Graph Inequalities — Notes Packet

My Notes Level 1 Support Level 2 Standard Level 3 Enrichment

Today's objectives

Content Objective: I can graph the solutions of an inequality on a number line.

Language Objective: I can explain my graph using the words number line, open circle, closed circle, and solution set.

📖 See Learn It for the explanation and worked examples, and the Vocab tab for the words. These are your notes to fill in and keep.

✏️ Fill in each blank as we go. Use the Word Bank to help you.

📚 Word Bank — fill each blank with the best word

👆 Tap any word to see what it means and a picture.

Level 3: try the blanks from memory first, then check the bank.

1A line with numbers in order used to show values and solutions is a .
2A hollow circle that shows a value is NOT included, used for < or >, is an .
3A filled-in circle that shows a value IS included, used for ≤ or ≥, is a .
4All the values that make an inequality true form the .
5A math sentence comparing two amounts with <, >, ≤, or ≥ is an .
6The number where the solution set begins on the number line is the .

Write About the Math Guided ESOL writing

Use the support level you need. Every level answers the same math question.

1. Understand the Question

explain

When you graphed x > 4 and x ≤ 7, why did you use an open circle on one and a closed circle on the other?

Your job: Answer the question. Use math evidence. Explain how the evidence proves your answer.Responde la pregunta. Usa evidencia matemática. Explica cómo la evidencia demuestra tu respuesta.

2. Plan Your Math Words

Check at least two words you will use.

Number line — A line with numbers in order. You use it to show answers.Recta numérica — Una línea con números en orden. La usas para mostrar respuestas. Open circle — An empty circle showing a number is NOT included.Círculo abierto — Un círculo vacío que muestra que un número NO está incluido. Closed circle — A filled-in circle showing a number IS included.Círculo cerrado — Un círculo relleno que muestra que un número SÍ está incluido. Solution set — All the numbers that make the inequality true.Conjunto solución — Todos los números que hacen verdadera la desigualdad. Inequality — A math sentence comparing two amounts with <, >, ≤, or ≥.Desigualdad — Una oración matemática que compara dos cantidades con <, >, ≤ o ≥.

Say it first: Say your idea to a partner or quietly to yourself before you write.Di tu idea a un compañero o en voz baja antes de escribir.

I used a ___ circle because the symbol ___ means the boundary is ___.Usé un círculo ___ porque el símbolo ___ significa que el límite ___.

3. Build Your Explanation

Model the parts: This model shows the parts of an explanation. It does not answer your writing question.

Claim: Because 2:00 itself counts, I use a closed circle at 2.

Evidence: Students choose a closed circle at 2 (because 'no earlier than' includes 2) and shade to the right since later times satisfy t ≥ 2.

Reasoning: This evidence connects the definition of number line to the mathematical claim.

Start

Most language support

Complete the frames. Use the word bank.Completa las oraciones. Usa el banco de palabras.

I used a ___ circle because the symbol ___ means the boundary is ___.Usé un círculo ___ porque el símbolo ___ significa que el límite ___.
I shaded ___ because the solution set includes ___.Sombreé ___ porque el conjunto solución incluye ___.

Build

Some language support

Write two connected sentences. Use because, so, or but.Escribe dos oraciones conectadas. Usa porque, entonces o pero.

My claim is ___.Mi afirmación es ___.
I know because ___.Lo sé porque ___.
So ___.Entonces ___.

Explain

Light language support

Write a claim, give math evidence, and explain your reasoning.Escribe una afirmación, da evidencia matemática y explica tu razonamiento.

My claim is ___.Mi afirmación es ___.
My math evidence is ___.Mi evidencia matemática es ___.
This proves ___ because ___.Esto demuestra ___ porque ___.

4. Check Your Explanation

I answered the question.Respondí la pregunta. I used math evidence: numbers, an equation, a model, or a comparison.Usé evidencia matemática: números, una ecuación, un modelo o una comparación. I explained how the evidence proves my answer.Expliqué cómo la evidencia demuestra mi respuesta. I used at least two math words.Usé por lo menos dos palabras matemáticas. I reread complete sentences and punctuation.Volví a leer mis oraciones completas y la puntuación.