1. Introduction to the K-8 mathematics standards in Washington State
Seattle University
2017
Introduction to the K-8 mathematics standards in Washington State
This is a 2-hour session. Its purpose is to introduce TEED 5021 students to the Common Core (and Washington state) K-8 math standards.
Dr. Mark Roddy - Seattle University

2. Today we will: Introduce the CC / Washington math standards
History: how did we get here?
Context: what are the math wars?
Standards: how they are structured?
Content: what’s addressed in grades K-8?
Activities, worksheets & technology
Bratz Dolls, Blasted Ratios and Standards
Mathematical Reasoning
2 minutes for this slide

3. Introduction to the math standards How did we get here?
1983 – “A Nation at Risk”
1989 – NCTM Standards
problem solving, reasoning, communication, connections
1993 – HB 1209
Standards (EALRs), Assessment (WASL), Accountability
1996 – WASL arrives (reading, writing, listening, math)
2000 – NCTM Standards revised
2004 – GLEs developed
2008 – Washington state math standards revised
2010 – WASL departs and the MSP (grades K-8) arrives
2010 – Common Core standards written for Math & English
2014 – CCSS (Math & English) become standard in our state
2015 – SBAC (“Smarter Balanced”) testing replaces MSP
10 minutes for this slide => whiz right along.
The pendulum of reform swings a little crazily. E.G., there was John Dewey in the early part of the 20th century talking about the need to get kids engaged in the work of the practitioner, there was Sputnik and new math in the late 50s and 60s. There was “back to basics” in the 70s and 80s. In 1983, there was …
A Nation at Risk: (US Dept of Ed - National Commission on Excellence in Education)
"If an unfriendly power had attempted to impose on America the mediocre educational performance that exists today, we might well have viewed it as an act of war. As it stands, we have allowed this to happen to ourselves. We have even squandered the gains in achievement made in the wake of the Sputnik challenge. We have, in effect, been committing an act of unthinking, unilateral educational disarmament.” (p.5)
The NCTM Standards were in part a reaction to the climate created or reflected by this report.
HB 1209 was Washington state’s reaction to the situation.
Etc.

4. Introduction to the math standards What are the math wars?
Concepts? Or Procedures?
~10 minutes Maybe Start with reference to the Seattle Times front page article from a few years back ( ) entitled “Which math book to use? A passionate debate rages.” This is a reflection of the “Math Wars.” Of course neither side is right. We need both. Also different approaches work for different groups of students who have different levels of support, etc. at home. The old WA State standards were a real attempt to locate a balance between conceptual understanding and procedural proficiency. The CCSSm are a less salubrious attempt…
(A few years ago now) there was an editorial in the Seattle Times by Mr Sparks, a longtime teacher in the Seattle schools praising the discovery math approach. There was an immediate reaction in the form of comments posted on the Times Web site booing this point of view. Etc. It’s a nice little demonstration of the math wars in full swing.

5. Concepts AND Procedures AND Problem Solving!
“An effective mathematics program balances three important components of mathematics—conceptual understanding (making sense of mathematics), procedural proficiency (skills, facts, and procedures), and problem solving and mathematical processes (using mathematics to reason, think, and apply mathematical knowledge).”
~10 minutes Here is a statement taken from the introduction portion of the 6-12 Math Standards (2008).
Then talk about the necessity of students having a comfortable, and competent grasp of mathematics aimed at using math to solve problems, (make sense of the world).
As an analogy, it’s not enough to give a person a skill saw, a tape measure, a nail gun and compressor and a hammer. They also need to understand how these tools connect with one another, how to use them flexibly, etc.
You need to develop deep understanding of and flexible, efficient familiarity with a strategically limited set of tools. (“Strategically limited” means that the curriculum has been pared back a bit - no longer a mile wide and an inch deep.)

6. Concepts AND Procedures AND Problem Solving!
“Mathematical understanding and procedural skill are equally important, and both are assessable using mathematical tasks of sufficient richness.”
~10 minutes Here is a statement taken from the introduction portion of the 6-12 Math Standards (2008).
Then talk about the necessity of students having a comfortable, and competent grasp of mathematics aimed at using math to solve problems, (make sense of the world).
As an analogy, it’s not enough to give a person a skill saw, a tape measure, a nail gun and compressor and a hammer. They also need to understand how these tools connect with one another, how to use them flexibly, etc.
You need to develop deep understanding of and flexible, efficient familiarity with a strategically limited set of tools. (“Strategically limited” means that the curriculum has been pared back a bit - no longer a mile wide and an inch deep.)

7. Introduction to the common core math standards
Standard & Strand
Explanation
~5 minutes Show this slide and point out the structure: Standards, Clusters, and overarching Domains …

8. Introduction to the math standards: What’s addressed in grades K-8?
Take a close look at one of the standards.
Turn and talk: discuss, compare and contrast.
Pick one component of the standard. What’s important?
How might you teach this?
~20 minutes For this activity people need to decide whether they want to deal with CCSSm or the old WA math standards. They should get in groups of ~ 3 or 4 who share a common preference in this regard. To each small group, handout a set of selected standards that cover a range of grades. They should avoid writing on these.
.Everyone should pick one of the standards and consider it for five minutes.
Then they can talk with someone who looked at a different standard and do as the slide’s bullets direct:
“Pick one component of the standard. How might you teach this?
What’s important? “
Make sure they get to the point where they are talking about HOW TO TEACH to this standard.
Perhaps get a couple of volunteers to talk about theirs. ….
NOW, pass out a list of all of the CCSSm standards for grades K-8. Let them consider where their standard fits in the list.

9. Activities, worksheets & technology
“Dirt Bike Proportions” or “Ratio Blaster”
“What’s Wrong with that Doll?”
~5 minutes Preview the activities

10. Ten minute break!
10 minutes

11. What’s wrong with that doll?
What’s wrong with us?
I think we look awesome!
What’s wrong with that doll?
~29 min. Do the activity in which students select a doll and then compare, using ratios, the doll’s measurements (e.g., foot length to total height) to their own.

12. Common Core State Standards – math in grades 6 and 7
Ratios and Proportional Relationships
6th grade: Understand ratio concepts and use ratio reasoning to solve problems
7th grade: Analyze proportional relationships and use them to solve real-world and mathematical problems
The Number System
Expressions and Equations
Geometry
Statistics and Probability
2 min. Referring to the previous activity, look at the 6th and 7th grade standards, noting the prominence of this important set of concepts and skills.

13. Common Core State Standards – math in grades 6 and 7
Ratios and Proportional Relationships RP
6th grade: Understand ratio concepts and use ratio reasoning to solve problems
1. Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, “The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak.” “For every vote candidate A received, candidate C received nearly three votes.”
2. Understand the concept of a unit rate a/b associated with a ratio a:b (with b ≠ 0), and use rate language in the context of a ratio relationship. For example, “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.”
3. Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent
4 min. Take a look at some of the details for 6th grade.

14. Common Core State Standards – math in grades 6 and 7
Ratios and Proportional Relationships RP
7th grade: Analyze proportional relationships and use them to solve real-world and mathematical problems.
1. Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units.
2. Recognize and represent proportional relationships between quantities…
3. Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.
4 min. Take a look at some of the details for 7th grade.

15. “Dirt Bike Proportions” or “Ratio Blaster”
~15 minutes Describe the alien fractions activity as you infer it.
What are we learning? Get them to consider the questions on the slide. They need to be ready to respond to these.
YOU BE READY to show them a way or two to practice these skills, including a worksheet. (Lowest link on the page…)
NOTE: When they have a comfortable command of this they will be much more ready to deal with the addition and subtraction of fractions! This is s major problem solving advantage!
What are we learning?
> Ratio & Proportion> Ratio Blaster or Fractions > Dirt Bike Proportions

16. Onward…
To conceptual understanding and procedural proficiency let me now add …
This is to introduce the idea of mathematical reasoning. This comes from math generally. (The original 1989 NCTM standards emphasized PS, Reasoning, Communication and Connections.) But over the years reasoning has not been given the attention it deserves. With the edTPA there is clear attention given to mathematical reasoning and the discourse that supports this in a classroom.
SO I have a separate PPT to work on mathematical reasoning. [Reasoning.pptx ]
Reasoning.pptx

18. Activities, worksheets & technology
Rubber Bands
Which rubber bands go the farthest?
How do you know?
How do you use math to make sense of this?
~40 minutes? Get them into small groups ( ~ 4?). Each group gets a bag of rubber bands containing ten each of the small, medium and large bands. Each group also gets a tape measure to measure how far the bands fly and a ruler for measuring the pull they apply to the bands before launching them from the ruler,which is to be held level with the ground. They do ten trials of each band size, record the results and analyze the data in order to make a mathematically supported statement about which size flies farthest. . Consider the standards….
~5 minutes: Explain the procedure. Don’t let them invent too much. The emphasis is on getting data that can be conveniently analyzed rather than on developing their understanding of the scientific method.
~15 minutes: Distribute the materials and let them go out and create the data by shooting the rubber bands and measuring the flight distance.
~10 minutes: They should analyze their data in order to be able to be able to make a mathematically defensible statement about which band goes furthest or farthest.
~5 minutes: Get groups to share their results. They should be able to say which band size goes farthest and explain how they used math to come to this conclusion.
~5 minutes: Give them a couple of minutes to decide which standards(s) were potentially addressed and do some whole group processing of this.

19. Introduction to the math standards How are the standards structured?
Standard & Strand
Explanation
~5 minutes Show this slide and point out the structure: Standard (explain naming convention), Explanation, Performance Expectation (PE), (sometimes with 10 or more parts but more often with just a few), and Explanatory Comments and Examples.
Performance Expectation, Comments & Examples

20. (the old) Washington State Standards
MULTIPLICATION & DIVISION OF FRACTIONS & DECIMALS
MATHEMATICAL EXPRESSIONS AND EQUATIONS (ALGEBRA)
RATIOS, RATES & PERCENTS
TWO-DIMENSIONAL FIGURES
RATIONAL NUMBERS AND LINEAR EQUATIONS
PROPORTIONALITY & SIMILARITY
SURFACE AREA & VOLUME
PROBABILITY & DATA
6th
7th

21. (the old) Washington State Standards
MULTIPLICATION & DIVISION OF FRACTIONS & DECIMALS
MATHEMATICAL EXPRESSIONS AND EQUATIONS (ALGEBRA)
RATIOS, RATES & PERCENTS
TWO-DIMENSIONAL FIGURES
RATIONAL NUMBERS AND LINEAR EQUATIONS
PROPORTIONALITY & SIMILARITY
SURFACE AREA & VOLUME
PROBABILITY & DATA
6th
7th