Grade 7
Glastonbury Public Schools Mathematics Curriculum
Proportional Relationships describe many real world situations.
Mathematics is learned through questions that arise while solving well-constructed problems. Our students begin with problems, they use strategies to solve the problems, and they learn the necessary mathematics along the way. Many classroom investigations are designed so that students will collaboratively or individually discover the mathematical properties. The properties are then discussed in class, summarized, and become part of the students’ mathematical knowledge to be applied to future problems.
The discovery of the mathematics is an essential part of the development of each student’s confidence as a mathematician. Knowledge that is gained through inquiry is more likely to be remembered for the long term. Teachers and parents work together to promote this discovery of math through investigation, problem solving, and reasoning. Our goal is for students to be problem solvers and understand that mathematics makes sense.
Seventh grade teachers guide students toward the development of a notebook as primary resource for mathematics. If your child has content questions, remind your child to reference his or her binder or iPad.
Unit 1: Rational Numbers
Conceptual Lens: Negative Numbers
Students will expand their understanding of numbers into those less than zero as necessitated through problem solving. They will wonder How are operations with negative numbers similar and different from other rational numbers? Students will learn that the absolute value of a number represents value, while the sign represents position and direction. The properties of operations will continue to make sense as students discover negative numbers through problem solving. In addition, Level 1 students will examine the differences between perfect roots and non-perfect roots which will create the need for the understandings of irrational numbers. Students will learn the appropriate use of rational approximations of irrational numbers to solve problems Students will develop the understanding that prior knowledge of properties of operations dictates procedures for all rational numbers.
Common Core State Standards: 7.NS.A.1(a-d), 7.NS.A.2(a-d), 7.EE.B.3, 7.NS.A.3, 8.NS.A.1, 8.NS.A.2
Unit 2: Expressions
Conceptual Lens: Variables
In this unit, students will focus on variables and representing relationships. Variables have many different meanings, depending on context and purpose and allow us to write expressions whose values are unknown. Students will use arithmetic and their understanding of rational numbers to create and manipulate expressions, paying particular attention to the structure of the expressions. An expression may be presented in many forms and two expressions may be equivalent, even if their symbolic forms differ. In addition, students will write and evaluate expressions for area and perimeter of polygons and surface area of cubes and right prisms using their knowledge of areas of triangles, quadrilaterals and polygons. By the end of the unit, students will recognize that expressions are powerful tools for exploring, reasoning about and representing situations.
Unit 3: Equation and Inequalities
Conceptual Lens: Properties
Students will solve multi-step equations characterized in terms of whether or not they involve equal parts of an amount or equal and unequal parts of an amount. The properties of equations will be used to provide logical arguments for the solutions to equations and formulas. Students will work with equivalent linear expressions, using properties of operations to explain equivalence. They will solve problems regarding interior and exterior angles of polygons, angles formed by parallel lines and transversals, and explain their answers using informal arguments. Students will then work with inequalities and examine values that make an inequality true or false, and use a number line to represent the true values. Students will use both equations and inequalities to solve application problems and understand how the properties of equality lead to logical steps and are essential to apply when solving a mathematical equation.
Common Core State Standards: 7.EE.B.3 & 4(a&b), 7.G.B.5 & 6, 8.EE.A.2, 8.EE.C.7(a&b), 8.G.C.9, 7.G.A.2, 8.G.A.5
Unit 4: Proportional Relationships
Conceptual Lens: Modeling
Students will face some new, more challenging problems and will quickly wonder How do I solve problems that have more than one relationship happening at the same time? They will solve problems and describe relationships that involve constant rates of change. Through investigations they will distinguish situations with changes in rate and with constant rates. These relationships will be represented and analyzed through graphs, tables and equations. Students will understand that proportional relationships are ratios and are useful in solving real world problems. In addition students will solve problems involving the circumference and area of a circle. Students will understand that the recognition of proportional relationships through analysis provides multiple strategies for problem solving.
Common Core State Standards: 7.RP.A.1-2, 7.EE.A.2, 7.G.A.3, 7.G.B.4 & 6, , 8.EE.B.5, 8.EE.B.6, 8.G.C.9,
Unit 5: Percent and Scaling
Conceptual Lens: Percent
Students will continue to build their understanding or proportional relationships as they solve real world problems involving percents. Students will understand that percents and other proportional relationships are ratios and are useful in solving real world problems. Students investigate the relationship between percent, part and whole and how percentages are used to represent changes in quantities. Students will solve both mark-up and mark-down problems involving percent. Lastly, students will apply their proportional reasoning to scale drawings and calculate the percent increase or decrease. Level 1 students will also use transformations to build the understanding of congruence of figures and dilation to understand similarity. Students will continue to gain an understanding of how proportional Relationships can be used to solve real world problems involving percents.
Common Core State Standards: 7.RP.A.3, , 7.G.A.1, 8.G.A.1, 8.G.A.2, 8.G.A.3, 8.G.A.4
Unit 6: Statistics
Conceptual Lens: Inference
Students will understand the need to study populations through representative and random sampling and use data to draw inferences about larger populations. Students calculate measures of center and variability of samples and use these measures to compare across different populations. Throughout this unit, students re-engage in ratios and proportions as well as decimals and percents. Students reason about data, make connections and defend their reasoning by constructing arguments. In these ways students will build the understanding that mathematicians infer generalizations regarding populations using representative samples.
Unit 7: Probability
Conceptual Lens: Likelihood of an event
Through investigations and experiments students will learn how to express the likelihood of events using the language of probability and using fractions, decimals, and percents. They will continue their development of the understanding of numbers through these applications of positive rational numbers. Students will make predictions regarding outcomes of simple and compound events using what they learn about theoretical probability and test their predictions using experimental probability (relative frequency). Students draw on and re-engage with concepts from ratios and proportions in order to fully understand probability as a ratio of desired outcomes to total outcomes. They also use proportional relationships to estimate long-run frequencies based on probabilities of experiments. Through experimentation, students will learn the models may be used to simulate real world situations, enabling us to make predictions.