FERN TRIBBEY ICTM PRESIDENT. Standards for Mathematical Practice Describe mathematical “habits of mind” Standards for mathematical proficiency: reasoning,

ICTM WESTERN REGIONAL

CONFERENCEFERN TRIBBEY

ICTM PRESIDENT

Standards for Mathematical Practice• Describe mathematical “habits of mind”

• Standards for mathematical proficiency: reasoning, problem solving, modeling, decision making, and engagement .

• Connect with content standards in each grade.

Common Core State Standards for Mathematics

Grade Level Standards• K-8 grade-by-grade standards

organized by domain.

• 9-12 high school standards organized by conceptual categories.

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Additional Points on the K-12 Math Standards

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The K-12 standards stress conceptual knowledge and understanding in addition to procedural skills.

Grades 9-12 require the application of mathematics to real world situations and issues.

Modeling is a requirement under the

Standards for Mathematical Practice.

Overview of K-8 Mathematics Standards

• The K-5 standards provide students with a solid foundation in whole numbers, addition, subtraction, multiplication, division, fractions and decimals.

• The 6-8 standards describe robust learning in geometry, algebra, and probability and statistics.

• Modeled after the focus of standards from high-performing nations, the standards for grades 7-8 include significant algebra and geometry content.

• Students who have completed 7th grade and mastered the content and skills will be prepared for algebra in 8th grade or after.

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To learn more, visit www.isbe.net

Where to Find More Information?

Two Wonderful, Fun Problems

Students Enjoy Exploring!

You are invited to a party celebrating the first day of “Real” Spring!

SPRING TIME PARTY

You are soooo excited!

You are wondering who else has been invited to the party!

You are wondering how many people will be coming to the Party!

In fact, you are really wondering how many handshakes would take place if everyone shook hands with each other!!!

Let’s Chart the Data!

Number of People (p) Number of Handshakes

What pattern did you notice?

What rule can you create that fits the pattern?

What equation can you

generate?

Graph the Data.

Does the Equation Fit the

Graph?

Next Problem . . .

You have hired your own children or nieces or nephews. They would love to do all of the dishes and anything else you need done after the party was over. In fact, they would not mind helping you for a full calendar year. In fact, everyday during the full calendar year!

Doing Dishes Now That The Party Is Over!

The children have created a great compensation plan!

Their plan is described as:

The first day they help you, each will earn a penny.The second day they help you, each will earn double what they earned the day before – two pennies.The third day they help you, each will earn double what they earned the day before – four pennies.

If they stayed with this plan, how much would each child earn after seven days?After two weeks? After four weeks? After . . .

Let’s Chart the Data!

Number of Days(d) Amount Payed (p)

What pattern did you notice?

What rule can you create that fits the pattern?

What equation can you

generate?

Graph the Data.

Does the Equation Fit the

Graph?

You Now Have Two Problems you can Do With Your Students on

Monday!

Where Did I Get These Two Problems?From Other Teachers and Conferences I have attended!

What you do with the problem becomes your own!

My information:Fern Tribbey

[email protected]

MORE PROBLEMS TO EXPLORE!

From NCTM’s Teaching Children Mathematics Feb. 2011 issue:“A Dime at a Time” (page 340-1)

Grades K – 2

Arrange 11 dimes into a circle. With a partner, take turns removing 1 or 2 dimes. Whenever it is your turn, you may remove 1 or 2 dimes. It is your choice. If you remove the last dime, you are the Survivor.

Can you figure out a strategy so that you can always be the Survivor?

Now use 13 dimes. Will your strategy still work? Explain how your strategy works.

Jose’s pocket change consists of 13 coins – pennies, nickels and dimes. Jose has more dimes than pennies and more dimes than nickels.

The number of each coin is divisible by 2.

How many of each coin does Jose have?

Is there more than one possible solution? Share your results.

Grades 3 – 4

Place 2 dimes in a cup. With a partner, take turns spilling the dimes onto a desktop.

One partner receives a point if both dimes are either heads or tails.

The other partner receives a point if 1 dime is heads and 1 is tails.

Predict who will win. Spill the dimes 30 times, and record the results.

Is this a fair game? Explain your reasoning. Represent the data.

Grades 5 – 6

Two Coin Problem continuation:

Will the results change if you collect data from the entire class? Explain your thinking.

Challenge: Would playing the game with 3 dimes in a cup change the outcome? Why, or why not?

From NCTM’s Mathematics Teaching in the Middle School Feb. 2011 issue:

“Palette of Problems” (page 327)

At an office supply store, 3 pencils cost $0.03 more than 2 pens, and 1 pen and 10 pencils together cost $2.40.

Determine the cost of each writing tool.

Is there more than one way to solve this problem? Explain your thinking.

Palette of Problems . . .

ENJOY!!