SBAC Practice Activities: The Basement

This activity is modified from SBAC released performance task called "Home Office", and includes portions of parts A, B, and C.  The flooring options were also changed to allow students to complete the task in a 50 minute class period.

As with other practice performance tasks, students will show work on a Google Doc.  The top of the page includes links to the various pieces of information and tools that the students will need to solve the problem.

In terms of showing work, it has been helpful to remind students to think about each problem as being worth 3 points (1 point for showing work, 1 point for explaining thinking, 1 point for answer with units).  We don't know ahead of time what rubric will be used, so giving students explicit directions on what to show on their Google Doc is helpful.

Once students navigate to the "Introduction and Specifications for Work" page, they will see the diagram below.  The first task is to determine how to split the basement into a home office and workshop.  The budget for this part of the project is $30,000 and the contractor charges $50 per square foot to finish the home office.  The workshop will be unfinished. 

 The first task asks students to finish the maximum area, and to draw a vertical line to separate the home office from the workshop.  The interactive diagram (image below) allows students to use the segment tool to add in the vertical line.

You can also show students how to use the text tool to add labels to the diagram.  When introducing the activity it will be helpful to let students know that the black points are 2 units apart.  

Students struggling to find the various dimensions of the workshop can turn on the grid (see image below), which is set up to scale by 2 units as well.

Students should add a screenshot of their image into the appropriate place on the Google worksheet.  

The second task asks students to pick a flooring for the home office from the table below.  The budget is $1500 for flooring, which is in addition to the $30,000 for the contractor.  Task 2 gives students an opportunity to justify their reasoning.  There are many flooring options to pick from that come in under budget.  Students receive full credit for choosing an option and providing an explanation for how they know that they are staying within the budget.

Task 3 asks students to find the dimensions of a bathroom that takes up 10% of the home office and is 3 feet longer than it is wide.  They are asked to do this by writing and solving a polynomial equation.  I included a link to Desmos so students can use it to solve the polynomial equation (quadratic), which is not factorable.  If this activity is given during a 50 minute class, students will most likely not get to task 3, or it can be completed by our early finishers that need the extra challenge.

The rubric and correct answers for this task are here.  The Google Doc for this assignment is here.

I Spy: Introduction to Congruent Triangles

Below is an introduction to congruent triangles that makes use of student prior knowledge of transformations.  It also encourages students to deduce information from a diagram and to justify their reasoning. 

Show students the following diagram, and go through the steps below.  Some questions/prompts are shown in blue.

1.  What type of transformation is shown in this diagram?

2.  Reveal the measures of ABC.  Ask students, “Who thinks they know another measure in the diagram?  Be ready to explain your answer.  Show me ONE other measure that you know, and hold up your whiteboard when you are ready.”  Teacher can show answers from students that used notation correctly.  Reveal the measures of AFE.

3. Show students the statement below.

Ask them how we might fill in the blank, and why.

4.  Move point C to the horizontal line (you can do this in the Geogebra applet).  

Leaving the measurements showing, ask students to tell you what they “spy”.  They can write on their whiteboards, “I spy __________________.”  Answers must be defended.  Make sure to have the list of possible answers written on the whiteboard.  

The choices are angle bisector, midpoint, isosceles triangle, parallel lines, and right angles.

3.  Move point B to F. Move point A down the vertical line so your diagram looks like the one below.

Leaving the measurements showing, ask student to tell you what they “spy”.  They can write on their whiteboards, “I spy __________________.”  Answers must be defended.

I SPY CHOICES:  angle bisector, midpoint, isosceles triangle, parallel lines, and right angles.

4.  Turn the measurements off.  Move point A back up to the horizontal line, and make sure point B is on point F.  Ask student to tell you what they “spy”.  They can write on their whiteboards, “I spy __________________.”  Answers must be defended.

I SPY CHOICES:  angle bisector, midpoint, isosceles triangle, parallel lines, and right angles.

Extension if there is time:  Since we haven’t seen parallel lines yet in this dynamic diagram, ask students how we can modify the diagram to form parallel lines (and explain why).

There is a second page in the Geogebra Book that has a triangle rotated around a vertex by 180 degrees to form the second triangle.  

Part II will have the I Spy Class Activity if you have time for it.

Symmetry Artist

I was observing a teacher today, and one of the lesson resources was Symmetry Artist from Mathisfun.com.  I was so excited by this resource that I could hardly focus on the lesson.  If you've never seen this resource before, it looks like the screenshot below:

 My five year old created the drawing above.  When she was finished I told her to pick a different number of "petals", and she chose 9 (shown below).

What an amazing resource!

Pierce, Rod. "Maths is Fun - Privacy Statement" Math Is Fun. Ed. Rod Pierce. 27 Feb 2012. 20 Oct 2014 <http://www.mathsisfun.com/Privacy.htm>

Transformations with Geogebra

Use this Geogebra Book to help demonstrate translations and reflections.

Use this Geogebra Book by Jed Butler to demonstrate rotations.

An organizer used during a Geogebra presentation can help students organize their thinking and study later on.  Follow this Dropbox link to download one that can be used for section 4-8.  Below is a sample of what is on the organizer:

Geometry: Slogan Project

Below are two examples from MVHS Geometry Slogan Project.  This project almost speaks for itself, but I will post a link to the directions soon to clarify directions/scoring.  Student posters were presented in class at the end of the project.

Translations with Geogebra

Unit planning for transformations is almost complete.  We have a set of notes/practice worksheets from the county office of ed (really great!), an FAL (Transforming 2d figures), and a common test.  The next step is thinking about how to use Geogebra to help with demonstrating the concepts and with practice.

There are a few different ways you can use Geogebra to look at translations.  The first way is to use a vector to translate a point or a figure.  The diagram below has a point and a polygon, so my next step will be to add a translation vector anywhere on the screen.  It doesn't matter where you put the vector.  You can find the vector tool under the dropdown menu for lines.

 For this example I'll use a vector to translate my point/figure 3 units right and 2 units down.  You can see the vector below, at the origin.

It might make more sense for students to see the vector starting at the point that will be translated, but then you need to construct a new vector each time if you want to stay consistent.  If I put the vector away from my diagram, I can use it each time I want to translate an object, and explain to students that the translate tool works by selecting the object first, then the vector that describes its translation (see pic below, located in a dropdown menu).

The diagram below shows my point and my polygon after translation.  Notice how the program automatically names the points in the image using the prime notation.

If you want students to focus on using the coordinate rule (x,y) -> (x+3,y-2), then you can do the transformations without using a vector by making use of the coordinates of your pre-image point(s). Before you give this a try, it is best to open a new window and add point A.  The way Geogebra names the coordinates of point A is (x(A),y(A)).  To translate point A 3 units right and 2 units down, create a point with coordinates (x(A)+3,y(A)-2).  Create this point by typing into the input bar at the bottom of the screen.  Better yet, give this new point the name A'.

Select the "move" tool, then drag point A around and watch how point A' moves.  Another helpful strategy is to turn the trace feature on for both points.  Do this by right clicking on the point and selecting "trace on".

Make sure the "move" tool is selected, then drag point A and watch as point A' follows along and traces out a figure that is congruent but translated 3 units right and 2 units down.  To clear the traces from the screen, type ZoomIn[1] into the input bar at the bottom of the screen.  (This command zooms in your screen, making it 1 times as large as it was before.  Clever trick to get the traces off the screen).

Geometers Sketchpad has lots of presentations on transformations that can be viewed on the Dynamic Number Project website.  My understanding is that students can access these presentations with the Sketchpad Viewer on an iPad.  I haven't thought too much yet about how I can use these in my class.  We don't have Sketchpad, and we also don't have ipads for each student.  For now I am trying some of their ideas on Geogebra, though I have to admit the experience isn't as smooth.  One strategy that Sketchpad uses is to attach a point to the perimeter of an object.  Geogebra has a similar tool, which is an option in the dropdown menu under polygons.  Make sure you have the object and a point created first.  Then when you select the "attach/detach point" tool select the point first, then the object to attach it too.  I found out the hard way to select the interior of the object.  By selecting the perimeter of a polygon, the point was confined to the line segment that created that side only.  

Once I had point A attached to the polygon below, I dragged point A to the edge and around the perimeter.  This created a congruent the congruent shape in orange traced out by point A'.

QR Code Scavenger Hunt for parallel lines cut by a transversal

You can use this activity to help students review the vocabulary and relationships amongst alternate interior angles, corresponding angles, etc.  

I've set up this activity so that you can start at any problem number.  The first step is to go to any of these problems, and scan the code to get your first clue.  If you are doing this activity with a class, the following ten papers will be displayed on the walls around the classroom.  Below the pictures in this blogpost is an organizer that students can use to record their work.  If you want to try the scavenger hunt first, scan any of the codes below and get your first clue.  The clue will give you a description for a pair of angles, and then you are to find the picture that meets your description.  When you have located the correct diagram, scan the code below to get your second clue.  Repeat this process until finished.  You can check your answers below when you are finished (or skip ahead if you aren't ready to play with QR codes yet.  An easy to use QR code reader is Inigma).

First things first.  The answer key is as follows:

QR code 1 sends you to problem 10, QR code 10 sends you to problem 7, then to 6, 2, 5, 3, 9, 4, 8, and QR code 8 sends you back to problem 1.  This way you can have students start at any QR code and they can make their way around the room back to where they started.  

The student record keeping sheet consists of a table, with the first row below:

This entry is to be used with the clue that matches diagram 1.  Students will label the diagram with the correct angles.  Next they will write their clue as a statement.  I chose this as a next step because students would be able to refer back to this activity later if needed, and the writing won't take that long.  The third column is a possible extension.  I was thinking to give students a word bank of angle vocabulary, and they can pick from the word bank when choosing the relationship for angles f and g.  A few teachers have already decided not to include the third column in the activity, or to leave it as a follow up activity for those that finish early.  I have added an extra record keeping sheet below in case you do not want the third column.

Since this activity focuses on vocabulary and is at the lower level in terms of depth of knowledge, this can be used as an opportunity to incorporate math practice standards.  Set the expectation that students will explain their thinking to a partner as they go through the problems, and count this as part of the activity score. 

I'm sure there are some things that can go wrong during this activity.  One thing I wonder about is whether the diagrams will be too small to have posted on the wall.  This made me wonder if it would be better to have students browse the diagrams as we have in this blogpost.  I also wonder if the conversations will be better if students aren't wandering the classroom.  Students also need to know that the QR code reader needs to be facing the right way.  Sometimes it is the simple details that make the difference!  

Below are the resources if you'd like to try this activity.  And if you try it, please let us know how it goes.

Problem Cards and Clues

Record Keeping Sheet

Record Keeping Sheet for a shorter version of the activity (no third column)

Make your own QR Code Scavenger Hunt! by iLearn Technology