ND Curriculum Initiative

Subject & Standards

Understandings & Goals

Enduring Understanding: I want students to understand the Cartesian coordinate plane by graphing ordered pairs of numbers or points. From there I want students to be introduced to the idea of functions and their representations as rules and data tables. This will lead into the recognition of independent and dependent variables. Finally students will explore the relationship between a function and it’s graph and be able to analyze graphs and tables and apply this knowledge to real life situations. Goal(s): To introduce students to graphing ordered pairs of numbers on the coordinate plane. To introduce students to the idea of functions and their representations as rules and data tables. To interpret and analyze change in various contexts. To apply functions to real life situations.

Questions Answered

Essential questions: What is the base for algebra? What are variables? How do their relationships form patterns, functions, and generalizations? How can I apply functions and variables to real life situations? Objectives: Students will be able to plot points on the coordinate plane. Students will be able to read coordinates for a point from a graph. Students will be able to identify terminology used with functions. Students will be able to describe functions with one operation by using words, data tables, and simple algebraic expressions. Students will be able to analyze and compare information from graphs,tables, and rules. Students will be able to use graphs to represent and understand and solve real world problems.

Assessment

What quiz and test items (e.g. simple content-focused questions that require a single, best answer) will provide evidence of understanding? I will assess students on their ability to plot points on the coordinate plane by incorporating it into the next quiz. Students will be required to plot given points and to name given points by their coordinates. On a quiz students will also be assessed on their ability to identify function terminology by the use of definitions and to develop simple functions from a given chart . What academic prompts (e.g. open-ended questions or problems that require students to think critically and then to prepare a response / product / performance) will provide evidence of understanding? The function machine game allows students to develop a simple function from given inputs and outputs. After the students play the game many times and develop many functions I will assess their understanding by asking three reflection questions. 1) What kind of functions are possible? 2) How many numbers does it take to know the rule of the function? Why? 3) Are there some numbers for imputs that make it easier to find the function rules? The students willl then go on to see functions graphed on the coordinate plane. They will use the applet GraphSketcher to graph linear functions. They will graph the function y=x and then graph functions that have numbers added or subtracted from x and numbers multipllied by x. For example, y=x+1 and y=2x. As they change their functions students will be asked to describe how their new functions compare to y=x. They will then use their developed information to predict what graphs would look like without graphing them. They will be answering these questions in a worksheet/journal. What performance tasks and projects e.g. complex challenges that are authentic, mirror the real world and require a performance or product) will you include that will provide evidence of student understanding? Students will simulate an activity that shows how variables can relate to each other. They will be develop data that shows their rate. In this activity students will do jumping jacks for 2 minutes and record their totals every ten seconds. They will then graph their data and be asked how their rate changes as time passes. They will then be asked to explain how this is shown in a table and how this is shown in a graph. Students will need to relate their information about rate to the possible rate of a bike trip. The next performance task will involve developing a table and graph from a narrative description of a bike trip. Students will be given broad notes about the day’s trip and apply them to create actual data. They will graph the data and explain how the graph represents what happened in the narative description. What other evidence (e.g. observations, work samples, dialogues, student self-assessment) of understanding will you collect?  I will observe students using the math applets. For example, practicing plotting points while playing The General Coordinates Game and The Line Game. This will allow me to see if they need more practice or explanation before the quiz assessment. I will also collect the reflections, work samples, and graphs. The students will work in cooperative learning groups while doing the jumping jack activity and bike trip narrative. A verbal ongoing assessment will take place by classroom discussion at the beginning and end of each hour.

Instructional Strategies

I think that my work on the coordinate graph and functions best fit into the inquiry-based strategies. For example, by using the math applets students are able to play an active and hands-on role in trying to understand how functions work. They are able to play games to practice plotting points and get immediate feedback. They are able to experiment and determine how thing work on their own with a little guidance from the teacher. The students are also able to repeat the process many time to look for patterns when develop functions. They can record their results of their findings and then see what functions actually look like in real life by graphing them. They are able to compare these graph by using the applet and graphing many linear functions on the same graph. This will help them determine what happens when you change functions. They will then apply what they have learned from the applets about functions to real life situations. By working in cooperative learning groups students can help to teach each other and determine what real life rate looks like as data and graphs. They will also be able to convert narrative explanations to data and graph representations.