2012 Mathematics Standards

CAIM Inservice: November 15, 2014

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Shifts in Mathematics1. Focus: 2-3 topics focused on deeply in

each grade.

2. Coherence: Concepts logically connected from one grade to the next and linked to other major topics within the grade.

3. Rigor: In major topics pursue conceptual understanding, procedural skill and fluency, and application with equal intensity.

Rigor Equation

Rigor = Conceptual understanding + Procedural skill and fluency + Application

Rigor…

Rigor requires a balance of the three discrete components of math instruction: conceptual understanding, procedural skills and fluency, and application. This is not simply a pedagogical option, but is required by the Standards. The majority of the Standards specifically call for conceptual understanding, fluency, or application, but not every standard will necessarily fit neatly into just one of these three discrete components.-For example, certain standards can be said to require procedural skill and conceptual understanding.

Procedural skill and Conceptual Understanding Example

6.EE.1 Write and evaluate numerical

expressions involving whole‐number exponents. ▪ For example, multiply by powers of 10 and

products of numbers using exponents (7•7•7 = 73).

Conceptual understanding

The Standards call for conceptual understanding of key concepts, such as place value and ratios. Teachers support students’ ability to access concepts from a number of perspectives so that students are able to see math as more than a set of mnemonics or discrete procedures. Conceptual understanding standards often use the terms “understand” and “recognize.”

Deep Conceptual Understanding Standards Example

6.NS.5 Understand that positive and negative

numbers describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real‐world contexts, explain the meaning of 0 in each situation.

Procedural skill and fluency

The Standards call for speed and accuracy in calculation. Teachers structure class time and/or homework time for students to practice core functions such as single‐digit multiplication so that students have access to more complex concepts and procedures. Fluency standards clearly state “fluently” in the standard.

Application

The Standards call for students to use math flexibly for applications. Teachers provide opportunities for students to apply math in context. Teachers in content areas outside of math, particularly science, ensure that students are using math to access and make meaning of content. Application standards typically state “apply” or “solve.”

Application Example

6.SP.4 Display numerical data in plots on a

number line, including dot or line plots, histograms, and box (box and whisker) plots.

Glass Frog Eggs

Specific Example

Priorities

What are the priorities we focus on in each grade?

Priorities in MathematicsGrade Priorities in Support of Rich Instruction and

Expectations of Fluency and Conceptual Understanding

K-2 Addition and subtraction, measurement using whole numbers

3-5 Multiplication and division of whole numbers and fractions

6 Ratios and proportional relationships; early expressions and equations

7 Ratios and proportional relationships; arithmetic of rational numbers

8 Linear algebra

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Performance Tasks

Activities that give students the opportunity to demonstrate their understanding and mastery of math skills and concepts covered in class.

Students Use an organized approach using one or more

strategies Explain the steps and strategies used to complete the

task Show evidence of checking answers for correctness and

reasonableness. The tasks require analysis to explain the methods

used and the reasoning behind choosing the method.

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http://insidemathematics.org/index.php/exemplary-lessons-integrating-practice-standards

Sidewalk Patterns

1. Draw the next pattern in this series.

In Prague some sidewalks are made of small square blocks of stone.

The blocks are in different shades to make patterns that are in various sizes.

National Council of Supervisors of Mathematics. http://www.mathedleadership.org/ccss/itp/sidewalk.html

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2. Complete the pattern below

3. What do you notice about the number of white and gray blocks?

a. Fill in the blank spaces in this list 25=52 81=_____ 169=_____ 289=172

b. How many blocks will pattern 5 need?

c. How many blocks will number n need?

Pattern number, n 1 2 3 4

Number of white blocks 12 40

Number of gray blocks 13

Total number of blocks 25

National Council of Supervisors of Mathematics. http://www.mathedleadership.org/ccss/itp/sidewalk.html

Tough Pattern Thursday…http://goo.gl/forms/DxvpNxYagy

Task Based Instruction

• Use performance tasks

• Focus on Mathematical Practices

• Students should be challenged and struggle

• Guide with open ended questions

• Allow students to work together to solve problems

Great Tasks

Revolve around an interesting problem that offers several methods of solution.

Addresses an essential mathematical concept outlined in the Alaska Standards.

Utilizes the Mathematical Practices.

Lesson Planning Model-Stage 3

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5 minutes

5 min-utes

5 min-utes

10 min-utes

35 min-utes

Self Re-flection

Activate Prior Knowledge

Review of Learning Targets

Mini Lesson

Guided Practice with Collaborative Conversa-tion

Planning Model

Adapted from Measured Progress Professional Development www.measuredprogress.org

What does it mean to me?

Full implementation of the new standards should be in effect for the 2014-2015 school year

When creating units of instruction for classroom use, new standards will be used

Shift in pedagogy Shift in assessment