection or acquisition of data with a focus on circle graphs.
Generate resourceDetermine the data needed to answer a formulated question and collect the data (or acquire existing data) using various methods (e.g., observations, measurement, surveys, experiments).
Generate resourceDetermine the factors that will ensure that the data collected is a sample that is representative of a larger population.
Generate resourceOrganize and represent data using circle graphs, with and without the use of technology tools. The number of data values should be limited to allow for comparisons that have denominators of 12 or less or those that are factors of 100 (e.g., in a class of 20 students, 7 choose apples as a favorite fruit, so the comparison is 7 out of 20, 7 20 , or 35%).
Generate resourceAnalyze data represented in a circle graph by making observations and drawing conclusions.
Generate resourceCompare data represented in a circle graph with the same data represented in other graphs, including but not limited to bar graphs, pictographs, and line plots (dot plots), and justify which graphical representation best represents the data.
Generate resourceThe student will represent the mean as a balance point and determine the effect on statistical measures when a data point is added, removed, or changed.
Generate resourceRepresent the mean of a set of data graphically as the balance point represented in a line plot (dot plot).
Generate resourceDetermine the effect on measures of center when a single value of a data set is added, removed, or changed.
Generate resourceObserve patterns in data to identify outliers and determine their effect on mean, median, mode, or range.
Generate resource