Introduction to the K-8 mathematics standards in Washington State

Seattle UniversitySeptember, 2015

Dr. Mark Roddy - Seattle University

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

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

Concepts? Or Procedures?Concepts? Or Procedures?

Concepts AND Procedures AND Concepts AND Procedures AND Problem Solving!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).”

Concepts AND Procedures AND Concepts AND Procedures AND Problem Solving!Problem Solving!

“Mathematical understanding and procedural skill are equally important, and both are assessable using mathematical tasks of sufficient richness.”

Introduction to the math standards How are the standards structured?

Introduction to the common core math standards

• Take a close look at one of the standards.

• Turn and talk: discuss, compare and contrast.

• Pick one component of the standard. How might you teach this? What’s important?

Introduction to the math standards: What’s addressed in grades K-8?

• “Dirt Bike Proportions” or “Ratio Blaster”• “What’s Wrong with that Doll?”

Activities, worksheets & technology

Ten minute break!

What’s wrong with that doll?

What’s wrong with us?

I think we look awesome!

• Ratios and Proportional Relationships– 66thth grade grade: Understand ratio concepts and use ratio reasoning to solve

problems– 77thth grade grade: Analyze proportional relationships and use them to solve real-

world and mathematical problems

• The Number System• Expressions and Equations• Geometry• Statistics and Probability

Common Core State Standards – math in grades 6 and 7

• Ratios and Proportional Relationships 6.RP– 66thth grade 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

Common Core State Standards – math in grades 6 and 7

• Ratios and Proportional Relationships 7.RP– 77thth grade 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.

Common Core State Standards – math in grades 6 and 7

“Dirt Bike Proportions” or “Ratio Blaster”

http://www.arcademicskillbuilders.com/ > Ratio & Proportion> Ratio Blaster or Fractions > Dirt Bike Proportions

http://www.homeschoolmath.net/worksheets/fraction-b.php

Onward…To conceptual understanding and procedural proficiency let me now add …

Reasoning.pptx

• Rubber Bands– Which rubber bands go the farthest? – How do you know? – How do you use math to make sense of this?

Activities, worksheets & technology

http://www.mathworksheetscenter.com/mathskills/graphing/boxwhiskerplot/ http://illuminations.nctm.org/ActivitySearch.aspx http://nlvm.usu.edu/

• 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

(the old) Washington State Standards

• MULTIPLICATION & DIVISION OF FRACTIONS & DECIMALS

• MATHEMATICAL EXPRESSIONS AND EQUATIONS (ALGEBRA)

• RATIOS, RATES & PERCENTSRATIOS, RATES & PERCENTS• TWO-DIMENSIONAL FIGURES

• RATIONAL NUMBERS AND LINEAR EQUATIONS • PROPORTIONALITY & SIMILARITY PROPORTIONALITY & SIMILARITY • SURFACE AREA & VOLUME • PROBABILITY & DATA

(the old) Washington State Standards