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- 8: Mathematical process standards
- 8.1: The student uses mathematical processes to acquire and demonstrate mathematical understanding.
- 8.1A: Apply mathematics to problems arising in everyday life, society, and the workplace.
- Are the statements correct?
- Let us tile the floor
- When will the riders meet?
- Divide the Chocolate bar equally
- Addition of rational numbers with different denominators (Practice)
- Subtraction of rational numbers with different denominators (Practice)
- Multiplication of Rational Numbers
- Division of Rational Numbers
- Integer Number Line
- Integer Millionaire
- Fill using Proportions
- Unitary Method - Word Problems
- Word Problems
- Let us calculate Simple Interest
- Bar graphs with multiple columns
- Find mean, mode, range and median
- Probability with balls
- Multiplication skill practice
- Skill Practice for Integer Multiplication & Division
- Let us arrange dinner tables
- Let us plant some flower pots
- 8.1B: Use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution.
- Multiplication as repeated addition
- Multiplication using flip over method
- Multiplication using array model
- Division using flip over method
- Combination of Multiplication & Division
- Model using a balance
- Check for Proportionality
- Represent in a number line and compare
- Represent on a grid
- Represent and Find Percentage
- Represent and Calculate Profit or Loss
- 8.1C: Select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques, including mental math, estimation, and number sense as appropriate, to solve problems.
- Identify the item purchased
- Round and find the result
- Estimate the result
- Recognize the pattern and fill the boxes
- Square numbers
- Triangular numbers
- Patterns in Number Operations
- Let us extend the patterns
- Broken Calculator
- Find the correct Trail
- Application Problems
- Car Expense Record
- Solve the word problems
- How many sea animals can you catch?
- Drag and place the numbers
- Fit the numbers and symbols
- 8.1D: Communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate.
- Absolute and Opposite numbers
- Identify the missing number
- Review of numbers
- Match the number to the number type
- Sieve the numbers
- Types of numbers
- Find all possible factors
- Represent the number using Dominos
- Introduction to simplest form
- Check for Proportionality
- Identify the type of triangle
- Pick the parts of a circle
- Draw the parts of a circle
- Constants, Coefficients and Terms
- Type of Polynomial
- 8.1E: Create and use representations to organize, record, and communicate mathematical ideas.
- Find using proportions
- Fill using Proportions
- Addition chips
- Subtraction chips
- Let us calculate Simple Interest
- Simple Interest Graph
- Properties of Prime Factors
- Addition with Fraction Strips
- Subtraction with Fraction Strips
- Let us arrange dinner tables
- Maximum area for a given perimeter
- Represent in Pictograph form
- Count the fruits and Represent in Pictograph
- Interpret Pictograph with half pictures
- Represent Pictograph with half pictures
- Frequency Table
- Interpret a Bar graph
- Represent in Bar graph form
- 8.1F: Analyze mathematical relationships to connect and communicate mathematical ideas.
- 8.1G: Display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication.
- Closure Property of Addition
- Additive Inverse property/ Identity
- Commutative Property of Addition (number line)
- Commutative Property of Subtraction (number line)
- Commutative property using numbers addition
- Commutative property using numbers subtraction
- Associative Property addition
- Associative Property subtraction
- Divisibility Test for the number 2
- Divisibility Test for the number 4
- Divisibility Test for the number 8
- Divisibility Test for the number 5
- Divisibility Test for the number 10
- Divisibility Test for the number 3
- Divisibility Test for the number 6
- Divisibility Test for the number 9
- Divisibility Test for the number 11
- 8.1A: Apply mathematics to problems arising in everyday life, society, and the workplace.
- 8.1: The student uses mathematical processes to acquire and demonstrate mathematical understanding.
- 8: Number and operations
- 8.2: The student applies mathematical process standards to represent and use real numbers in a variety of forms.
- 8.2A: Extend previous knowledge of sets and subsets using a visual representation to describe relationships between sets of real numbers.
- 8.2B: Approximate the value of an irrational number, including π and square roots of numbers less than 225, and locate that rational number approximation on a number line.
- 8.2C: Convert between standard decimal notation and scientific notation.
- 8.2D: Order a set of real numbers arising from mathematical and real-world contexts.
- 8.2: The student applies mathematical process standards to represent and use real numbers in a variety of forms.
- 8: Proportionality
- 8.3: The student applies mathematical process standards to use proportional relationships to describe dilations.
- 8.3A: Generalize that the ratio of corresponding sides of similar shapes are proportional, including a shape and its dilation.
- 8.3B: Compare and contrast the attributes of a shape and its dilation(s) on a coordinate plane.
- 8.3C: Use an algebraic representation to explain the effect of a given positive rational scale factor applied to two-dimensional figures on a coordinate plane with the origin as the center of dilation.
- 8.4: The student applies mathematical process standards to explain proportional and non-proportional relationships involving slope.
- 8.4A: Use similar right triangles to develop an understanding that slope, m, given as the rate comparing the change in y-values to the change in x-values, (y2 - y1)/ (x2 - x1), is the same for any two points (x1, y1) and (x2, y2) on the same line.
- 8.4B: Graph proportional relationships, interpreting the unit rate as the slope of the line that models the relationship.
- 8.4C: Use data from a table or graph to determine the rate of change or slope and y-intercept in mathematical and real-world problems.
- 8.5: The student applies mathematical process standards to use proportional and non-proportional relationships to develop foundational concepts of functions.
- 8.5A: Represent linear proportional situations with tables, graphs, and equations in the form of y = kx.
- 8.5B: Represent linear non-proportional situations with tables, graphs, and equations in the form of y = mx b, where b ≠ 0.
- 8.5C: Contrast bivariate sets of data that suggest a linear relationship with bivariate sets of data that do not suggest a linear relationship from a graphical representation.
- 8.5D: Use a trend line that approximates the linear relationship between bivariate sets of data to make predictions.
- 8.5E: Solve problems involving direct variation.
- 8.5F: Distinguish between proportional and non-proportional situations using tables, graphs, and equations in the form y = kx or y = mx b, where b ≠ 0.
- 8.5G: Identify functions using sets of ordered pairs, tables, mappings, and graphs.
- 8.5H: Identify examples of proportional and non-proportional functions that arise from mathematical and real-world problems.
- 8.5I: Write an equation in the form y = mx b to model a linear relationship between two quantities using verbal, numerical, tabular, and graphical representations.
- 8.3: The student applies mathematical process standards to use proportional relationships to describe dilations.
- 8: Expressions, equations, and relationships
- 8.6: The student applies mathematical process standards to develop mathematical relationships and make connections to geometric formulas.
- 8.6A: Describe the volume formula V = Bh of a cylinder in terms of its base area and its height.
- 8.6B: Model the relationship between the volume of a cylinder and a cone having both congruent bases and heights and connect that relationship to the formulas.
- 8.6C: Use models and diagrams to explain the Pythagorean theorem.
- 8.7: The student applies mathematical process standards to use geometry to solve problems.
- 8.7A: Solve problems involving the volume of cylinders, cones, and spheres.
- 8.7B: Use previous knowledge of surface area to make connections to the formulas for lateral and total surface area and determine solutions for problems involving rectangular prisms, triangular prisms, and cylinders.
- 8.7C: Use the Pythagorean Theorem and its converse to solve problems.
- 8.7D: Determine the distance between two points on a coordinate plane using the Pythagorean Theorem.
- 8.8: The student applies mathematical process standards to use one-variable equations or inequalities in problem situations.
- 8.8A: Write one-variable equations or inequalities with variables on both sides that represent problems using rational number coefficients and constants.
- 8.8B: Write a corresponding real-world problem when given a one-variable equation or inequality with variables on both sides of the equal sign using rational number coefficients and constants.
- 8.8C: Model and solve one-variable equations with variables on both sides of the equal sign that represent mathematical and real-world problems using rational number coefficients and constants.
- 8.8D: Use informal arguments to establish facts about the angle sum and exterior angle of triangles, the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles.
- Sum of Angles in a Triangle - Paper folding
- Sum of Angles in a Triangle - Parallel lines at vertices
- Exterior Angle Property
- Testing for Parallel lines
- Properties of angles made by a transversal - Corresponding angles
- Properties of angles made by a transversal - Alternate Angles
- Properties of angles made by a transversal - Interior Opposite Angles
- AAA Similarity Criterion
- 8.9: The student applies mathematical process standards to use multiple representations to develop foundational concepts of simultaneous linear equations.
- 8.6: The student applies mathematical process standards to develop mathematical relationships and make connections to geometric formulas.
- 8: Two-dimensional shapes
- 8.10: The student applies mathematical process standards to develop transformational geometry concepts.
- 8.10A: Generalize the properties of orientation and congruence of rotations, reflections, translations, and dilations of two-dimensional shapes on a coordinate plane.
- 8.10B: Differentiate between transformations that preserve congruence and those that do not.
- 8.10C: Explain the effect of translations, reflections over the x- or y-axis, and rotations limited to 90°, 180°, 270°, and 360° as applied to two-dimensional shapes on a coordinate plane using an algebraic representation.
- 8.10D: Model the effect on linear and area measurements of dilated two-dimensional shapes.
- 8.10: The student applies mathematical process standards to develop transformational geometry concepts.
- 8: Measurement and data
- 8.11: The student applies mathematical process standards to use statistical procedures to describe data.
- 8.11A: Construct a scatterplot and describe the observed data to address questions of association such as linear, non-linear, and no association between bivariate data.
- 8.11B: Determine the mean absolute deviation and use this quantity as a measure of the average distance data are from the mean using a data set of no more than 10 data points.
- 8.11C: Simulate generating random samples of the same size from a population with known characteristics to develop the notion of a random sample being representative of the population from which it was selected.
- 8.11A: Construct a scatterplot and describe the observed data to address questions of association such as linear, non-linear, and no association between bivariate data.
- 8.11: The student applies mathematical process standards to use statistical procedures to describe data.
- 8: Personal financial literacy
- 8.12: The student applies mathematical process standards to develop an economic way of thinking and problem solving useful in one's life as a knowledgeable consumer and investor.
- 8.12A: Solve real-world problems comparing how interest rate and loan length affect the cost of credit.
- 8.12B: Calculate the total cost of repaying a loan, including credit cards and easy access loans, under various rates of interest and over different periods using an online calculator.
- 8.12C: Explain how small amounts of money invested regularly, including money saved for college and retirement, grow over time.
- 8.12D: Calculate and compare simple interest and compound interest earnings.
- 8.12E: Identify and explain the advantages and disadvantages of different payment methods.
- 8.12F: Analyze situations to determine if they represent financially responsible decisions and identify the benefits of financial responsibility and the costs of financial irresponsibility.
- 8.12G: Estimate the cost of a two-year and four-year college education, including family contribution, and devise a periodic savings plan for accumulating the money needed to contribute to the total cost of attendance for at least the first year of college.
- 8.12A: Solve real-world problems comparing how interest rate and loan length affect the cost of credit.
- 8.12: The student applies mathematical process standards to develop an economic way of thinking and problem solving useful in one's life as a knowledgeable consumer and investor.