Middle School Mathematics  Lesson 1  You can Depend on Me
Lesson Overview
Users will enter a value and receive a value. The value entered is the independent variable, the value received is the dependent variable. The dependent variable, for this lesson, is affected by one of addition, subtraction, multiplication or division.
 perimeter, equation, length, width,
Content Sections
Middle School Mathematics  Lesson 1  You can Depend on Me
Lesson Overview
Users will enter a value and receive a value. The value entered is the independent variable, the value received is the dependent variable. The dependent variable, for this lesson, is affected by one of addition, subtraction, multiplication or division.
 perimeter, equation, length, width,
 experience with expressions and equations
 Tablet with Bluetooth 4.2+
 Mathematics  Angles

 Activity pages
 Marty the Robot V2
 A device with MartyBlocks to code the equations
Learning Objectives
 I can predict the value of a dependent variable.
 I can determine the constant affecting an independent variable.
PreLesson Preparation
Open the Marty the Robot app and build the code, that is described in the teacher guide, in MartyBlocks.
This code will have Marty walk right or left the nunmber of steps indicated by the x variable and then forward or back depending on the entered calculated value for y. The equation used creates x as the independent variable and y as the dependent one.
Save this code in the app and give it an appropriate name so that it can be opened for the lesson.
WarmUp
Share with learners the objectives and success criteria for the day's lesson, from slide 2 of the presentation in the educator resource section; perhaps display this before the lesson starts and keep it displayed until another slide is needed.
The slides following the objectives and success criteria show pairs of numbers that are related to to a constant change, via one of the four operations. In their groups, learners need to see if they can determine the change that is occurring between the two values.
The first slide shows 3 12. At this point, learners could think, 'it's adding 9,' or 'it's multiplying by 4.' When you click the slide, a second pair appears, it shows 5 20. Learners will be able to confidently decide whether the change is addition by 9 or multiplication by 4. Clicking the slide again will show 0 (the second number, in this case 0, will be shown by a second click). Ask learners what they think the second number should be. Reveal 0 once ideas have been shared.
There are two examples of number pairs with the process of revealing numbers as outlined above. Feel free to do more of these with learners to warm them up.
Get Learning
Share with learners that there are often equations that are used in our regular, everday life that we take for granted. Examples can include:
 bus fares  the total is the number of people in a group multiplied by the cost for each individual
 pizza  the number of piece each person gets is the number of pizza pieces, in total, divided by the number of people
 sale prices  the total cost of the goods and subtract the discount
 age differences  your older siblings will always be older than you by the same number of years and months
Tell learners that they are going to do some predictions today based on code that Marty will run. They will need to see or hear the number of steps Marty takes to the side (along the xaxis) and the number of steps they take forward or back (parallel to the yaxis) from the origin of a graph.
The warmup showed pairs of numbers, for this work, learners will need to populate a table by counting Marty's steps to the side and forward/back. When they have determined the pattern or constant used to affect the independent variable, they should complete two other pairs of values included in the table.
The last table example shows an equation with either an x or y value. Learners will need to use the independent variable to solve for the dependent one and could use a range of strategies to determine the independent variable from the dependent one, depending on the learning they have had with you.
The final group task shows a grid alongside an equation. The grid is used to show how the equations look with changing independent variables and the resulting dependent variable.
Time for Practice
Learners are to complete the remaining tables of values in groups or individually. If you have Martys available for the class, learners would have the opportunity to check their thinking by creating a equation for Marty to walk the steps as recorded in the workbook. If learners do not have access, it would be a good idea to walk around the room with the Marty, asking about their thinking and testing their equations by running Marty with what they wrote, inputting the independent variables from the workbook.
Learners will note that on the second page of independent work, there are a mixture of empty grids and those with a line drawn on them. These are used to connect the values to the the path of coordinates on the graph. Through using the table and the graph together, learners will more readily see the pattern that exists between the independent and dependent variables. When learners are asked to input the coordinates from the table onto the grid, there are at least two coordinates listed with other partial coordinates to complete. For questions where the line is drawn on the grid, only partial coordinates are included and some of these extend beyond the graph.
Cool Down
Bring learners back together to discuss the challenges they faced and overcame. Have learners share any strategies they used to identify the effect that a constant value had on the independent variable, resulting in the dependent variable.
Suggested questions you might ask:
 How many coordinates did you need to determine an equation?
 Were there any values for the x coordinate that you liked to use to determine the y coordinate? Why did you like this one?
 What did the line drawn on the grid help you to see?
Carry out any end of lesson routines.
Extensions & Support
Extend
Have learners create descriptions for the equations: for y = x  6, you could say for every x, y is 6 less than this value; for y = 3x, you could say that for every x, y is three times as much.
Support
Remind learners what Marty does to display the x and y values for the equation. x is a sidestep and y is a forward or back step. Bring learners back to the origin and have them count from the start how far they need to move for x (which is whatever the independent variable is that they choose) and how much of a change results in the y, or dependent, variable. Physically moving a pencil, or physically stepping for each of the values, will support the consolidation of this learning.
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