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# 27 Writing in Math

### Start-Up Activity

On the board, write the expression, "5 + 2 = 7". Then ask a volunteer to read the expression. As the person does, write "Five plus two equals seven" underneath the original expression. Point out that the equation is actually a sentence.

• "Five" is the subject.

• "Plus" is a preposition.

• "Two" is the object of the preposition.

• "Equals" is the verb.

• "Seven" is the direct object.

Now write the expression "a + b = c". Under it, write, "10 + 11 = 21." Note that this equation is just as true as "5 + 2 = 7."

Now write, "Noun plus noun equals noun." Under it, write, "Dave plus Karl equals trouble." By substituting actual nouns, you can write an infinite number of true sentences.

In other words, equations are sentences, and sentences are equations. It should be no surprise, then, that writing can help students learn math.

"Equations are the devil's sentences."

—Stephen Colbert

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# Taking Notes in Math

Use this page to teach students best practices for taking notes in math. The bolded tips at the top of the page will help students quickly and accurately record information. The example notes at the bottom show students how a combination of words and figures can help them record ideas.

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# Keeping a Math Log

A math log can help students break through the "plug-and-chug" mentality of simply inserting values in formulas and doing the calculations. It helps students know what the parts of a formula mean, and what the result means, and why any of it is significant. A math log can also help students connect the abstraction of mathematics to real-world applications.

Use the material at the top of the page to help students set up and work in their math logs. Use the example at the bottom of the page to show the kinds of reflections that can help them think more deeply about math.

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# Guidelines: Analyzing Mathematical Data

Students can find mathematical data in many news sources. Use this page to help them analyze such sources and summarize the key pieces of data.

Before students do their own analysis, have them review the article and summary on page 381.

Afterward, have students find articles with mathematical data and use SQ3R to closely read the material. Then lead them through the tips for writing the summary: topic sentence, body sentences, and closing sentence.

To help them improve their work, provide the Checklist for Revising and Editing Math Summaries.

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### Article and Summary

Have students closely read the article, noting the data contained in the text and in the table. Then have them read the summary.

Point out that the topic sentence of the summary names the article and author and reports the thesis of the article. The body sentences provide the main trends from the data, and the closing sentence draws the writing to a close.

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# Guidelines: Graphing Math Data

Many real-world situations—sporting events, tests and quizzes, fund-raisers, blood-drives—generate lots of data. Students can gather and organize figures into spreadsheets and then output the data in graphics that show major trends. Present to students the spreadsheets and graphics on page 383.

Afterward, lead them through the process of gathering data about a topic of their own choosing and organizing it into a spreadsheet. Help them think through the different types of graphic outputs they could use to display the data.

When students have graphed their data, help them perfect their work using the Checklist for Revising and Editing Math Graphs.

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# Math Graphs

Note that the multiple bar chart helps students compare and contrast amounts at different times. The pie chart compares the proportions of a whole at one specific time. Point out how much more accessible the data is when in graph form rather than in spreadsheet form. Graphs allow readers to see the quantities that numbers refer to.

Inspire students to graph their own math data, showing the critical trends.

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# Guidelines: Developing a Proof

Proofs delve into the logic side of geometry. Students begin with a set of "givens" and must apply logical operations to arrive at certain conclusions. One type of proof uses a set of "transformations" to geometric figures to show that they are equivalent (or not).

Before students create their own proofs, lead them through the examples on page 385.

Then teach students how to analyze the prompt and extract the "givens." Equip them with the four main transformations—translating, reflecting, rotating, and dilating. Then let students experiment with the figures, working out their proofs.

Once they are ready to write their proofs, lead students through the process.

Also, provide them the Checklist for Revising and Editing Proofs. Of course, they will not use this formal checklist most times when they are working with proofs, but it can teach them the kinds of questions they can ask themselves to improve their work.

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### Prompts and Responses

Guide students through the prompts and responses on this page. Help students analyze each prompt, listing the givens that the text and figures provide. Then lead them through the transformations that the student uses to complete the proof.

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# Using Graphic Organizers

Flowcharts visually represent the steps and decision points of a process. Often engineers and computer programmers use flowcharts to demonstrate the logical architecture of systems.

Teach students the basic shapes used in flowcharting, and lead them through the process shown on the right.

Then have students select their own processes to flowchart. You can use the minilesson to provide them support.

For more on flowcharts, see "Reading Graphics."

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