S

Engaging Students

in the Standards for Mathematical

Practice!!

Two Kinds of Standards!!

The Common Core Standards are really made up of two kinds of standards:

Content Standards: These explain, for teachers and parents, the specific mathematical content that each grade level should master.

Practice Standards: These explain HOW students should engage in the content regardless of grade level.

and….

The Standards for Mathematical Practice (SMP’s)

There are 8 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

What’s this got to do with “A Story of Units”???

All 8 practices have been woven into the “A Story of Units” curriculum.

You should always see evidence that your child is engaged in one or more of these practices.

Working on one practice often means you are using others as well!

We, as teachers, are learning to use them in the way we think of math and in the way we teach it!

Let’s look at some examples!!

SMP #1: Make sense of problems and persevere in solving them

Mathematically proficient students explain to themselves the meaning of a problem, look for entry points to begin work on the problem, and plan and choose a solution pathway.

A farmer harvested 23 bushels of soybeans. A local restaurant bought 16 gallons of the soybeans. How many bushels remained? If the farmer put the remaining soybeans into pint containers to sell at the farmer’s market, how many could she fill?

•What am I being asked?•Do I understand all the vocabulary?

•Is there something I could draw that would help me visualize the problem?

•What do the numbers mean?

•How will I begin?

•What are the units?

SMP #2: Reason abstractly and quantitatively

Mathematically proficient students make sense of quantities and their relationships in problem situations. They can contextualize quantities and operations by using images or stories. They interpret symbols as having meaning, not just as directions to carry out a

procedure

There were 9 cupcakes on a plate. Three of them were chocolate and the rest were vanilla. What fraction of the cupcakes were vanilla?

Solution A:

(9 – 3) ÷ 9 =

Solution B: Cupcakes

!

Chocolate!

Vanilla!

2 out of 3 groups =

Two thirds of the cupcakes were vanilla!

SMP #3: Construct viable arguments and critique the reasoning of others

Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments.

A class of fifth graders were asked to compare these two amounts:

35 hundredths and 28 tenths 3.15

Jenna says that the first one is greater because it has more digits. Lenny thinks the second one is greater because it has 3 wholes and the first number only has two. Sanaa thinks the two values are equal. Decide who is correct and defend your answer.

SMP #4: Model with mathematics

Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace.

Pencils are packaged in groups of 12. A case of pencils contains 48 packages. If a school has 591 students, will one case be enough? If not, how many cases will they need to order?

48 Packages of Pencils

12

12

12

12

12

….

?

48x 12 96 480 576 pencilsOne case will not be enough. The school will have to

order two!

SMP #5: Use appropriate tools strategically

Mathematically proficient students consider the available tools when solving a mathematical problem.

Is closer to 0, ½, or 1?

0 1

½

1/6 is closer to 0!!

SMP #6: Attend to precision

Mathematically proficient students try to communicate precisely to others. They are careful about specifying units of measure. They calculate accurately and efficiently and express numerical answers with a degree of precision appropriate for the problem context.

How tall is an average student in the fifth grade?

Measurement

What unit will be used? (inches, feet, cm, meters?)

How will measurements be standardized? (shoes on/off, standing against wall?)

Calculations

Correct measurements of heights Which kind of average is appropriate? (mean, median, mode?)

Organized and accurate calculation of numbers.

Communication

Does the answer include the correct units? Is correct mathematical vocabulary used to describe the solution?

SMP #7: Look for and make use of structureMathematically proficient students look closely to discern a pattern or structure.

What is the volume of the rectangular prism shown below?

The volume is 4 layers of 18 m2 or 72 m3!

6 m

3 m

4 m

SMP #8: Look for and express regularity in repeated reasoning.

Mathematically proficient students notice if calculations are repeated, and look both for general methods and for shortcuts.

To make one dozen ice-cream sandwiches, Katie used ¾ gallon of ice cream. How much ice cream did she need for 60 ice cream sandwiches? Write an expression that would show how many gallons of ice cream would be needed for any number of ice cream sandwiches.

We can figure out how much ice cream was needed for any number of ice cream sandwiches with the formula (n ÷ 12) x 3/4 !

Number of Ice Cream Sandwiches

12 24 36 48 60 n

Gallons of Ice Cream ¾ 1 ½ 2 ¼ 3 3 ¾ (n ÷ 12) x

¾

So, here are some common questions you can ask your child to help them be more independent

problem solvers!:

What is the question?

What information is given that is related to the question?

Does this problem remind you of others you’ve solved?

How will you start to solve this problem?

Is there a picture or model you could draw that would help you understand the problem?

Is your answer reasonable? How do you know?