Since our September JiTT

Since our September JiTT

• On a green note card, write a description of a lesson, strategy, or activity you learned about in our last JiTT and used in class.

8 Mathematical Practice Standards

Building More Awareness&

Ideas for Implementation!

The Standards for Mathematical Practice

Math Practice 1

Make sense of problems and persevere in solving them(May combine easily with MP 2, 4, 5, 7, 8)

Word problems involving critical math knowledge (e.g., a multiplication or division word problem in Grade 3 or addition and subtraction of fractions in Grade 4)

Problems that require careful review and thought Problems that take a long time to solve Problems that require a number of routine steps Problems in which each step leads to a more difficult problem

Note: These are general examples related to the Math Practices. They do NOT represent PARCC items.

Math Practice 2

Reason abstractly and quantitatively(May combine easily with MP 1, 4, 7, 8)

Problems where students must compute and interpret remainders in word problems. Kim is making candy bags. There will be 5 pieces of candy

in each bag. She had 53 pieces of candy. She ate 14 pieces of candy. How many candy bags can Kim make now? Is there any left over? Show your work.


Math Practice 2

Reason abstractly and quantitatively(May combine easily with MP 1, 4, 7, 8)

Contextual problems in which the student can gain insight into the problem by relating the algebraic form of an answer or intermediate step to the given context

R1 = ax + b and R2 = cx + d ax + b = cx + d ax – cx = d – b x(a – c) = (d – b) x = (d – b)/(a – c)


Math Practice 3

Construct viable arguments and critique the reasoning of others(May combine easily with MP 6)

Gr. 3-HS

Basing explanations/reasoning on evidence such as diagrams, calculations, terms, etc.

Distinguishing correct explanation/reasoning from that which is flawed, and—if there is a flaw in the argument—explaining what it is.

Gr. 6- HS Testing propositions or conjectures with specific examples. Justifying or refuting propositions or conjectures.

HS Stating logical assumptions being used. Determining conditions under which an argument does and does

not apply.


Math Practice 4

Model with Mathematics (Grade 3 – HS)(May combine easily with MP 1, 2, 5, 7, 8)

Word problems involving critical math knowledge (e.g., a multiplication or division word problem in Gr. 3 or addition and subtraction of fractions in Gr. 4) Each hat has 8 stars on it. How many total stars are on 9

hats? Multi-step contextual word problems in which the problem isn’t

necessarily broken into sub-parts. 9 large trucks are carrying ½ ton of lumber each. 7 small

trucks are carrying ¼ ton of lumber each. How many total tons are being carried by all of the trucks?


Math Practice 4

Model with Mathematics (Grade 6 – HS)(May combine easily with MP 1, 2, 5, 7, 8)

Applying math techniques to real-world situations Using estimates of known quantities in a chain of

reasoning that yields an estimate of an unknown quantity.


Math Practice 4

Model with Mathematics (High School)(May combine easily with MP 1, 2, 5, 7, 8)

Select from a data source, analyze the data, draw conclusions, and make an evaluation or recommendation. The purpose of such tasks is not to provide a setting for the student to

demonstrate data analysis skills such as box-and-whisker plots, etc. Rather, the purpose is for the student to draw conclusions in a realistic setting, generally using elementary techniques.

Tasks that require the execution of some or all of the modeling cycle in high school (see CCSSM pp. 72,73)


Math Practice 5

Use appropriate tools strategically(May combine easily with MP 1, 4, 7)

Using coordinates, diagrams, formulas, conversions, and other math knowledge as a tool without prompting students to use a specific tool.

Use calculators to: do messy calculations, simplify expressions, solve data problems, test conjectures, etc.

Note: MP 5 is not code word for “use a calculator” Note: If a student is not being strategic in using tools, then

the student is not meeting the standard


Math Practice 6

Attend to precision(May combine easily with MP 3)

Presenting solutions to multi-step problems with valid chains of reasoning, using symbols appropriately Not “1 + 4 = 5 + 7 = 12” Rather, “1 + 4 = 5 5 + 7 = 12”• Or, “1 + 4 = 5 and 5 + 7 = 12”

Being clear and precise when defining variables• Not “Let G be gasoline” – Rather, “Let G represent the amount of gasoline

in gallons”• Not “A = apples” – Rather, “A represents the number of apples”

• Math Terms and Calculations

• Knowing when a “solution” is extraneous


Math Practice 7

Look for and make use of structure(May combine easily with MP 1, 2, 4, 5)

Mathematical and real-world problems that involve rewriting an expression for a purpose

Numerical problems that reward seeing structure to simplify calculations, such as: 357 + 17,999 + 1 or 37 x 25 x 4

Analyzing parts of geometric figures to solve problems Using auxiliary lines to help solve problems or prove

something


Math Practice 8

Look for and express regularity in repeated reasoning(May combine easily with MP 1, 2, 4)

Problems in which repeated calculations or repetitions of some sort lead to a conjecture “Initially for most students, multi-digit division problems take time

and effort, so they also require perseverance (MP.1) and looking for and expressing regularity in repeated reasoning (MP.8).”

Problems in which working repetitively with numerical examples leads to writing an equation or function that describes a situation

Problems in which students are regularly checking the reasonableness of their results


Ages of Famous Personalities

• Questions involve scatter plots, line of best fit, extrapolation, interpolation and examination of data.

Interpolation is prediction within the range of the data

Extrapolation is a prediction outside the range of our data

Documents

Since our September JiTT