Math /Algebra Talks:Mental Math Strategies

Session GoalTo consider discussion-based activities that:

Develop targeted CCSS Standards for Mathematical Practice (SMPs).

Expand number sense to develop algebraic thinking.

Build in formative assessment.

Session OutlineWatch and discuss an elementary number

talk. Try some number talks and algebra talks

together.Understand the purpose and structure of

number talks.

Key Components of Number Talks

Classroom Environment and CommunityClassroom DiscussionsThe Teacher’s RoleThe Role of Mental MathPurposeful Computation Problems

Overarching Goals of Number Talks

Number SensePlace ValueFluencyPropertiesConnecting Mathematical Ideas

Number Talks

Whole-class activities centered around mental math tasks.

Students explain and justify multiple solution strategies.

Teacher acts as a facilitator.Time required: 5-10 minutes.

Let’s try this problem:26 + 27

Remember this is a mental math problem…

No paper or pencil…

An Elementary Number Talk

How would you mentally calculate. 32 x 15?

Try to find the product in two or more ways.

Video Clip

Classroom Discussions: Using Math Talk to Help Students Learn

Students find 32 x 15

How does this teacher…

Use wait time? Assess understanding? Record student

thinking? Extend student

thinking?

How do these students…

Meet the Standards for Mathematical Practice?

Show algebraic thinking?

What aspects of this activity would you use in your classroom?

Which would you change?

7 128 13

Compare and explain your reasoning.

6 710 10

1 1 3 8

2 1 5 4

2 2 5 8

3 1 5 2

5 18 6 16

6 8 7 9

7 128 13

What Makes it a Math Talk as opposed to a Lesson?

• Understanding how numbers work, rather than learning various skills.

• Empowers students to examine problems in their own way.• Short term practice toward long term goals.• Increased difficulty levels - encourages students to find more

efficient ways to solve problems.• Never expect students to see the problem the “teacher’s” way.• Not predictable.• Don’t replace current curriculum or lesson; only 10-15 minutes

of each day.

Algebra Talks

At the secondary level, build on number sense to make connections to algebra.Choose a topic and build a scaffolded “string” of mental math tasks.Examples: percents, function concepts, solving equations, and factoring patterns.

Percent StringFind and compare each pair of numbers. Be ready to explain how you arrived at your answers. 60% of 40 and 40% of 6025% of 80 and 80% of 255% of 110 and 110% of 5n% of 100 and 100% of nDescribe the pattern. Will this hold every time? Why?

Guess My RuleInput Output

Guess My RuleInput Output

1

2

-3

5

x

0

3

8

24

x2 – 1

Equation String

Use only mental math to find a value for the variable that makes the equation true. Be prepared to explain your solution.

Equation Stringx + 1 = 5x + ½ = 4½ 2x + ½ = 4½ 2(x + ½ ) = 95.5 = 3x +

2.5

Product String

Estimate each product first.

Do not calculate until told to do so!

Product StringEstimate First 19 x 2199 x 101199 x 20139 x 41299 x 301 (n – 1)(n + 1)

Standards for Mathematical Practice

1. Make sense of problems, and persevere in solving them.

2. Reason abstractly and quantitatively.

3. Construct viable arguments, and critique the reasoning of others.

4. Model with mathematics.

5. Use appropriate tools strategically.

6. Attend to precision.

7. Look for and make use of structure.

8. Look for and express regularity in repeated reasoning.

Standards for Mathematical Practice

1. Make sense of problems, and persevere in solving them.

2. Reason abstractly, and quantitatively.

3. Construct viable arguments and critique the reasoning of others.

4. Model with mathematics.

5. Use appropriate tools strategically.

6. Attend to precision.

7. Look for and make use of structure.

8. Look for and express regularity in repeated reasoning.

How to Get StartedChoose a topic, skill or problem that will be

taught in the next two weeks. This will be your target.

Choose a starter question. It should involve a prerequisite skill or topic. Make it accessible!

How will you scaffold questions to build complexity towards the target?

What tools will be available to students? What will you listen for in student responses?

Some ExamplesTalk Starters, and Targets

Which is larger, 4/7 or 3/8?

Find 13% of 30 mentally. I paid $54 for an item

that was discounted 40%. What was my savings?

Write a numerical expression equal to 46. Find as many as you can.

Write an equation equivalent to x = 6. Find as many as you can.

Estimate the number of hairs on your head.

(x – 7)(x + 2) = 0 Simplify Use estimation. Suggest

the equation of a parabola passing through the points below:

Benefits of Math Talks Clarify thinking (MP 1,2). Consider and test other strategies to see

if they make sense (MP 1). Investigate and apply mathematical

relationships (MP 2,3,7,8). Build a repertoire of efficient strategies

(MP 1,3,5,8). Make decisions about choosing efficient

strategies for specific problems (MP 5,7,8).

Teachers don’t always understand the student’s

thinking. It’s OK to say, “I’d like to study this further and

get back with you.”

“When kids listen to each other, they understand it better than when they hear it directly from me. It makes more sense to them…I really see a lot of learning going on by children listening to the other children, I really do. I mean I see some of the slower kids really picking up on concepts…really learning a lot from listening to other kids.”

Susan Gehn, first and third-grade teacherChildren’s Mathematics, CGI (98)

Thank you!

Teachers are the key to changing the way students learn mathematics

-Dana and Yendol-Silva

Questions?Contact us:Madeleine JetterDepartment of MathematicsCal State University, San Bernardinomjetter@csusb.ca.edu

Vicky KukurdaInstructional ServicesRiverside County Office of Educationvlkukuruda@rcoe.us

Recommended ResourcesChapin, O’Connor and Anderson, Classroom

Discussions: Using Math Talk to Help Students Learn. Math Solutions

Anderson and Schuster, Good Questions for Math Teaching: Why Ask Them and What to Ask, Grades 5-8. Math Solutions

Classroom Video Visits at www.insidemathematics.org

Parrish, Sherry, Number Talks: Helping Children Build Mental Math and Computation Strategies, Grade K-5. Math Solutions.