This post explores some ideas for reviewing concepts for TEKS A.2A.
determine the domain and range of a linear function in mathematical problems; determine reasonable domain and range values for real-world situations, both continuous and discrete; and represent domain and range using inequalities
Staar Performance
On recent STAAR tests, here is how students across the state of Texas have performed.
2023 #7 - 33% full credit, 22% partial credit, 44% no credit
2023 #46 - 34% correct
Active, Playful Learning
The activities shared in this post are designed to follow the six principles of Active, Playful Learning:
Active
Engaging
Meaningful
Social
Iterative
Joyful
These six principles, together with a clear learning goal, help students learn.
Students learn through active, engaged, meaningful, socially interactive, iterative and joyful experiences in the classroom and out. When we add a learning goal or engage in guided play we achieve Active Playful Learning.
In other words, math review doesn't have to be boring STAAR prep or mindless worksheets. Instead, students' learning is enhanced when playing with numeracy and algebraic concepts in a guided context. Who says math can't be fun? You can watch a video to learn more about Active, Playful learning here.
Activities
Here's a walkthrough of all the activities on this blog post.
Talk a Mile a Minute
Learning objective: Students will name terms associated with key ideas related to the domain and range of linear functions.
Pair students together.
Display a term related to TEKS A.2A on the board (e.g., domain, range, x-axis, y-axis, closed circle, open circle, continuous, discrete).
Partner A has one minute to name as many phrases related to the shown term while partner B writes them down.
Show another term for one minute while partner B names related terms and partner A writes them down.
Give partners 3 minutes to circle, from each list, one term they think will be on someone else's list and one term they think will not be on anyone else's list.
As a class, go over the circled terms from each list. Pairs earn one point for each term they correctly guess will or will not be on another list (4 points max).
Have students provide a rationale for obscure terms and let the class decide whether or not they relate to the given term.
Variations
Provide a list of closely related terms to ban for each target word, forcing students to cast a wider net for points.
Create a list of bonus words that earn an extra point if they appear on students' lists, regardless of whether or not they are selected as a circled term.
Have pairs work on different words simultaneously, rotating several turns until every pair as gone through every term before the class debrief. This will forestall pairs from picking up words from their neighbors.
Allow pairs to select two words that will be on other's lists to reinforce common terms related to target vocabulary.
Graphing Manipulation
Learning objective: Students will use an online graphing tool to manipulate the domain and range of a linear equation.
On their laptops/Chromebooks, have students open Desmos.
Give a linear equation for students to graph (e.g., y=5x).
Have students restrict the domain and/or range using curly braces (e.g., {x>=1}{y<11}).
Give students a series of clues so their graph can match the clues by further restricting the domain and or range. For example, restrict the range so that the graph doesn't appear in Quadrant 1 or restrict the domain so that the x values are negative.
Have students change the slope to match clues as well. For example, make the line slope down from left to right or make the line steeper.
For each manipulation, have students share their changes and discuss commonalities as a class.
Variations
Give multiple clues at once and have students create a graph that meets all of them. For example, graph a linear equation that has a shallow slope that descends from left to right that only appears in quadrant III.
Allow students to lead the activity, giving directions and/or restrictions to the class and then checking for correctness.
Have students draw line segments with specifications. For example, graph a line segment with a length of 5 units.
Ask students to draw basic shapes using a series of linear equations. For example, draw a right isosceles triangle using 3 linear equations. Ensure that students restrict the domain and range to create line segments.
Linear Card Sort
Learning objective: Students will sort linear functions based on restrictions in the domain and/or range.
Partner students together and give each pair a set of graphed linear functions (see example).
Ask student to find any cards that meet a certain criteria.
If you want students to find multiple cards, give only one limit on the domain or range. For example, Find all the cards with a domain > 2.
If you want students to find one exact card, give the full domain or range. For example, Find the card with a range greater than 6 and less than 10.
Have the students write the domain and range of any cards you call for as inequalities.
Variations
Create additional cards that list the domain and range of each graph and turn this into a memory match game.
Create additional cards that list the domain and range of each graph. In addition, create one extra card (graph or inequalities) that has no match. Give to pairs to play using the rules of Old Maid.
Have pairs select 9 images and arrange them in a 3 x 3 grid. Call out the domain and range of graphs one at a time. The first pair to create three in a row (vertical, horizontal, or diagonal) wins.
Show one of the graphs as either a bell ringer or exit ticket and have students describe the domain and range as inequalities.
Race to the Inequality
Learning objective: Students work collaboratively to describe the domain or range of a linear equation with inequalities.
Ask for (or designate) 15 volunteers. The first 10 volunteers will each represent one digit (either printed up or written on white boards). The remaining five volunteers will represent x or y (depending on whether you want to focus on domain or range) and each of the four inequality symbols (>, >=, <, <=).
Split the rest of the class into two teams.
Display the graph of a linear equation on the board or interactive white board. The 15 volunteers should each be facing the class with their backs to the board.
The first team is told to either represent the domain or range. As quickly as they can, the team directs the 15 volunteers (not all will be used) to arrange themselves to represent either the domain or range. Ensure that whatever students are solving for does not require a digit to be repeated.
Reset the volunteers. The second team works on a different linear equation, trying to beat the time of the first team.
Variations
If you have a smaller class, you can get by with less volunteers if you have each one represent two digits (e.g., 0 or 1) or two symbols (e.g., > or >=).
For alternate scoring, give teams points based on whether or not they solve within stepped time frames. For example, 5 points for solving in 20 seconds or less, 4 points for solving in 30 seconds or less, etc.
For an extra challenge, have a team arrange the volunteers to represent both the domain and range in succession under a predetermined time limit.
Use domain and range limitations that require two digits (e.g., 21). Ensure that a digit is not used more than once.
Discrete Challenge
Learning objective: Students will create and solve world problems for linear equations that have discrete data sets.
Review with students the difference between discrete and continuous data.
Share exemplars, such as released STAAR questions (redesign practice #37, 2017 #5).
Put students into pairs to work together to write problem situations that represent linear equations with discrete data.
Each pair then swaps their problem with another pair and solves for either the domain, range, or both.
Variations
If students need extra support, you can provide the problem situation and allow students to use that to write a problem. For example, you are saving the same amount each month to make a large purchase.
If students still need support, you can provide some sample equations for students to build a word problem around. For example, f(x) = 480 - 96x.
Save student problems that are high quality and use them as bell ringers or exit tickets.
Have students create a graph of their problem showing the discrete domain and range for additional practice.
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