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Unit | Timeframe | Big Ideas | Major Learning Experiences |
Unit 0 Mathematical Mindsets
| August/Sept. | We can all learn math to the highest levels.
Mistakes make our brains grow.
We learn more when we work together as a team. |
Students will |
Unit 1 Rational Numbers
| September |
The Number System unifies positive and negative integers and rational numbers through a coherent set of properties that define how numbers interact.
Rational number operations will help us solve real world problems about temperature, elevation, deposit and withdrawal, position, direction, and speed. |
Students will: Discover the rules for integer operations using concrete manipulatives and number lines. Add, subtract, multiply, and divide positive and negative rational numbers. Apply their understanding of integers and elevation to a project on the Columbian Trade Route. Calculate the distance between numbers on a number line by finding the absolute value of their difference. Create a comic strip about distance in a real world setting. Solve real-world and mathematical problems using operations of positive and negative numbers.
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Unit 2 Ratios and Proportions
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Nov/Dec |
Proportional relationships describe how quantities are related to each other through a constant ratio. By reasoning about these relationships, we can solve problems in mathematics, science, and everyday life (real-world problems).
| Students will: Identify if a relationship is proportional from a graph and a table and explain why or why not. Represent proportional relationships with a verbal description, graph, table and an equation in the form y = kx. Explain what a point on the graph means using context. Create a scale drawing of a flag that reflects a student’s identity. Compute and compare unit rates with ratios of fractions. Create a story involving unit rates. Share a recipe with their classmates and explain how to alter the ingredients to create enough food for one person, a family, and for the whole class.
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Unit 3 Expressions and Equations
| Dec./Feb. |
Expressions, equations, and inequalities can be used to model real-world and mathematical situations, and equivalent expressions and solution sets can illuminate relationships within those situations.
| Students will: Create equivalent expressions using the properties of operations to add, subtract, factor, and expand linear expressions. Evaluate algebraic expressions involving rational numbers. Solve real-world problems by creating and solving equations in the form px +q = r, and p(x + q) = r. Explain how to solve equations using an arithmetic approach and an equation approach. Solve real-world problems by creating, solving, and graphing inequalities in the form px +q < r or px + q < r. Apply their understanding of inequalities to real life situations, such as minimum wage. Create an example of a real world situation that involves a two step equation and explain how to solve the equation visually and algebraically.
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Unit 4 Percents and Proportional Relationships
| Feb./March |
Percentages are used worldwide to communicate information about sports, shopping, stocks, weather conditions, survey results, and many more ratio relationships.
We can solve percent problems using visual diagrams, tables, and equations.
| Students will: Solve percent problems about simple interest, tax, markups, markdowns, gratuities and commissions, and fees. Calculate percent increase, percent decrease, and percent error. Simulate the experience of going out to a restaurant and finding the total cost of the meal, including tax and tip. Create their own food truck business and determine profit projections using all of their percent skills.
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Unit 5 Geometry | March/April |
Two- and three-dimensional figures can be composed and decomposed to understand the connections between area, surface area, and volume and to solve real-world problems.
| Students will: Discover angle relationships and solve equations to solve problems about supplementary, complementary, vertical, and adjacent angles. Explain how the formula for the circumference of a circle and the area of a circle are connected. Discover the triangle inequality theorem, and explain whether a given set of side lengths or a given set of angles will form a unique triangle. Describe the two-dimensional figures that result from slicing three dimensional figures by using geometry software and clay models. Solve real-world and mathematical problems involving area, volume and surface area of 3-D and composite shapes. Apply their understanding of area, volume and surface area to design a new building/structure for the community.
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Unit 6 Statistics and Probability
| April/May | We can use random sampling to draw inferences about a population. We can compare two populations by graphing and analyzing data.
We can use probability models and experiments to predict the outcomes of events. | Students will: Create a random sample that is representative of a population, to draw inferences about the population. Compare two populations by finding the difference between measures of center and variability. Apply these statistical skills to compare the water quality between two different continents in the world. Approximate the probability of a chance event by collecting data and finding the relative frequency. Find the theoretical probability of an event occuring by finding the fraction of favorable outcomes out of all possible outcomes. Find the probability of compound events using organized lists, tables, tree diagrams and simulations. Create a compound probability game, and collect experimental data at the Probability Fair.
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