To better understand how I group students into cooperative teams and how I provide feedback to students, click on the links below to watch a short video on each strategy. After my inroduction, students start with : Complementary and Supplementary angles, then work with : Vertical Angles. The goal here was to give students the time they need to observe the relationship between different types of angles. Of course students will work at their own pace and that is encouraged. After allowing time for groups to correctly graph and label ask one group to place their papers under the document camera and share how they created the linear graphs. As they proceed they gain experience with identifying and reasoning about angles. The goals are the same as on the angles activity prior to this: move angles through transformations to map relationships between certain pairs of angles.
Click here to watch a short video on what it means to clarify and share learning intentions and criteria for success with students: The learning goals for today are to continue to focus on graphing linear equations with the purpose of using those lines to see angle relationships. My goal is to connect their work in the module to the formal definitions we are about to give. Once all students have correct graphs, it is time to begin answering the angle relationship questions. This is a key time to provide feedback to students both yourself and through partners within small groups. Lesson 23 Angle Relationships Answer Key can be very useful guide, and lesson 23 angle relationships answer key play an important role in your products.
Choose this group as you are providing feedback and let them know you would like for them to present their correct work. Students need to be able to discuss ideas and questions. You just want to at least get everyone through question 4 by the end of the first class period. Working in Cooperative Groups to Graph Allow students time to graph the three given equations and number the angles as the directions indicate. These questions are challenging and ask students to think about and prove angle relationships. Students as resources for one another Where to End the Lesson The goal for the first day is to reach at least question 4 and discuss the answers to these questions in a mini wrap-up before the end of class.
Tell students that they will be graphing two different intersections which will create eight angles for this activity. Each module is interactive and set up to minimize unnecessary distractions. I find it helps students to make meaning of angle relationships if they write about their observations as they work. The math standards of focus in this lesson today include : 8. I often had to remind students to use their tracing paper in order to compare angles and find their relationship first congruent or supplementary and then begin to think through the transformations that would move and map angles together. I also believe that it helps to first form observations and explanations in their own words, without the burden of definitions and calculations. When possible, I quote students when they describe an angle relationship in their own words.
We use small lesson closers after a small chunk of material has been completed. Sometimes students don't acknowledge the relationships between angles and instead make statements about each angle. An isosceles triangle has 2 angles that are equal in value. Watch a short video explaining the rational for this lesson and why I have chosen to apply transformations to parallel lines cut by a transversal. Students should work within their partnership or small group to correctly graph and label. I use the first few slides of the PowerPoint to introduce students to the GeogebraTube modules that I created for them to use today. Let students know that there will be a lot of vocabulary throughout the activity and it is important to know these angle pair names.
If two angles are supplementary and one equals 65 °, then the other equals 115°. Click below to watch a short video on how students provide feedback to one another within small groups. Click below to watch a short video on how I use the mini wrap-up strategy. Clarifying and Sharing Learning Goals Always begin by clarifying for the students what it is they will be learning from the activity today. The following lesson plans and worksheets are from the New York State Education Department Common Core-aligned educational resources. This is a very different approach from starting with formal language and finishing with inferences. The sum of the interior angles in a quadrilateral is 360°.
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Grade 7 Homework, Lesson Plans, and Worksheets Module 1 Topics and Objectives , : An Experience in Relationships as Measuring Rate , : Proportional Relationships , , , : Identifying Proportional and Non-Proportional Relationships in Tables , Identifying Proportional and Non-Proportional Relationships in Graphs , : Identifying Proportional and Non-Proportional Relationships in Graphs , : Unit Rate as the Constant of Proportionality , , , : Representing Proportional Relationships with Equations , : Interpreting Graphs of Proportional Relationships Topics A through B assessment 1 day, return 1 day, remediation or further applications 2 days , , , : Ratios of Fractions and Their Unit Rates , : Finding Equivalent Ratios Given the Total Quantity , : Multistep Ratio Problems , : Equations and Graphs of Proportional Relationships Involving Fractions , : Relating Scale Drawings to Ratios and Rates , : The Unit Rate as the Scale Factor , : Computing Actual Lengths from a Scale Drawing , : Computing Actual Areas from a Scale Drawing , : An Exercise in Creating a Scale Drawing , , , : An Exercise in Changing Scales Topics A through D assessment 1 day, return 1 day, remediation or further applications 2 days Module 2 Topics and Objectives , : Opposite Quantities Combine to Make Zero , : Using the Number Line to Model the Addition of Integers , : Understanding Addition of Integers , : Efficiently Adding Integers and Other Rational Numbers , : Understanding Subtraction of Integers and Other Rational Numbers , : The Distance Between Two Rational Numbers , : Addition and Subtraction of Rational Numbers , , , : Applying the Properties of Operations to Add and Subtract Rational Numbers , : Understanding Multiplication of Integers , : Develop Rules for Multiplying Signed Numbers , : Division of Integers , : Converting Between Fractions and Decimals Using Equivalent Fractions , : Converting Rational Numbers to Decimals Using Long Division , : Multiplication and Division of Rational Numbers , : Applying the Properties of Operations to Multiply and Divide Rational Numbers Topics A through B assessment 1 day, return 1 day, remediation or further applications 2 days , : Comparing Tape Diagram Solutions to Algebraic Solutions , , , : Writing, Evaluating, and Finding Equivalent Expressions with Rational Numbers , : Investments - Performing Operations with Rational Numbers , : If-Then Moves with Integer Number Cards , , , : Solving Equations Using Algebra Topics A through C assessment 1 day, return 1 day, remediation or further applications 2 days Module 3 Topics and Objectives , : Generating Equivalent Expressions , : Writing Products as Sums and Sums as Products : Using the Identity and Inverse to Write Equivalent Expressions : Collecting Rational Number Like Terms : Understanding Equations , : Using the If-Then Moves in Solving Equations , : Angle Problems and Solving Equations : Properties of Inequalities : Inequalities : Solving Inequalities : Graphing Solutions to Inequalities Topics A through B assessment 1 day, return 1 day, remediation or further applications 2 days : The Most Famous Ratio of All : The Area of a Circle : More Problems on Area and Circumference : Unknown Area Problems on the Coordinate Plane : Composite Area Problems , : Surface Area , : The Volume of a Right Prism , : Volume and Surface Area Topics A through C assessment 1 day, return 1 day, remediation or further applications 2 days Module 4 Topics and Objectives : Percent : Part of a Whole as a Percent : Comparing Quantities with Percent : Percent Increase and Decrease : Finding One-Hundred Percent Given Another Percent : Fluency with Percents : Markup and Markdown Problems : Percent Error Problems : Problem-Solving when the Percent Changes : Simple Interest : Tax, Commissions, Fees, and Other Real-World Percent Problems Topics A through B assessment 1 day, return 1 day, remediation or further applications 2 days : The Scale Factor as a Percent for a Scale Drawing : Changing Scales : Computing Actual Lengths from a Scale Drawing : Solving Area Problems Using Scale Drawings : Population Problems : Mixture Problems : Counting Problems Topics A through D assessment 1 day, return 1 day, remediation or further applications 2 days Module 5 Topics and Objectives : Chance Experiments : Estimating Probabilities by Collecting Data : Chance Experiments with Equally Likely Outcomes : Calculating Probabilities for Chance Experiments with Equally Likely Outcomes : Chance Experiments with Outcomes that Are Not Equally Likely : Using Tree Diagrams to Represent a Sample Space and to Calculate Probabilities : Calculating Probabilities of Compound Events :The Difference Between Theoretical Probabilities and Estimated Probabilities : Comparing Estimated Probabilities to Probabilities Predicted by a Model , : Using Simulation to Estimate a Probability : Using Probability to Make Decisions Topics A through B assessment 1 day, return 1 day, remediation or further applications 2 days : Populations, Samples, and Generalizing from a Sample to a Population : Selecting a Sample : Random Sampling : Methods for Selecting a Random Sample : Sampling Variability : Sampling Variability and the Effect of Sample Size : Understanding Variability when Estimating a Population Proportion : Estimating a Population Proportion : Why Worry About Sampling Variability? Use what you know about the relationships between angles to solve the problems. The sum of the interior angles in a triangle is 180°. I sometimes allow more than one presentation if multiple graphing strategies were used and each is a viable method of graphing. With this established, the conversation often evolves toward the sum of the two angles. Although the students are looking at complementary and supplementary angles, they might not notice that they add up to 180 or 90.
Supplementary angles add to a total of 180°. Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure. An organizer to help with the vocabulary will be used on the last day of the activity. Finally, when students reach Module 5, they work with all of the standard angles around transversals and parallel lines. Some of the key ideas to focus on throughout the lesson today include: graphing linear equations fluency , understanding algebraically why two lines are parallel same slope different y-intercepts , and the definition of a transversal. After these conceptual conversations, the students are ready to define the angles because our definition started with their ideas.
. In my class, I have students work in partnerships and use the worksheet to guide them through each module. Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. Complementary angles add to a total of 90°. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so. If a triangle has an angle of 40° and angle of 95 °, the third angle has a value of 45°.