Unit 01: Number and Operations (9 days for the entire unit)
Expected Unit Test Date - September 7th
During this unit, students use a visual representation to organize and display the relationship of the sets and subsets of rational numbers, which include counting (natural) numbers, whole numbers, integers, and rational numbers. Students also apply and extend operations with rational numbers to include negative fractions and decimals. Grade 7 students are expected to fluently add, subtract, multiply, and divide various forms of positive and negative rational numbers which include integers, decimals, fractions, and percents converted to equivalent decimals or fractions for multiplying or dividing. Students also create and organize a financial assets and liabilities record, construct a net worth statement, calculate sales tax for a given purchase, and calculate income tax for earned wages.
Unit 02: One-Variable Equations and Inequalities (16 days for the entire unit)
Expected Unit Test Date - September 28th
During this unit, students extend their previous work with one-variable, one-step equations and inequalities to one-variable, two-step equations and inequalities. Students model and solve one-variable, two-step equations and inequalities with concrete and pictorial models and algebraic representations. Solutions to equations and inequalities are represented on number lines and given values are used to determine if they make an equation or inequality true. Students are expected to write an equation or inequality to represent conditions or constraints within a problem and then, conversely, when given an equation or inequality out of context, students are expected to write a corresponding real-world problem to represent the equation or inequality. Additionally, students write and solve equations using geometry concepts, including the sum of the angles in a triangle, and angle relationships. Equations and inequalities are extended to include problem situations involving monetary incentives such as sales, rebates, or coupons. Financial literacy aspects such as calculating and comparing simple and compound interest as well as utilizing a family budget estimator to determine the minimum household budget needed for a family to meet its basic needs is also explored. Although the formula for compound interest utilizes an exponent, students experiences for writing, modeling, solving, and evaluating equations and inequalities should focus primarily on linear relationships.
Unit 03: Proportional Reasoning with Ratios and Rates (11 days for the entire unit)
Expected Unit Test Date - October 14th,
During this unit, students examine proportional reasoning with ratios and rates through the lens of constant rates of change. Students are expected to represent constant rates of change given pictorial, tabular, verbal, numeric, graphical and algebraic representations, including d = rt. The development of rates lends itself to students examining d = rt and reveals the amount of variation that can occur when various constant rates can be applied to a situation to reveal the same outcome (e.g., the distance traveled remains the same in a situation if the speed is doubled and the time is halved, etc.). Exploring the relationship between distance, rate, and time allows students to generalize the effects when rates within any problem situation are changed. Students solve problems involving ratios, rates, and percents. Computations with percents are now inclusive of solving problems involving percent increase, percent decrease, and financial literacy. Percents are also used as students identify the components of a personal budget and calculate what percentage each category comprises of the total budget. They also calculate unit rates from rates and determine the constant of proportionality within mathematical and real-world problems. Students use proportions and unit rates as they extend previous understandings of converting units within a measurement system to now include converting units between both customary and metric measurement systems.
Unit 04: Graphs and Two-Variable Equations (14 days for the entire unit)
Expected Unit Test Date - November 3rd
During this unit, students use bivariate data, data with two variables, to reexamine constant rates of change given pictorial, tabular, verbal, numeric, graphical and algebraic representations and extend their understandings of the constant of proportionality. Students are formally introduced to the slope intercept form of equations, y = mx + b, to represent linear relationships. Although students are not formally introduced to slope or y-intercept in linear proportional and non-proportional relationships until Grade 8, students are expected to relate the constant rate of change to m, and the y-coordinate, when the x-coordinate is zero, tob in equations that simplify to the form y = mx + b. This relationship is examined through the ratio of rise to run and the change in the y-values to the change in the x-values.
Unit 05: Similarity (12 days for the entire unit)
Expected Unit Test Date - November 18th
During this unit, students extend concepts of proportionality to two-dimensional figures as they solve mathematical and real-world problems involving similar shapes and scale drawings. Students generalize the critical attributes of similarity which include examining the multiplicative relationship within and between similar shapes.
Unit 06: Probability (13 days for the entire unit)
Expected Unit Test Date - December 14th
During this unit, students extend the use of proportional reasoning to solve problems as they are formally introduced to probability concepts. Students use various representations, including lists, tree diagrams, tables, and the Fundamental Counting Principle to represent the sample spaces for simple and compound events. Compound events are inclusive of both compound independent and compound dependent events. Students select, design, develop, and use various methods to simulate simple and compound events. Methods for simulation may or may not include the use of technology. When conducting simulations or investigating data from simulations, students develop an understanding of how the Law of Large Numbers will affect the experimental probability. Students are expected to distinguish between theoretical and experimental data and find the probabilities of a simple event. Students analyze and describe the relationship between the probability of a simple event and its complement. Probabilities may be represented as a decimal, fraction, or percent. Data and sample spaces are used to determine experimental and theoretical probabilities to simple and compound events. Data from experiments, experimental data, theoretical probability, and random samples are used to make qualitative and quantitative inferences about a population. Qualitative and quantitative predictions and comparisons from simple experiments are used to solve problems. Students should consider the proportional relationships within and between probabilistic situations when making predictions and inferences.
Unit 07: Circles and Composite Figures (13 days for the entire unit)
Expected Unit Test Date - January 13th
During this unit, students convert between measurement systems, including the use of proportions and the use of unit rates. Students are introduced to the measurement of circles as they describe p as the ratio of the circumference of a circle to its diameter. Models are used to the approximate formulas for the circumference and area of a circle and for students to make connections between the models for the actual formulas. The formulas for circumference and area of a circle are used to solve problems. Students extend previous knowledge of the area of rectangles, parallelograms, trapezoids, and triangles along with the new content of the area of circles and determining the area of composite figures consisting of rectangles, triangles, parallelograms, squares, quarter circles, semicircles, and trapezoids.
Unit 08: Volume and Surface Area (12 days for the entire unit)
Expected Unit Test Date - February 2nd
During this unit, students model the relationship between the volume of rectangular prism and a rectangular pyramid having both congruent bases and heights as well as connect that relationship to their respective formulas. Students are expected to explain verbally and symbolically the relationship between the volume of a triangular prism and a triangular pyramid having both congruent bases and heights as well as connect that relationship to their respective formulas. Students solve problems involving volume, including the volume of rectangular prisms, triangular prisms, rectangular pyramids, and triangular pyramids. Students also solve problems involving surface area by determining the area of the shape's net, including lateral and total surface area of a rectangular prism, rectangular pyramid, triangular prism, and triangular pyramid.
Unit 09: Data Representations (15 days for the entire unit)
Expected Unit Test Date - February 23rd
During this unit, students solve problems using data represented in bar graphs, dot plots, and circle graphs, including part-to-whole and part-to-part comparisons and equivalents. Students use data from random samples to make inferences about a population and compare two populations based on data from random samples, including informal comparative inferences about differences between the two populations. Two groups of numeric data are compared using comparative dot plots or box plots by describing their shapes, centers, and spreads. Descriptions of shape, center, and spread include skewed right, skewed left, symmetrical, mean, median, mode, range, and interquartile rage. Percents are also incorporated within this unit as students calculate the components of a personal budget in conjunction with circle graphs and bar graphs.
Unit 10: Making Connections (10 days for the entire unit)
Expected Unit Test Date - March 9th
During this unit, students continue to apply operations with rational numbers to calculate unit rates from rates and determine the constant of proportionality within mathematical and real-world problems. Students are expected to represent constant rates of change given pictorial, tabular, verbal, numeric, graphical, and algebraic representations. Students use the slope-intercept form of equations, y = mx + b, to represent linear relationships. Finally, students revisit concepts of proportionality to two-dimensional figures as they solve mathematical and real-world problems involving similar shapes.
Unit 11: Essential Understandings of Algebra (13 days for the entire unit)
Expected Unit Test Date - April 5th
During this unit, students revisit and solidify essential understandings of algebra. Students model and solve one-variable, two-step equations and inequalities with concrete and pictorial models and algebraic representations. Solutions to equations and inequalities are represented on number lines and given values are used to determine if they make an equation or inequality true. Students are expected to write an inequality to represent conditions or constraints within a problem and then, conversely, when given an inequality out of context, students are expected to write a corresponding real-world problem to represent the inequality.
Unit 12: Essential Understandings of Geometry (12 days for the entire unit)
Expected Unit Test Date - April 25th
During this unit, students revisit and solidify essential understandings of geometry. Students use the formulas for circumference and area of a circle to solve problems. Students extend previous knowledge of the area of rectangles, parallelograms, trapezoids, and triangles along with the area of circles in determining the area of composite figures consisting of rectangles, triangles, parallelograms, squares, quarter circles, semicircles, and trapezoids. Students also solve problems involving the volume of rectangular and triangular prisms and pyramids.
STAAR Review days - April 26th - May ??? (about 2 units/day)
Expected STAAR test date : May ???
Rest of the year - Accelerate into Algebra standards OR catch up work (depending on the students' grades)
- Financial Planning Project
OR
– Road trip planning project
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