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.

SBAC Practice Activities: Regression and Desmos

Links:
Assignment (Google Doc)
SBAC High School Calculator
Desmos

This task is for students in Algebra II or Trig/Math Analysis.  The problems on the Google doc are modified from the textbook for Trig/Math Analysis.  The mathematical goal for this lesson is to find the equation of a linear regression for a set of data, and use the equation to make predictions.  The technology goal was to find needed information and solve problems by navigating between various windows.  Below is one of the problem sets we asked students to work on.

We had students open a separate link to access data so that they could easily copy and paste the data into Desmos in order to find the regression equation.  Below is a snapshot of the data stored in a Google Sheet.

After you copy the data from a spreadsheet, you can go to the first input line in a Desmos sheet and paste the data.  It's as simple as control-C and control-V copy and pasting.  In line 2 you type y1~ax1+b.  Desmos automatically makes the subscripts for you.  Note that we use "~" instead of "=" when finding a regression equation.  See the regression parameters on line 2.

You might be asking why we used Desmos for regression when SBAC has its own regression calculator.  The answer is that Desmos makes regresssion sooooo easy, and it also automatically scales your graph to fit the data (see below).  We didn't want students to be focusing on too many new technology skills for this lesson, so we stuck to Desmos for the regression piece.

Once students find the regression equation, they need to use the equation to make predictions/answer the questions on the worksheet.  For this part we encouraged students to have two browser windows open side by side.  They can also use paper to do some of the work, though final answers will be scored from the Google Doc. Below is a screenshot of what students see when they are working with the SBAC calculator to answer questions 9 and 10.

One of our findings from this activity was that students were not clear on how to show their math work on the computer, or they weren't sure how much work to show.  We have started coaching students on the expectations by adopting a 3-point rubric for each problem.  Students can earn credit on each problem for the following items:

-1 point earned for showing work

-1 point earned for explaining thinking (when the problem specifies)

-1 point for final answer with units.

Below is a sample response for problem 9 that earns full credit.  

SBAC Practice Activities: Patterns and Formulas

This activity will provide students with a chance to review recursive and explicit formulas for arithmetic and geometric sequences.  Students will build formulas to model both patterns and real world situations.  They will check their formulas by using Desmos, and answer questions relating to each situation.  The Google Doc is available at this link.

Problem 1 is below, and asks students to use a recursive formula to identify a pattern from this page.

All patterns are from Fawn Nguyen's Visual Patterns website.  A few of the patterns that students will be looking at are below.  You can see that pattern 7 fits our recursive description for problem 1.

Once students have identified the correct pattern, we send them over to Desmos to add their data to a table.  When we are talking about patterns in math, we describe them as starting with stage 1, and then progressing to stages 2, 3, etc.  In the table below, we are saying that stage 1 has 5 blocks, stage 2 has 7 blocks, and so on.  You can see the each stage has two more blocks than the previous stage.

Students love using Desmos to see their pattern data plotted in real time.  Once students have the points plotted, we discuss how a recursive formula is limited in its usefulness because it doesn't have predictive power.  For example, I can't use a recursive formula to predict how many blocks will be in stage 100.  To do this we need an explicit formula.  Students can input an explicit formula into line 2, and immediately see whether or not they have the correct formula based on whether the line goes through the data points.

After practicing a few more problems with patterns, we move on to real world scenarios.  The scenario below was adapted from a worksheet found on betterlessons.com by Colleen Werner.

As with other SBAC practice activities, teachers coach students on how to answer the questions in order to receive full credit. We never know what the rubric will look like on standardized tests, so we've created three areas of focus:

-1 point for showing work
-1 point for explaining your thinking
-1 point for giving the answer with units

Part III of the lesson is a mini-performance task, modified from the SBAC Practice Test performance task. This is great if you have an extended period of time for the lesson (90 minute block).  Otherwise we found parts I and II to be great practice activities to help students get ready for SBAC.

SBAC Practice Activities: The Park

This assignment is modeled after the first part of an 8th grade performance task released by SBAC called "The Park".  It is intended for students in grades 9-11.  We chose to focus on lower level content to give as many students as possible access to the problem while focusing on using technology to show work and explain thinking.  Our modified Park task asks students to make use of a grant to design a park given certain restrictions.  Students are finding the lowest bid to place benches, lamp posts, and bathrooms in the park.  A copy of the assignment can be viewed here, and screenshots of the assignment will be shown below.

Diagram 1:  Students receive the page below via Google Drive.  All of the information that they need to solve the problem can be found at the various links (shown in yellow, green, blue, and purple), and students will give all final answers/work on this page.  As with SBAC performance tasks, we spend some time together making sure that students understand the relevant vocabulary.  We also walked students through the task and fielded any questions that came up before the work period began.

Diagram 2:  When students open the "Introduction and Park Specifications" page from the yellow box, they see the park below, along with a description of the grant requirements.  The requirements are to place benches all along the three paths in the middle of the park, beginning by placing three benches where the paths meet.  Next to each bench we place a lamppost, and then also we add two buildings that contain restrooms.

Diagram 3:  Students will open the "Work Bids" page from the green box, and view the three bids below.  

Diagram 4:  Students will open the "Interactive Diagram" page.  We give students the choice to either use the interactive diagram to add benches/lampposts, or to draw on a piece of paper.  The important part is that student work will only be scored from the original Google Doc.  This is like the SBAC test in that paper is a tool for answering questions, but all final answers will be inputted on the computer.

The last link on the Google Doc opens up the SBAC calculator.  This is the calculator that students will be using on the SBAC test, so we want to make sure students get a chance to practice using the calculator before the actual exam.

While students work on the problem, the teacher is circulating to coach students on best practices for answering the questions.  We emphasize three key areas, and encourage students to think about each area as earning them 1 point towards a final score.  These key areas are:

• 1 point for showing your work
• 1 point for explaining your thinking 
• 1 point for giving your final answer with units