Course Overview
FIRST SEMESTER
Unit 1: Making Relevant Connections within the Number System
Expected Dates: Beginning of School Year to Mid-September In this unit, students will build upon the understanding of rational numbers developed in 6th grade, transitioning from exploring to ultimately formalizing rules for basic arithmetic operations (addition, subtraction, multiplication, and division) with rational numbers. Using both contextual and numerical problems, students explore arithmetic combinations of negative numbers and positive numbers. Students will explore the results of adding, subtracting, multiplying, and dividing pairs of numbers in context, leading to the generalization of rules. Rational numbers in different forms (integers, percents, fractions, and decimal numbers) should be used in computations and explorations. Unit 2: Reasoning with Expressions, Equations, and Inequalities Expected Dates: Mid-September to Early November This unit will build on what students build on what was learned in previous grades regarding mathematical properties (such as commutative, associative, and distributive properties) and conventions (such as order of operations), use these conventions and properties of operations to rewrite equivalent expressions, and interpret expressions in context. Students extend properties used with whole numbers to rational numbers in multiple formats (fractions and decimals). Students construct and solve equations and inequalities to solve contextual problems, and interpret solutions based on the context. Unit 3a: Exploring Ratios and Proportional Relationships Expected Dates: Early November to December (Holiday) The units in this instructional framework emphasize key standards that assist students to develop a deeper understanding of numbers. They learn to express different representations of rational numbers (e.g., fractions, decimals, and percent’s), discover how to identify and explain the constant of proportionality, and represent proportional relationships and scale drawings within real-world contexts. The Big Ideas that are expressed in this unit are integrated with such routine topics as estimation, mental and basic computation. All of these concepts need to be reviewed throughout the year. Standard 7.PAR.4 extends what students learned in Grade 6 about rate and ratios to analyzing proportions and proportional relationships. Students calculate unit rates and move to recognizing and representing proportional relationships in equations and on graphs. These skills and understandings are used to solve multistep ratio and percent problems involving real-world scenarios such as interest, sales tax, and shopping. Students in Grade 7 will compute and solve problems involving unit rate presented in practical, real-life situations. Students will determine and represent unit rates in graphs, tables, equations and diagrams. Students will deepen their understanding of ratios to investigate proportional relationships to solve real-world problems using a variety of strategies. Students will extend their proportional reasoning as they use similar triangles to explain slope. Students graph proportional relationships and understand the unit rate informally as a measure of the steepness of the related line, called the slope. They distinguish proportional relationships from other relationships. Students in 7th grade will use proportional reasoning to explain why the slope is the same between any two points in a similar triangle. |
SECOND SEMESTERUnit 3b: Exploring Ratios and Proportional Relationships
Expected Dates: January to Mid-February The units in this instructional framework emphasize key standards that assist students to develop a deeper understanding of numbers. They learn to express different representations of rational numbers (e.g., fractions, decimals, and percent’s), discover how to identify and explain the constant of proportionality, and represent proportional relationships and scale drawings within real-world contexts. The Big Ideas that are expressed in this unit are integrated with such routine topics as estimation, mental and basic computation. All of these concepts need to be reviewed throughout the year. Standard 7.PAR.4 extends what students learned in Grade 6 about rate and ratios to analyzing proportions and proportional relationships. Students calculate unit rates and move to recognizing and representing proportional relationships in equations and on graphs. These skills and understandings are used to solve multistep ratio and percent problems involving real-world scenarios such as interest, sales tax, and shopping. Students in Grade 7 will compute and solve problems involving unit rate presented in practical, real-life situations. Students will determine and represent unit rates in graphs, tables, equations and diagrams. Students will deepen their understanding of ratios to investigate proportional relationships to solve real-world problems using a variety of strategies. Students will extend their proportional reasoning as they use similar triangles to explain slope. Students graph proportional relationships and understand the unit rate informally as a measure of the steepness of the related line, called the slope. They distinguish proportional relationships from other relationships. Students in 7th grade will use proportional reasoning to explain why the slope is the same between any two points in a similar triangle. Unit 4: Making Relevant Connections with Geometry Expected Dates: Mid-February to End March In this unit students will be engaged in using what they have previously learned about drawing geometric figures using rulers and protractors with an emphasis on triangles, students will also write and solve equations involving angle relationships, area, volume, and surface area of fundamental solid figures. The challenges in this unit include understanding the geometric figures and solving equations involving geometric figures. The students also should be guided to realize how geometry works in real world situations. The concepts that are expressed in this unit are integrated with such routine topics as estimation, mental and basic computation. All of these concepts need to be reviewed throughout the year. In 6th grade students were able to solve for the area of triangles, quadrilaterals, and polygons. In 7th grade students continue to deepen their knowledge of area and explore the area and circumference of a circle. 7th grade students will also solve real life mathematical problems involving surface area and volume of right prisms. In 8th grade, students will extend their knowledge of volume to cones and spheres. Students will write and solve equations using facts involving measures of angles. Students will study circles and use proportional reasoning to understand the relationship between the diameter and circumference, deriving formulas for circumference and area to solve problems. Students will solve problems involving surface area and volume of right prisms and cylinders and explore two-dimensional cross sections of three dimensional solids. Unit 5: Investigating Probability Expected Dates: Early March to May In this unit, students will begin an exploration of probability and chance processes. Students will develop probability models to find the likelihood of simple events and make predictions using simulations' information. Students will compare theoretical and experimental probabilities of events and explain discrepancies. In 6th grade students were able to build a solid foundation in numeracy to apply that foundational knowledge and apply part whole strategies in context. In 7th grade students continue to deepen their knowledge of these strategies by exploring and developing probability models using simple events. Students investigate and learn the probability of a chance event is a number between 0 and 1. They develop a probability model and use it to find probabilities of events. |