Link to Slides: https://docs.google.com/presentation/d/1tcFk3vm55ah5qx_Sj_eaNHijIoKXOQv89YX8g9HQ2Uw/edit?usp=sharing
Tuesday, January 21st
Students will be going in and out of different small groups in this Jigsaw activity. There are three different problems whose purpose is to connect features of an equation representing a function to what that means in a context. Each student will be an expert of one problem. They will have time to complete their problem and then confer with peers that had the same problem to make sure they are on the same page. Next, they will create new groups where there is an expert of each problem in each group. We will have time for each expert to share how they solved their problem and then check as a class to discuss different strategies.
Learning Goals: Comprehend that any linear function can be represented by an equation in the form , where and are rate of change and initial value of the function, respectively. Coordinate (orally and in writing) the graph of a linear function and its rate of change and initial value.
Wednesday, January 22nd
Students will be using white board sleeves as they look at two different real world problems in our activities for the day. The purpose of the first activity is for students to determine if a given set of data can be modeled by a linear function. The purpose of the second activity is for students to approximate different parts of a graph with an appropriate line segment. This graph is from a previous activity, but students interact with it differently by sketching a linear function that models a certain part of the data.
Learning Goals: Compare and contrast (orally and in writing) different linear models of the same data, and determine (in writing) the range of values for which a given model is a good fit for the data. Create a model of a non-linear data using a linear function, and justify (orally and in writing) whether the model is a good fit for the data.
Thursday, January 23rd
In the first activity, students work with a graph that clearly cannot be modeled by a single linear function, but pieces of the graph could be reasonably modeled using different linear functions, leading to the introduction of piecewise linear functions. Students find the slopes of their piecewise linear model and interpret them in context. The purpose of the second activity is to give students more exposure to working with a situation that can be modeled with a piecewise linear function. Here, the situation has already been modeled and students must calculate the rate of change for the different pieces of the model and interpret it in the context.
Learning Goals: Calculate the different rates of change of a piecewise linear function using a graph, and interpret (orally and in writing) the rates of change in context. Create a model of a nonlinear function using a piecewise linear function, and describe (orally) the benefits of having more or less segments in the model.
Friday, January 24th
Students will begin the class period with a mini quiz covering the main points of the functions half of Unit 5.
After we check the mini quiz as a class, students will be working in stations depending on their Learning Checks from last week. There will be four stations: three of these correspond to questions taken from last week’s learning check covering lessons 1-7. There will be a brief reteach and examples for students to refresh their memories and correct misunderstandings. After the short reteach, students will answer a similar quiz like questions and turn it in; this grade should improve and will replace their mastery score from last week’s Learning Check. I will be at the station where the most students had trouble with. The final station will be an extension station for those students that earned full mastery last week and do not need to visit any of the remedial stations.
Learning Goals: Compare and contrast real world functions represented in equations, graphs, and tables. Describe what a function looks like in a graph and a table.
Link to Slides: https://docs.google.com/presentation/d/1ccFCDKnZVKEy1wegYOcvj6FbZRCzKRlNH0ySHer52Zc/edit?usp=sharing
Monday, January 13th
Before we begin our new lesson, we will check a few of the most important questions from their notes on Friday when I was absent. Once that has been checked and questions have been answered, we will move on to our next lesson. The purpose of the first activity is for students to begin using a graph of a functional relationship between two quantities to make quantitative observations about their relationship. For some questions students must identify specific input-output pairs while in others they can use the shape of the graph.
The purpose of this activity is for students to identify where a function is increasing or decreasing from a graphical representation. In the previous activity students focused more on single points. In this activity they focus on collections of points within time intervals and what the overall shape of the graph says about the relationship between the two quantities.
Learning Goals: Describe (orally and in writing) a graph of a function as “increasing” or “decreasing” over an interval, and explain (orally) the reasoning. Interpret (orally and in writing) a graph of temperature as a function of time, using language such as “input” and “output”.
Tuesday, January 14th
As a class, we will be completing an online Desmos activity for students to start practicing how they can draw the graph of a function. On the front board I will show a series of short video clips where someone is performing an action. A couple examples are pouring water into a bowl and spinning around on a merry go round. Students will watch the video a few times, define what the independent and dependent variables are, and then sketch a graph on the dry erase sleeves of what they think the graph could look like. This is a challenging exercise because up to this point, students have always been given the graph.
Learning Goals: Compare and contrast (orally) peers’ graphs that represent the same context. Comprehend that graphs representing the same context can appear different, depending on the variables chosen. Draw the graph of a function that represents a context, and explain (orally) which quantity is a function of which.
Wednesday, January 15th
Thursday, January 16th
The first activity is the first of three activities where students make connections between different functions represented in different ways. In this activity, students are given a graph and a table of temperatures from two different cities and are asked to make sense of the representations in order to answer questions about the context. The next part of the lesson is the second of three activities where students make connections between different functions represented in different ways. In this activity, students are given an equation and a graph of the volumes of two different objects. Students then compare inputs and outputs of both functions and what those values mean in the context of the shapes.
Learning Goals: Compare and contrast (orally) representations of functions, and describe (orally) the strengths and weaknesses of each type of representation. Interpret multiple representations of functions, including graphs, tables, and equations, and explain (orally) how to find information in each type of representation.
Friday, January 17th
Full Mastery Video Link
Students will first take a learning check that includes material from lessons 1-7. They will have about eight minutes to complete a few questions relating to a real world function. Once students are finished, we will immediately check for correctness. Students will correct their own papers in order to self-reflect and immediately understand errors that were made. Next, I will be pulling a small group of students to work with me on Unit 5 related material that they may be missing. These skills will be skills that support this unit that students should have learned in previous grades, but may have forgotten. As I work with small groups, there will be differentiated practice going on with the rest of the class. They will have practice problems to work on depending on how well they did on the learning check. If they earned full mastery, they will have a challenging tasks that require them to think deeper about the particular function.
Learning Goals: Compare and contrast functions represented in different ways. Determine what makes a function a function. Relate situations of functions to graphs and tables as well as be able to interpret specific input output pairs as they relate to the situation.
Link to Slides: https://docs.google.com/presentation/d/1FB9rX-U63bDw1c6jYzkG3WMSuiGRGTChGyaC-Rss3SU/edit?usp=sharing
Monday, January 6th
Students will be completing their Unit 4 Test Analysis. This is a table that helps them to reflect on what they did well on their test and what did not go so well. Next, they will go through the problems they missed and try to re-work them. I will have a key on the board for them to check their answers after reworking. Next, we will play our Unit 4 Jeopardy! Game that we did not have time to play the week before break. This will help students to review all of the topics from Unit 4 in a fun way that involves students talking to each other and working as a team to solve.
Learning Goals: Reflect upon their Unit 4 test in order to understand what they know and what they still need practice with in solving equations and systems of equations.
Tuesday, January 7th
The purpose of the first activity is to introduce the idea of input-output rules. One student chooses inputs to tell a partner who uses a rule written on a card only they can see to respond with the corresponding output. The first student then guesses the rule on the card once they think they have enough input-output pairs to know what it is. Partners then reverse roles. The purpose of the second activity is for students to think of rules more broadly than simple arithmetic operations in preparation for the more abstract idea of a function, which is introduced in the next lesson. Each problem begins with a diagram representing a rule followed by a table for students to complete with input-output pairs that follow the rule.
Learning Goals: Describe (orally) how input-output diagrams represent rules. Identify a rule that describes the relationship between input-output pairs and explain (orally) a strategy used for figuring out the rule.
Wednesday, January 8th
In this activity students are presented with a series of questions like, “A person is 60 inches tall. Do you know their height in feet?” For some of the questions the answer is "yes" (because you can convert from inches to feet by dividing by 12). In other cases the answer is "no" (for example, “A person is 14 years old. Do you know their height?”). The purpose is to develop students’ understanding of the structure of a function as something that has one and only one output for each allowable input. In cases where the answer is yes, students draw an input-output diagram with the rule in the box. In cases where the answer is no, they give examples of an input with two or more outputs. In the Activity Synthesis, the word function is introduced to students for the first time.
In the next activity students revisit the questions in the previous activity and start using the language of functions to describe the way one quantity depends on another. For the "yes: questions students write a statement like, “[the output] depends on [the input]” and “[the output] is a function of [the input].” For the "no" questions, they write a statement like, “[the output] does not depend on [the input].” Students will use this language throughout the rest of the unit and course when describing functions.
Learning Goals: Comprehend the structure of a function as having one and only one output for each allowable input. Describe (orally and in writing) a context using function language, e.g., “the [output] is a function of the [input]” or “the [output] depends on the [input]”. Identify (orally) rules that produce exactly one output for each allowable input and rules that do not.
Thursday, January 9th
The purpose of the first activity is for students to make connections between different representations of functions and start transitioning from input-output diagrams to other representations of functions. Students match input-output diagrams to descriptions and come up with equations for each of those matches. Students then calculate an output given a specific input and determine the independent and dependent variables.
The purpose of the next activity is for students to work with a function where either variable could be the independent variable. Knowing the total value for an unknown number of dimes and quarters, students are first asked to consider if the number of dimes could be a function of the number of quarters and then asked if the reverse is also true.
Learning Goals: Calculate the output of a function for a given input using an equation in two variables, and interpret (orally and in writing) the output in context. Create an equation that represents a function rule. Determine (orally and in writing) the independent and dependent variables of a function, and explain (orally) the reasoning.
Friday, January 10th
The purpose of this activity is for students to connect different function representations and learn the conventions used to label a graph of a function. Students first match function contexts and equations to graphs. They next label the axes and calculate input-output pairs for each function. The purpose of the second activity is for students to interpret coordinates on graphs of functions and non-functions as well as understand that context does not dictate the independent and dependent variables.
Learning Goals: Determine whether a graph represents a function, and explain (orally) the reasoning. Identify the graph of an equation that represents a function, and explain (orally and in writing) the reasoning. Interpret (orally and in writing) points on a graph, including a graph of a function and a graph that does not represent a function.
KEY to Unit 4 What Should I Study: UNIT 4/QUARTER TWO FINAL
Monday, December 16th
Monday Stations Link (Solutions): https://docs.google.com/document/d/1FXis2uacxP3vvDOeMCM_p3XGLWIoYECZtVHV6GS5igI/edit?usp=sharing
We will begin class with an around the room station activity. There will be ten questions about solving equations posted around the room. Students will have a recording sheet to work these problems out on. Once they solve one problem, their solution will tell them which question to visit next. The goal is to go around the room to each station in the correct order. This activity is to review their equation solving skills of combining like terms, distribution, and problems where a variable appears on both sides. We will discuss as a whole class some of the questions students struggled with the most. The rest of the class period will be spend working on the finals study guide.
Tuesday, December 17th
We will start class will a task rotation combining word problems and systems of equations. Each table group will have four different word problems. I will set a timer for the four steps we have learned to solve these types of problems. Once the timer goes off, students will pass their paper to the person beside them at their table group. That person will then check the previous person's work and continue with the next step of the problem. We will continue this until all four steps have been completed. We will discuss the solutions and questions students have at the end of class.
Wednesday, December 18th
At the beginning of class students will have some time to look through their study guide and pick out problems they want me to work out on the board as a class. Once we have worked through those problems and I have discussed some questions I anticipate students would struggle with, we will play a Jeopardy! game that reviews all of the key concepts from Unit 4.
Thursday - Friday
We will have an altered schedule where students complete their Quarter 2 Finals.
Monday, December 9th
We will begin class by finishing up some notes from last week. Students will then have a chance to practice solving systems of equations with their elbow buddy. This activity represents the first time students solve a system of equations using algebraic methods. They first match systems of equations to their graphs and then calculate the solutions to each system. The purpose of matching is so students have a way to check that their algebraic solutions are correct, but not to shortcut the algebraic process since the graphs themselves do not include enough detail to accurately guess the coordinates of the solution.
Learning Targets: I can graph a system of equations. I can solve systems of equations using algebra.
Tuesday, December 10th
In the first activity, students solve systems of linear equations that lend themselves to substitution. There are 4 kinds of systems presented: one kind has both equations given with the y value isolated on one side of the equation, another kind has one of the variables given as a constant, a third kind has one variable given as a multiple of the other, and the last kind has one equation given as a linear combination. This progression of systems nudges students towards the idea of substituting an expression in place of the variable it is equal to.
In the second activity, students are asked to make sense of a fictional student's justification for the number of solutions to the system of equations. This activity continues the thread of reasoning about the structure of an equation and the focus should be on what, specifically, in the equations students think this student sees that makes him believe the system has no solutions.
Learning Target: I can use the structure of equations to help me figure out how many solutions a system of equations has.
Wednesday, December 11th
In the first activity, students are presented with a number of scenarios that could be solved using a system of equations. Students are not asked to solve the systems of equations, since the focus at this time is for students to understand how to set up the equations for the system and to understand what the solution represents in context.
In the next activity, students solve a variety of systems of equations, some involving fractions, some involving substitution, and some involving inspection. This gives students a chance to practice using the methods they have learned in this section for solving systems of equations to solidify that learning.
Learning Target: I can write a system of equations from a real-world situation.
Thursday, December 12th
In this activity, students reason about situations involving two different relationships between the same two quantities. Then they invent their own problem of the same type. While students are encouraged by the language of the activity to use a system of equations to solve the problems, they may elect to use a different representation to explain their thinking
Learning Target: I can use a system of equations to represent a real-world situation and answer questions about the situation.
Friday, December 13th
At the beginning of class we will finish up any notes or activities that were not fully completed or discussed from earlier in the week. Next, students will take a learning check to see how well they are able to solve systems of equations after learning and practicing this skill all week. After we have checked the learning check as a class, students will have differentiated practice depending on their learning check score. If they earned full mastery, they will be challenged with more complex equations. I will be working with those students that did not master the learning check to clear up any misconceptions.
Learning Targets: I can graph a system of equations. I can solve systems of equations using algebra.
Monday, December 2nd
Group A Link
Group B Link
Group C Link
To start class, students will be in groups for station tasks. Each group will be given instructions and each student will have a laptop. The tasks for the groups correspond with how well students did on a warm up they turned in before Thanksgiving Break. The second part of class students will review their knowledge of equation solving and relate it to a real world situation. They will be given time to complete an extended response question (like they would see on state testing). They will then self assess their work based on a rubric for grading the question, which they got before starting to answer the question.
Calculate a value that is a solution for a linear equation in one variable.
Implement knowledge of equation solving to a real world, multi-step problem.
Tuesday, December 3rd
In previous lessons, students have set two expressions equal to one another to find a common value where both expressions are true.
In this activity, students focus on a context involving coins and use multiple representations to think about the context in different ways. The goal of the first activity is not for students to write equations or learn the language “system of equations,” but rather investigate the mathematical structure with two stated facts using familiar representations and context while reasoning about what must be true.
In the second activity, the system of equations is partially given in words, but key elements are only provided in the graph. Students have worked with lines that represent a context before. Now they must work with two lines at the same time to determine whether a point lies on one line, both lines, or neither line.
Determine (in writing) a point that satisfies two relationships simultaneously, using tables or graphs.
Interpret (orally and in writing) points that lie on one, both, or neither line on a graph of two simultaneous equations in context.
Wednesday, December 4th
Students will be completing their winter STAR testing. Results of this test will be sent home with students on Thursday.
Thursday, December 5th
In the first task, students find and graph a linear equation given only the graph of another equation, information about the slope, and the coordinates where the lines intersect. The purpose of this task is to check student understanding about the point of intersection in relationship to the context while applying previously learned skills of equation writing and graphing.
In previous lessons, students encountered equations with a single variable that had infinitely many solutions. In this activity, students interpret a situation with infinitely many solutions. A race is described using different representations (a table and a description in words). Students will graph the relationships given by the descriptions and notice that the lines overlap so that both relationships are true for any pair of values along the graphed line.
Create a graph that represents two linear relationships in context, and interpret (orally and in writing) the point of intersection.
Interpret a graph of two equivalent lines in context.
Friday, December 6th
In the first activity, students start with an equation relating distance and time for Han’s hike and enough information to write a second equation relating distance and time for Jada’s hike. After writing Jada’s equation and graphing both lines, students then use the lines to identify the point of intersection and make sense of the point’s meaning in the context. Students will then explore a system of equations with no solutions in the familiar context of cup stacking (Unit 3). The context reinforces a discussion about what it means for a system of equations to have no solutions, both in terms of a graph and in terms of the equations
Comprehend that solving a system of equations means finding values of the variables that makes both equations true at the same time.
Coordinate (orally and in writing) graphs of parallel lines and a system of equations that has no solutions.
Create a graph of two lines that represents a system of equations in context.
Monday, November 25th
We will begin the lesson finishing up with our second activity from last Thursday. This activity has students finish the end of an equation in order to make different types of solutions: no solution or infinitely many solutions. The second half of class will be combining everything students know about equation solving. They will work with a partner to solve out a variety of different equations. They will then sort them into different categories of their own choosing. We will have a discussion at the end of class about how they could have been sorted. Finally, I made some practice equation solving problems for students to take home and complete if they need extra practice. I will have a key available Tuesday.
Describe (orally) a linear equation as having “one solution”, “no solutions”, or “an infinite number of solutions”, and solve equations in one variable with one solution.
Describe (orally) features of linear equations with one solution, no solution, or an infinite number of solutions.
Tuesday, November 26th
Students will turn in their warm up to me which asks them to solve a couple different types of equations. I will use this data and the data from their learning checks to give them targeted practice the Monday we return from break. Next students will work with their table groups to create a poster based on a real work situation. They must draw a picture representing what is going on and then use an equation to answer a couple of questions. We will have a gallery walk and discussion at the end of class.
November 27th-29th: Thanksgiving Break!
Monday, November 18th
Before students work on solving complex equations on their own, in this activity they examine the work (both good and bad) of others. The purpose of this activity is to build student fluency solving equations by examining the solutions of others for both appropriate and inappropriate strategies. The purpose of this lesson is to increase fluency in solving equations. Students will solve equations individually and then compare differing, though accurate, solution paths in order to compare their work with others. This will help students recognize that while the final solution will be the same, there is more than one path to the correct answer that uses principles of balancing equations learned in previous lessons.
Calculate a value that is a solution for a linear equation in one variable, and compare and contrast (orally) solution strategies with others.
Critique (in writing) the reasoning of others in solving a linear equation in one variable.
Tuesday, November 19th
Today students will take a Learning Check to see how well students are understanding the material of the first three lessons. Next week, they will be expected to solve more complex equations on their own. They must understand what a balanced equation is before moving on to this more challenging task. Once this is complete, we will be moving on to lesson 5. The goal of this activity is for students to build fluency solving equations with variables on each side. Students describe each step in their solution process to a partner and justify how each of their changes maintains the equality of the two expressions.
Calculate a value that is a solution to a linear equation in one variable, and explain (orally) the steps used to solve.
Create an expression to represent a number puzzle, and justify (orally) that it is equivalent to another expression.
Justify (orally) that each step used in solving a linear equation maintains equality.
- Demonstrate understanding of what a balanced equation is and the moves that will keep the equation balanced.
Wednesday, November 20th
The purpose of the first activity is to shift the focus from solving an equation to thinking about what it means for a number to be a solution of an equation. Students inspect each equation, looking at the structure, the signs, and the operations in it to decide if the solution is positive, negative, or zero. The purpose of the second activity is for students to think about what they see as “least difficult” and “most difficult” when looking at equations and to practice solving equations. Students will also discuss strategies for dealing with “difficult” parts of equations.
Categorize (orally and in writing) linear equations in one variable based on their structure, and solve equations from each category.
Describe (orally and in writing) features of linear equations that have one solution, no solution, or many solutions.
Describe (orally) strategies for solving linear equations in one variable with different features or structures.
Thursday, November 21st
Students begin the first activity sorting a variety of equations into categories based on their number of solutions. The activity ends with students filling in the blank side of an equation to make an equation that is always true and then again to make an equation that is never true. In the next activity, students are presented with three equations all with a missing term. They are asked to fill in the missing term to create equations with either no solution or infinitely many solutions, building on the work begun in the previous activity. At the end, students summarize what they have learned about how to tell if an equation is true for all values of x or no values of x.
Compare and contrast (orally and in writing) equations that have no solutions or infinitely many solutions.
Create linear equations in one variable that have either no solutions or infinitely many solutions, using structure, and explain (orally) the solution method.
Friday, November 22nd
The eighth grade will be taking a field trip most of the day. For classes that come to math this day, we will be working on practice problems from the week's lessons.
Link to Slides: https://docs.google.com/presentation/d/16nv485ljTtFjSpr0h41bnXnqfExOT6ZnEFLV-LZ86CQ/edit?usp=sharing
Monday, November 11th
Students will review their Unit 3 test from Friday and complete a test analysis. When this is finished they will begin to work on a series of number puzzles preparing them for balancing equations in the coming lessons.
Calculate a missing value for a number puzzle that can be represented by a linear equation in one variable, and explain (orally and in writing) the solution method.
Create a number puzzle that can be represented by a linear equation in one variable.
Tuesday, November 12th
Wednesday, November 13th
Thursday, November 14th
We will begin Unit 4 with the visual of hangers that have different sized weights on them. They will solve a variety of "hanger problems" throughout class. The hangers represent balanced equations; through the different moves and steps they take with the hangers, they will begin to see what keeps an equation balanced and what does not.
Friday, November 15th
In the first activity, students match a card with two equations to another card describing the move that turns the first equation into the second. The goal is to help students think about equations the same way they have been thinking about hangers: objects where equality is maintained so long as the same move is made on each side. The purpose of the next activity is to get students thinking about strategically solving equations by paying attention to their structure.
Compare and contrast (orally and in writing) solution paths to solve an equation in one variable by performing the same operation on each side.
Correlate (orally and in writing) changes on hanger diagrams with moves that create equivalent equations.
Link to Slides: https://docs.google.com/presentation/d/1x1YRXXLW2HH1jywCfyrV-LJBTRuSpVUsRLY7vWT4Z9U/edit?usp=sharing
Monday, November 4th
Students will work with two word problems today that represent real world situations. They will answer a series of questions about these problems individually and as a team before we discuss patterns as a whole group. Students will graph these situations and see that the coordinates on the graph are solutions to the word problem they were presented. We will define the word solution and look at other examples with equations and their solutions.
Learning Targets: I know that the graph of an equation is a visual representation of all the solutions to the equation. I understand what the solution to an equation in two variables is.
Wednesday, November 6th
Students will first work with their elbow buddy to determine if a number of statements about lines on a graph are true or false. Next, as a class we will discuss the solutions and big idea of the exercise. The big ideas are: A solution of an equation in two variables is an ordered pair of numbers an solutions of an equation lie on the graph of an equation. Finally students will play a partner card game that matches equations to their solutions.
Learning Targets: I can find solutions (x, y) to linear equations given either the x- or the y-value to start from.
Thursday, November 7th
Link to Unit 3 Study Guide KEY
Today we are putting everything we learned in Unit 3 together with a complicated real world problem that requires multiple steps to solve. Students will be given some time to answer and complete as much as possible before a timer goes off. After we discuss these solutions, the rest of class will be spent preparing for their test tomorrow. I will answer any questions they have about their study guide and give them some in class time to review it.
Learning Targets: I can write linear equations to reason about real-world situations.
Friday, November 8th
Students will take the Unit 3 Test on Linear Relationships. I will have these graded and in Infinite Campus by the end of the day. They will review, and analyze their results first thing on Monday.
Learning Target: I can show what I know about linear relationships on my Unit 3 Test.
Link to slides: https://docs.google.com/presentation/d/1ls2cIKvEIMJH-A6UpshSmMR0_GRokqiXglEWW9Ow7As/edit?usp=sharing
Monday, October 28th
Students will complete differentiated practice today based on their score on the Learning Check they took on Friday. Students that did not master their Learning Check will be working on a real world task in small groups and with myself. The task will require them to compare two different pricing options for a school's soccer jerseys using rate of change, y-intercept, tables, and a graph. Students that did master their learning check will work on a challenging Desmos activity; this is an online game that pushes what they know about the parts of a linear equation.
Learning targets: I can explain where to find the slope and vertical intercept in both an equation and its graph. I can write equations of lines using y=mx+b.
Tuesday, October 29th
Today we will begin to look at negative slope in the context of fare cards for people taking the subway. They will answer questions about why negative slope makes sense in this situation, as well as graph specific points and write an equation for the line. The last part of the lesson will be spent investigating what zero slope looks like on a graph. Students will work with their elbow buddies to answer a few questions and then create their own graph with a slope of zero.
Learning Targets: I can give an example of a situation that would have a negative slope when graphed. I can look at a graph and tell if the slope is positive or negative and explain how I know.
Wednesday, October 30th
The first activity prompts students to use whatever problem solving strategy works best for them to find the slope of a line. the tricky part is they are only given two coordinates. Students may choose to graph them and draw a slope triangle or they may attempt to use a general problem solving strategy to solve using the definition of slope. We will discuss as a class how students can tell whether a slope is positive or negative just by drawing a quick sketch of the coordinates. We will end the lesson with an partner activity called an Information Gap. Students have different roles in this game; the main purpose is for students to improve their math communication skills to give information about slope, and coordinates of a line their partner cannot see.
Learning Targets: I can calculate positive and negative slopes given two points on the line. I can describe a line precisely enough that another student can draw it.
Thursday, October 31st
Link to Activity: Equations of All Lines Applet
Students will use computers to investigate how to create an equation for horizontal and vertical lines. They will plot a variety of points on their computer and see what they all have in common with their coordinates. They will also create as many rectangles on their computer with the same perimeter. They will notice a pattern that the vertices of the rectangles form. The big idea is for students to understand that for horizontal and vertical lines, one of the two variables does not vary, while the other can take any value.
Learning Targets: I can write equations of lines that have a positive or a negative slope. I can write equations of vertical and horizontal lines.
Friday, November 1st
Students will begin class by completing a Learning check over what they have learned about linear relationships, including negative slope. Next week, we will put everything together and review for our Unit 3 test next Thursday. I want to make sure we are able to write equations of lines and interpret them no matter what the slope is before adding in multiple different word problems Monday.
Link to Slides: https://docs.google.com/presentation/d/1anBmlvCPcINyhmDlSLVA3T5bXUh1JfF2lXWKiQYMlNI/edit?usp=sharing
Monday, October 21st
Students will be completing a hands on activity using stacked styrofoam cups to make connections about proportional relationships and how they compare to our new kind of relationships, linear relationships. They will work with a partner to predict the height of a larger number of stacked cups than the ones they are given. We will then discuss whole group why it is not a proportional relationship and the strategies that could've been taken to solve the problem. Next, students will use the information they gathered from the stacking cups activity to make a graph and analyze the rate of change in the situation.
Learning Target: I can find the rate of change of a linear relationship by figuring out the slope of the line representing the relationship.
Tuesday, October 22nd
Students will first complete a card sort with their elbow buddy. They will be matching situations to graphs; there will be both proportional relationships represented and non proportional relationships shown. This will lead us to defining what a y-intercept is. After discussing the definition, students will determine what the y-intercept means in terms of the situations they just matched. Finally, they will work on a task about a student and her summer reading. They must create a graph from a situation and then answer questions about what the graph means.
Learning Targets: I can interpret the vertical intercept of a graph of a real-world situation. I can match graphs to the real-world situations they represent by identifying the slope and the vertical intercept.
Wednesday, October 23rd
Students will be using a computer generated situation about the volume of water in a cup and how it changes when virtual marbles are dropped into it. This situation represents a linear, non proportional relationship. They will find the equation that would represent what is going on and then answer some questions about different scenarios. Students will then be working individually to record the slopes of three different graphs in a table. The goal of the table is for students to be able to generalize an equation for slope for any given line.
Learning Targets: I can use patterns to write a linear equation to represent a situation. I can write an equation for the relationship between the total volume in a graduated cylinder and the number of objects added to the graduated cylinder.
Thursday, October 24th
The first activity is about a student's savings account. They will be given a graph and be asked to answer questions about what the line is representing. They will also graph another line on the same graph based on a different scenario and then compare and contrast it from the given line. The second activity relates what students learned about translations in Unit 1 to the equation of a line. They will learn that the equation for any line is y=mx+b. The only difference in this equation and the equation for a proportional relationship is the starting point b, or the y-intercept. We will see how a line can be translated up or down from the origin to a new y-intercept other than 0.
Learning Targets: I can explain where to find the slope and vertical intercept in both an equation and its graph. I can write equations of lines using y=mx+b.
Friday, October 25th
Students will begin class by completing a Learning check over what they have learned about linear relationships. Next week, students will be learning about negative slope. I want to make sure we are able to write equations of lines and interpret them with a positive slope first. After checking these, we will complete a Desmos activity on the computer that summarizes our understanding of linear relationships.
Link to Slides: https://docs.google.com/presentation/d/1CoK9ayS82uWyxn0C1Kk30UfX2y_Ue-1tGQ8NpLpEJeg/edit?usp=sharing
Monday, October 14th
We will begin class with a Jolly Rancher activity about proportional relationships. The purpose of this is to grab students' attention with something fun and review the key aspects of what a proportional relationship is from seventh grade. After this introduction activity, students will work with their table groups to complete two tasks. Both of these tasks involve real world situations displayed in multiple formats. They are all proportional relationships, but some are represented as a graph, others as a table, or equation. We will conclude class with a discussion about what students learned from the tasks.
Learning Target: I can graph a proportional relationship from a story.
Tuesday, October 15th
Our first activity is a card sort that students will complete with their elbow buddy. They must match cards of graphs that show the same proportional relationship. Once they believe they have all of their matches, they must write the equation for each match. After giving them time to work, we will check these matches and discuss what their strategy was to find the same proportional relationship. Finally, students will be able to choose any topic they are interested in that can be made into a proportional relationship. They will create a table with fictional numbers representing their chosen situation. Next, they will write out the equation for their proportional relationship and graph it on a coordinate plane. If time allows students will walk around the room to share what they created.
Learning Targets: I can graph a proportional relationship from an equation. I can tell when two graphs are of the same proportional relationship even if the scales are different.
Wednesday, October 16th
Students will start out with three different tasks that all involve Halloween and fall related topics. Each of the tasks represents proportional relationships with double number lines, tables, and equations. Each task has different values that are left blank. Students must use what they know about the constant of proportionality to fill in the missing values. Once they have finished with the questions on the tasks, they will choose one of the tasks. They will use the information from their selection to create a graph. The tricky part will be coming up with scales for the x and y axes that will allow them to plot all of the data from the task. I will display student work on the doc camera at the end of class.
Learning Target:I can scale and label a coordinate axes in order to graph a proportional relationship.
Thursday, October 17th
Today the main activity will include task rotations. Students will rotate around the room to different stations that all contain a different task. Each task has two different proportional relationships displayed in different ways. There are questions that students must answer comparing and contrasting the information they show. They will take notes as they rotate around the room and work together as a team. We will conclude by reviewing what the solutions should be and how they were found.
Learning Target: I can compare proportional relationships represented in different ways.
Friday, October 18th
Students will begin class with a challenging warm up. they must draw a graph for a situation and equation given. They will have individual think time to record what they think the solution graph should look like. Next they will have a couple minutes to compare their responses with the people at their table. We will look through the doc cam at samples of student work as they explain their process for graphing. Next they will take a learning check that covers the first four lessons of the unit (proportional relationships). After students are finished, they will immediately check their own work so they can self assess right away what they are doing well and what they need to work on. Finally, the rest of class will include students doing individual practice problems.
Learning Target: I can summarize what I know about proportional relationships and represent them through tables, graphs, and equations.
Link to Slides: https://docs.google.com/presentation/d/1H_2LZy-LTuEX1AMy-dXoVeq7gM_PiLl1g3RXAS6ZHOk/edit?usp=sharing
Monday, September 30th
Students will have different tasks to finish throughout the class period. Their first priority is to get their Unit 2 Test finished if they did not already do so on Friday. If this was completed on Friday, they will get their results back and complete a test analysis to look over their results. If there were standards that students did not perform well on, they will be given a practice worksheet aimed at correcting misconceptions from the test. If this is finished and turned in to me, they will be given the opportunity to have their Unit 2 standard grades replaced with the ones they earn on the final (if they end up being better). Finally, students will be given a study guide to help them prepare for the final. They may work on this if the other two tasks are finished.
Tuesday, October 1st
We will begin class with students looking over their study guides to see if there are questions they don't understand. I will work these problems on the board for the class to see. Once all questions are answered, we will play a Jeopardy! game. Students will be in teams with their table groups competing for a prize. The subjects for the game are: rigid transformations, dilations, similarity, slope, and miscellaneous. Another way students can prepare for the final is by clicking my "Math IXL Practice" tab to the left. There are skills they can work on online for each unit to supplement the study guide.
Quarter 1 Finals Study Guide KEY
Wednesday & Thursday October 2nd-3rd
We will have an altered schedule for students to take their Quarter 1 final exams.
Link to Slides: https://docs.google.com/presentation/d/10aV8fLWdwdUMTKsKsx0d_eACJVMhJ7lp2GYwvS9UsMs/edit?usp=sharing
Monday, September 23rd
In the first activity, students explain why certain triangles with one side along the same line are similar. This fact about the triangles will be used to define the slope of the line. In the next activity, students practice graphing lines with a given slope. They observe two important properties of slope: Lines with the same slope are parallel, and as the slope of a line increases so does its steepness (from left to right).
Learning Targets: I can draw a line on a grid with a given slope. I can find the slope of a line on a grid.
Tuesday, September 24th
We will be using the laptops today completing an interactive Desmos activity. This activity starts with students identifying what the slope of a line. They will refer back to this value throughout the virtual activity. Through analyzing different ratios of the slopes, they will see how the slope triangles relate to similar triangles.
Learning Target: I can use similar triangles to determine that slope is the same between any two distinct points on a line.
Wednesday, September 25th
We will begin class by reviewing the two concepts we have learned in the past week: slope and similar triangles. After we look at a few examples of each, we will watch a short animated video about a character and how he uses slope in real life. Students will then work with their table groups to answer questions about the video and how it relates to similar triangles. If they finish before we are ready to discuss as a class, they may work on their study guide for the test on Friday.
Learning Target: I can explain how similar triangles can be used to explain the concept of slope.
Thursday, September 26th
We will begin class with a short review game to get students up and moving, thinking about key content they will see on their test tomorrow. The second part of the class will consist of students finishing up their Unit 2 What Should I Study. I will give them the opportunity to ask me questions they want to see performed on the board as a class. The KEY will be posted online and paper copies will be made available.
Learning Target: I can feel prepared to show what I know about dilations, similarity, and slope on my Unit 2 test tomorrow.
Link to What Should I Study Answer KEY
Friday, September 27th
Students will be completing their Unit 2 test today on dilations, similarity, and introduction to slope. This test includes both multiple choice and short answer questions. It should take the entire class period to complete.
Learning Target: I can feel prepared to show what I know about dilations, similarity, and slope on my Unit 2 test today.
Link to Slides: https://docs.google.com/presentation/d/1avxY_CNEGLF8FuKCiGzdjbwFPGnJTY1-xbQB0ul-Cug/edit?usp=sharing
Monday, September 16th
In previous lessons, students perform dilations on a circular grid and with no grid. In this activity, they perform dilations on a square grid. A square grid is particularly helpful if the center of dilation and the points being dilated are grid points. The next activity adds the structure of coordinates and this extra structure plays a key role, allowing students to name points. Students match figures with their dilated images, using coordinates to describe the center of dilation and the vertices. The same strategies that were used previously in dilating images,on a circular grid and with no grid, will be useful here.
Learning Targets: I can apply dilations to figures on a rectangular grid. If I know the angle measures and side lengths of a polygon, I know the angles measures and side lengths of the polygon if I apply a dilation with a certain scale factor.
Tuesday, September 17th
This info gap activity gives students an opportunity to determine and request the information needed for a dilation, and to realize that using coordinates greatly simplifies talking about specific points. In order to perform a dilation, students will need to know the center of dilation (which can be communicated using the coordinate grid), the coordinates of the polygon that they are dilating (also communicated using the coordinate grid), and the scale factor. With this information, they can find the dilation as in previous activities.
The info gap structure requires students to make sense of problems by determining what information is necessary, and then to ask for the information they need to solve the problem. This may take several rounds of discussion if their first request does not yield the information they need. It also allows them to refine the language they use and ask increasingly more precise questions until they get the information they need.
Learning Target: I can apply dilations to polygons on a rectangular grid if I know the coordinates of the vertices and of the center of dilation.
Wednesday, September 18th
In this activity, students learn that two figures are similar when there is a sequence of translations, reflections, rotations and dilations that takes one figure to the other. Students practice discovering these sequences for two pairs of figures. When two shapes are similar but not congruent, the sequence of steps showing the similarity usually has a single dilation and then the rest of the steps are rigid transformations. The next activity helps students visualize what happens to figures under different kinds of transformations. Students practice identifying which transformations might be used in the sequence of translations, rotations, reflections, and dilations in order to show figures are similar.
Learning Targets: I can apply a sequence of transformations to one figure to get a similar figure. I can use a sequence of transformations to explain why two figures are similar.
Thursday, September 19th
In the previous lesson, students saw that figures are similar when there is a sequence of translations, rotations, reflections, and dilations that map one figure onto the other. This activity focuses on some common misconceptions about similar figures, and students have an opportunity to critique the reasoning of others. Two polygons with proportional side lengths but different angles are not similar and two polygons with the same angles but side lengths that are not proportional are also not similar. Reasoning through these problems will help foster student thinking about when two polygons are not similar. In the next activity, students apply the knowledge learned from the first activity. Each student has a card with a figure on it and they identify someone with a similar (but not congruent) figure.
Learning Targets: I can use angle measures and side lengths to conclude that two polygons are not similar. I know the relationship between angle measures and side lengths in similar polygons.
Friday, September 20th
In this activity, students create triangles with given angles and dry spaghetti noodles and compare them to classmates’ triangles to see that they are not necessarily congruent, but they are similar. Students will then share some of the triangles they found and explain how they determined the triangles to be similar. We will conclude class with the list of different ways to show that two triangles are similar, including: using transformations (cutting out the triangle and placing it appropriately), finding two congruent corresponding angles in the triangles, finding three congruent corresponding angles in the triangles
Learning Target: I know how to decide if two triangles are similar just by looking at their angle measures.
Link to Slides: https://docs.google.com/presentation/d/1P1cOkl3PonolvFIW69ISk1CJTFmy5IkRAvhWKoMpmtQ/edit?usp=sharing
Monday, September 9th
We will first go through all of the expectations for completing the test analysis and test corrections (A step-by-step explanation can be found in the slides link above). Every student will be analyzing their test and correcting the problems that they missed. Once students finish with their test corrections, and I have checked for correctness, they will take a pre-assessment for Unit 2. There are some students that have already seen some of the material. If students earn full mastery on this assessment, I will have an alternate assignment planned for them to work on. Students that finish with all tasks before the end of the period will continue working on their tessellations activity from last week. It must be neatly done and colored before they are able to turn it in.
Learning Targets: I can analyze what went well and what I need to work on after reviewing my Unit 1 Test. I can show what I know about the topics in Unit 2 on the pre-assessment.
Tuesday, September 10th
As soon as students walk in the room there are instructions posted on the board for every place a student could be in the activities we have been working on. The tasks that students will be working on include: test analysis/ corrections, Unit 2 pretest, tessellation activity, or “Rotate This” challenge activity. Every student will be simultaneously working on whatever they need to finish up before we move on to the next unit tomorrow.
Learning Targets: I can analyze what went well and what I need to work on after reviewing my Unit 1 Test. I can show what I know about the topics in Unit 2 on the pre-assessment.
Wednesday, September 11th
The first activity recalls work from grade 7 on scaled copies, purposefully arranging a set of scaled copies to prepare students to understand the process of dilation. Students will arrange a set of rectangles into groups with shared diagonals and examine the scale factors relating the rectangles. Afterward, during the discussion, the word dilation is first used, in an informal way, as a way to make scaled copies. The next activity continues to examine scaled copies of a rectangle via dividing a rectangle into smaller rectangles. The focus is more on the scale factor and the language of scaled copies, emphasizing the link with work students did in grade 7. Unlike in the previous task, there are no given dimensions for any of the rectangles.
Learning Targets: I can decide if one rectangle is a dilation of another rectangle. I know how to use a center and a scale factor to describe a dilation.
Thursday, September 12th
The purpose of this activity is to begin to think of a dilation with a scale factor as a rule or operation on points in the plane. Students will work on a circular grid with center of dilation at the center of the grid. They will examine what happens to different points on a given circle when the dilation is applied and observe that these points all map to another circle whose radius is scaled by the scale factor of the dilation. The second activity continues studying dilations on a circular grid, this time focusing on what happens to points lying on a polygon. Students first dilate the vertices of a polygon as in the previous activity. Then they examine what happens to points on the sides of the polygon.
Learning Target: I can apply dilations to figures on a circular grid when the center of dilation is the center of the grid.
Friday, September 13th
Students will begin class by investigating dilations with no grid. Students have seen these for the first time in the warm-up, which had a ray drawn between two points. After doing a few of the problems, the students should notice that the dilated point is always one of the labeled points and then use this observation to expedite the work. In the final activity, students continue to apply dilations without a grid. Unlike in the previous activity, the dilated images of the points are not plotted. So rather than identifying the correct point, they will need to find an appropriate way to take measurements (with a ruler or index card).
Learning Target: I can apply a dilation to a polygon using a ruler.
Link to Slides: https://docs.google.com/presentation/d/1XQPDj6uOmjOWgVbxoSTy2-WMrVBM2IDPjnrml_Cep5s/edit?usp=sharing
Monday, September 2nd
Tuesday, September 3rd
In this activity, students experiment with the following question: If we know the measures of three angles sum to 180 degrees, can these three angles be the interior angles in a triangle? Students will cut out three angles that form a line, and then try to use these three angles to make a triangle. Students also get to create their own three angles from a line and check whether they can construct a triangle with their angles. We will bring it back together for a whole group discussion about what we learned and then students will have the rest of class to individually work on some practice problems.
HOMEWORK: Finish the practice problems if not completed in class
Learning Target: If I know two of the angle measures in a triangle, I can find the third angle measure.
Wednesday, September 4th
In the previous lesson, students conjectured that the measures of the interior angles of a triangle add up to 180 degrees. The purpose of this activity is to explain this structure in some cases. Students will now apply rotations to a triangle in order to calculate the sum of its three angles. They have applied these transformations earlier in the context of building shapes using rigid transformations. The purpose of the second activity is to provide a complete argument, not depending on the grid, of why the sum of the three angles in a triangle is 180 degrees.
HOMEWORK: Complete most of the problems on the What Should I Study for the Unit 1 Test. Come to class prepared with questions
Learning Target: I can explain using pictures why the sum of the angles in any triangle is 180 degrees.
Thursday, September 5th
The first half of class will be spent with students finishing up their What Should I Study for their Unit 1 Test that will be tomorrow. Next, we will come together as a whole class to talk about any questions or confusion with the study guide. I will review a few of the most important topics from the study guide if there are few questions. The second half of class will be spent working on a tessellation activity, which combines everything students have learned so far in the unit. They will get a rectangular piece of paper, scissors, and tape. They will be cutting and manipulating their rectangle in order to make their own unique shape. They will then trace their shape on a blank piece of paper. They will continue to translate and trace their shape, fitting together each piece like a puzzle. The finished product will be a tessellation; students will be asked to color their tessellation so that I can hang them up. If they do not finish, they will keep it to work on after the test tomorrow.
HOMEWORK: Study for the Unit 1 Test; Unit 1 Study Guide KEY
Learning Targets: I can repeatedly use rigid transformations to make interesting repeating patterns of figures. I can feel ready to show what I know about rigid transformations in Unit 1
Friday, September 6th
Students will be taking the Unit 1 Test on Rigid Transformations and Congruence. I should have their grades in Infinite Campus by the end of the day. Students will get them back on Monday and perform a Test Analysis to analyze what they missed and why.
Learning Target: I can show what I know about rigid transformations, congruence, and angle measures on my Unit 1 test.
Link to Slides: https://docs.google.com/presentation/d/1ZJKfLMJicHmtop05BOmsHNtmv10p3oDo9hNlJaHFiUU/edit?usp=sharing
Monday, August 26th
In the first activity, students express what it means for two shapes to be the same by considering carefully chosen examples. Students work to decide whether or not the different pairs of shapes are the same. Then the class discusses their findings and comes to a consensus for what it means for two shapes to be the same: the word “same” is replaced by “congruent” moving forward. One important takeaway from the second activity is that measuring perimeter and area is a good method to show that two shapes are not congruent if these measurements differ. When the measurements are the same, more work is needed to decide whether or not two shapes are congruent.
Learning Target:I can decide visually whether or not two figures are congruent.
Tuesday, August 27th
In the previous lesson, students formulated a precise mathematical definition for congruence and began to apply this to determine whether or not pairs of figures are congruent. This activity is a direct continuation of that work with the extra structure of a square grid. The square grid can be a helpful structure for describing the different transformations in a precise way. Students may also wish to use tracing paper to help execute these transformations. Students are given several pairs of shapes on grids and asked to determine if the shapes are congruent. The congruent shapes are deliberately chosen so that more than one transformation will likely be required to show the congruence. In these cases, students will likely find different ways to show the congruence. In the second part of the lesson, students take turns with a partner claiming that two given polygons are or are not congruent and explaining their reasoning. The partner's job is to listen for understanding and challenge their partner if their reasoning is incorrect or incomplete. This activity presents an opportunity for students to justify their reasoning and critique the reasoning of others.
Learning Target: I can decide using rigid transformations whether or not two figures are congruent.
Wednesday, August 28th
In this activity, students begin to explore the subtleties of congruence for curved shapes. I will make sure that students provide a solid mathematical argument for the shapes which are congruent, beyond saying that they look the same. Providing a viable argument requires careful thinking about the meaning of congruence and the structure of the shapes.
In the second half of class, students will be answering questions about two partially labeled polygons. They must label some corresponding parts and investigate different distances between points on each figure. There are two likely strategies for identifying corresponding points on the two corresponding figures:
Through experimenting with rigid motions, we will increase our visual intuition about which shapes are congruent.
Learning Target: I can use distances between points to decide if two figures are congruent.
Thursday, August 29th
In the first task, students explore the relationship between angles formed when two parallel lines are cut by a transversal line. Students investigate whether knowing the measure of one angle is sufficient to figure out all the angle measures in this situation. They also consider whether the relationships they found hold true for any two lines cut by a transversal. As students work with their partners, they begin to fill in supplementary angles and vertical angles. To find the measures of corresponding and alternate interior, students may use tracing paper and some of the strategies found earlier in the unit. The goal of the second task is to experiment with rigid motions to help visualize why alternate interior angles (made by a transversal connecting two parallel lines) are congruent. This result will be used in a future lesson to establish that the sum of the angles in a triangle is 180 degrees.
Learning Target: If I have two parallel lines cut by a transversal, I can identify alternate interior angles and use that to find missing angle measurements.
Friday, August 30th
Students will have a Learning Check at the beginning of class; it will cover the four new lessons we have learned this week (congruence and alternate interior angles). I will have a timer on the board letting students know how much time they have to complete it. Once the timer goes off, we will check it as a whole class. This way students get immediate feedback about what they do and do not understand.
The rest of the class will be devoted to individual practice. Students will be encouraged to see what they can accomplish without the help of myself or their peers. I will have DCA like questions for them to practice with since the test is the following week. I will also be walking around to help the students that are still struggling. For the students that get it and are ready to move on, I will have an extension activity ready for them. It will involve deeper thinking but also be like a puzzle that is not boring or a punishment for finishing early.
Learning Target: I can show what I know about congruent figures and alternate interior angles made by a transversal.
Link to Slides
Monday, August 19th
To begin the lesson, students that scored “Full Mastery” on their first Learning Check will be taking a pre-assessment to tell me what they already know about Unit 1. Students that did not, will be reviewing the concepts with myself so that they are ready to confidently start performing sequences of transformations individually.
The main activity is called an “Info Gap”; this is where students will practice performing different transformations. The Info Gap structure requires students to make sense of problems by determining what information is necessary, and then to ask for information they need to solve it. Students will need several rounds to determine the information they need. They need to know which transformations were applied (i.e., translation, rotation, or reflection) They need to determine the order in which the transformations were applied. They will also need to remember what information is needed to describe a translation, rotation, or reflection. After this main activity, the rest of class will be spent with individual practice performing sequences of transformations in a certain order.
Learning Target: I can apply transformations to a polygon on a grid if I know the coordinates of its vertices.
Tuesday, August 20th
The purpose of the first activity is for students to see that translations, rotations, and reflections preserve lengths and angle measures. Students will be able to use tracing paper to help them draw the figures and make observations about the preservation of side lengths and angle measures under transformations. While the grid helps measure lengths of horizontal and vertical segments, I expect that the students may need more guidance when asked to measure diagonal lengths. The purpose of the second activity is to decide if there is a sequence of translations, rotations, and reflections that take one figure to another and, if so, to produce one such sequence. Deciding whether or not such a sequence is possible uses the knowledge that translations, rotations, and reflections do not change side lengths or angle measures. The triangles ABC and CFG form part of a large pattern of images of triangle ABC that will be examined more closely in future lessons.
Learning Target: I can describe the effects of a rigid transformation on the lengths and angles of a polygon.
Wednesday, August 21st
We will begin the class practicing how to rotate a figure about a point using tracing paper, without a coordinate grid. Next, we will be working as a class to discover an easier way to rotate figures on a grid with the use of coordinates. Students will first rotate the figure in their notes the old way with tracing paper. Next, they will label each of the points on the original figure and it’s image. I will give students time to think about a rule that would describe what the image of a point would be after a rotation, just by knowing the original coordinates. Students will share ideas, and then we will come together as a class to formally define the rule that we saw. Finally, students will finish the class with individual practice rotating different shapes on a grid. Whatever is not finished will become homework.
Learning Target: I can describe how to rotate a figure on a coordinate plane.
Thursday, August 22nd
In this activity, students will investigate the question, “What happens to parallel lines under rigid transformations?” by performing three different transformations on a set of parallel lines. After applying each transformation, they will jot down what they notice by answering the questions for each listed transformation. As students work through these problems they may remember essential features of parallel lines (they do not meet, they remain the same distance apart). Rigid transformations do not change either of these features which means that the image of a set of parallel lines after a rigid transformation is another set of parallel lines. In the second activity, students will apply their understanding of the properties of rigid transformations to 180 degrees rotations of a line about a point on the line in order to establish the vertical angle theorem. Students have likely already used this theorem in grade 7, but this lesson informally demonstrates why the theorem is true.
Learning Targets: I can describe the effects of a rigid transformation on a pair of parallel lines. If I have a pair of vertical angles and know the angle measure of one of them, I can find the angle measure of the other.
Friday, August 23rd
The purpose of this task is to use rigid transformations to describe an important picture that students have seen in grade 6 when they developed the formula for the area of a triangle. The language “compose” is a grade 6 appropriate way of talking about a 180 degree rotation. The focus of this activity is on developing this precise language to describe a familiar geometric situation. The second activity continues the previous one, building a more complex shape this time by adding an additional copy of the original triangle. The three triangle picture in the task statement will be important later in this unit when students show that the sum of the three angles in a triangle is 180. To this end, encourage students to notice that the points E, A, and D all lie on a line. As with many of the lessons applying transformations to build shapes, students are constantly using their structural properties to make conclusions about their shapes. Specifically, that rigid transformations preserve angles and side lengths.
Learning Target: I can find missing side lengths or angle measures using properties of rigid transformations.
Link to Weekly Slides
Monday, August 12th
To introduce the first Unit (Transformations), we will be playing an online Desmos game in class. It closely follows the game "Guess Who." Students will be given code names of mathematicians and randomly paired with another student in the class. One partner will choose a card that shows a transformation (this term will be defined Tuesday). Their partner will type in yes or no questions in order to figure out which card the other partner chose. The purpose of this activity is to get students thinking about the different ways a figure can move on a graph. It is also good practice writing out with descriptive language what they are noticing.
Learning Target: I can describe how a figure moves and turns to get from one position to another.
Tuesday, August 13th
Students will start the class working with their elbow buddy to sort cards with transformations on them into categories. The purpose of this card sort activity is to give students further practice identifying translations, rotations, and reflections. We will then discuss what categories groups chose as a whole class; this is when the academic vocabulary will be introduced. The purpose of the next activity is for students to interpret the information needed to perform a transformation and draw an image resulting from the transformation. Through hands-on experience with transformations, students prepare for the more precise definitions they will learn in later grades.
Learning Targets: I know the difference between translations, rotations, and reflections. I can identify corresponding points before and after a transformation. I can use grids to carry out transformations of figures.
Link to Homework
Wednesday, August 14th
The purpose of the first activity is for students to give precise descriptions of translations, rotations, and reflections. By the end of the previous lesson, students have identified and sketched these transformations from written directions, however they have not used this more precise language themselves to give descriptions of the three motions. The images in this activity are given on grids to allow and to encourage students to describe the transformation in terms of specific points, lines or angles. The second activity involves more student practice. They will continue to identify the sequence of transformations that carry one figure to another. The challenge is that students will be working with an isometric grid, which they most likely have never seen before.
Learning Target: I can use the terms terms translation, rotation, and reflection to precisely describe transformations.
Link to Homework
Thursday, August 15th
The goal of this activity is for students to work through multiple examples of specific points reflected over the x-axis and then generalize to describe where a reflection takes any point. If any students struggle getting started because they are confused about where to plot the points, I’ll refer them back to the warm-up activity and practice plotting a few example points with them. The second activity concludes looking at how the different basic transformations (translations, rotations, and reflections) behave when applied to points on a coordinate grid. In general, it is difficult to use coordinates to describe rotations. But when the center of the rotation is (0,0) and the rotation is 90 degrees (clockwise or counterclockwise), there is a straightforward description of rotations using coordinates.
Learning Target: I can use the terms terms translation, rotation, and reflection to precisely describe transformations.
Friday, August 16th
We will be STAR testing today. The STAR tests measures the level of a student's math abilities. It also provides specific contents and skills that the student needs to work. I will be sending home a snapshot of each students' STAR math test on Monday. I will explain to students what the report means and how they can improve on any gaps they may have in learning.
Learning Target:I can show what I remember about math from last school year.
Wednesday, August 7th
We will be in homeroom the majority of the day taking care of paperwork, PBIS reminders, and safety regulations. Students will rotate to each of the classes on their schedule at the end of the day. If time permits, students in my homework will complete a Student Handbook scavenger hunt and play a team building activity.
Thursday, August 8th
We will review the syllabus (posted on a tab on my website) at the beginning of class. I will also explain the grading policies in my room (very similar to 7th grade math teachers). Next, we will play a team building activity for students to get to know each other. We will have many opportunities to work in partners and group throughout the year; I believe it is important for students to learn more about each other to foster a more respectful environment. At the end of class students will work on an individual activity called "Math All About Me." They will draw about unique facts describing themselves which have a number attached to it. These will be hung up around me room.
Friday, August 9th
We will review some of my most important expectations that were discussed Thursday. Next, students will finish up their "Math All About Me." If they finish early, they will have a choice of math puzzles to work on while the rest of the class finishes up. We will also play another team building game. If there is time, we will practice some of our math curriculum activities with non math related topics so that they get the hang of the processes before jumping into Unit 1 Monday.