Graphing Inequalities Foldable: Four Flaps for One-Variable Number Lines

Algebra and Function Practice

This lesson describes a foldable for graphing one-variable inequalities on a number line. The foldable has four flaps: symbol and circle type, solve step, number-line graph, and check a test value. Each flap includes a worked example and a blank practice strip. The convention for graphing is explicit: an open circle means the endpoint is not included, a closed circle means it is included, and the arrow points in the direction of all solutions. Letter styles and handwriting vary, so the rubric accepts any legible notation that matches the stated convention. All numerical values in examples are hypothetical and chosen for easy arithmetic.

Practice materials: Printable downloads are not available for this lesson yet. Use the instructions and four exercises below.

Foldable setup and flap one: symbol and circle type

Make a four-flap foldable from a rectangular sheet. Fold the sheet in half lengthwise, then fold the top half down to create four equal flaps. Label the flaps: Symbol and Circle, Solve, Graph, Check. On the inside of each flap, write a worked example and leave a blank practice strip.

Flap one records the inequality symbol and the circle type. Use less than or greater than for an open circle; use less than or equal to or greater than or equal to for a closed circle. Write the symbol, the circle word, and a small sketch of the circle on a number line. For example, x < 3 uses an open circle at 3; x ≥ 3 uses a closed circle at 3.

1. Fold the sheet into four equal flaps and label them.
2. On flap one, write each symbol and whether it gives an open or closed circle.
3. Draw a small number line with the correct circle for one example.
4. Leave a blank strip for a practice symbol and circle.

Flap two: solve step and flap three: number-line graph

Flap two records the solve step. Solve the inequality as you would an equation, but reverse the inequality symbol when you multiply or divide by a negative number. Write each step on its own line. For example, to solve 2x + 1 < 7, subtract 1 to get 2x < 6, then divide by 2 to get x < 3. No reversal is needed because 2 is positive.

Flap three records the number-line graph. Draw a horizontal line, mark the endpoint, choose the circle type from flap one, and draw an arrow in the solution direction. For x < 3, place an open circle at 3 and draw an arrow to the left. For x ≥ 3, place a closed circle at 3 and draw an arrow to the right. Label the endpoint and the arrow direction.

1. Write the original inequality on flap two.
2. Show each solve step, reversing the symbol only for multiplication or division by a negative.
3. On flap three, mark the endpoint on a number line.
4. Choose open or closed circle and draw the arrow in the correct direction.

Flap four: check a test value

Flap four records a check. Choose a test value on the arrow side of the graph and substitute it into the original inequality. If the test value makes the inequality true, the graph direction is consistent. Also choose a value on the other side and confirm it makes the inequality false. This check catches reversed symbols and wrong arrow directions.

For x < 3, test x = 0: 2(0) + 1 < 7 is 1 < 7, true. Test x = 4: 2(4) + 1 < 7 is 9 < 7, false. The graph should include 0 and exclude 4, so the arrow points left from an open circle at 3.

1. Pick a test value on the arrow side and substitute it into the original inequality.
2. Confirm the result is true.
3. Pick a test value on the other side and confirm it is false.
4. Record both checks on flap four.

Worked example

Solve and graph 3x - 2 ≤ 10 on a number line, then check a test value.

Four practice exercises

Common mistakes

• Using a closed circle for less than or greater than. Match the symbol to the circle: less than and greater than use open circles; less than or equal to and greater than or equal to use closed circles.
• Forgetting to reverse the inequality symbol when dividing by a negative number. Write a reminder on flap two: reverse the symbol when multiplying or dividing by a negative.
• Drawing the arrow in the wrong direction. Use the test-value check on flap four to confirm the arrow side.
• Treating the endpoint as included when the circle is open. State the circle type aloud and check whether the endpoint value makes the inequality true.

Self-check rubric

• Flap one correctly pairs each symbol with open or closed circle.
• Flap two shows each solve step and reverses the symbol only when required.
• Flap three uses the correct circle type and arrow direction.
• Flap four includes one true test value and one false test value.
• Handwriting is legible and follows the stated convention; valid alternative letter styles are accepted.

Questions and answers