Strong Start Math

Tuesday, June 28, 2016

Strong Start Math Project

This material was developed for the Strong Start Math project through the University of Wisconsin-Milwaukee, Center for Mathematics and Science Education Research (CMSER). This material may be used by schools to support learning of teachers and staff provided appropriate attribution and acknowledgement of its source. Other use of this work without prior written permission is prohibited—including reproduction, modification, distribution, or re-publication and use by non-profit organizations and commercial vendors.

Agenda

• Learning Trajectory: Composing Numbers

• Comparing Quantity: K.CC.6 and K.CC.7

• Story Problem Structures (K.OA.1, K.OA.2, 1.OA.1, 2.OA.1)

• Lunch

• Mathematical Curiosity: Revisiting Spot It

• Story Problem Structures continued

LEARNING TRAJECTORY: COMPOSING NUMBER

Composing Trajectory

• Name the 4 Number Relationships. Review with your table what they mean and what a student would understand if they were working on them.

• Read through the Composing Trajectory. As you read through a second time, take notes in the right column of how the 4 Number Relationships are embedded in and interact with the Trajectory.

Hip Hop Hippos

• As I read, model the pages on your Number Path.

• What mathematical understandings does a student need to have as they model this book?

COMPARING QUANTITY: K.CC.6 & K.CC.7

Learning Intentions and Success Criteria

We are learning to…

• Understand the skills and understandings young children need to compare quantities and numbers using “more,” “less,” and “the same.”

We will be successful when we can…

• Explain K.CC.6 and K.CC.7 and provide examples of the mathematics.

K.CC. 6 and K.CC.7

• Divide your whiteboard in half.

• Rephrase the standard in your own language.

• Provide an example.

Complete the phrase:

In order to be successful with K.CC.6 or K.CC.7 young children need to be able to _________.

The Concepts of More and Less

Read and Highlight

“What You Need to Know About the Concepts of More and Less”

What did this reading affirm for you?

What additional insights did you gain?

Turn and share with your partner.

Which has more?

“More” and “less” are difficult concepts for many young children.

Set A

Set B

https://www.youtube.com/watch?v=gnArvcWaH6I

Foundational Math Concept: Sets

Cultivating an understanding of comparison and ordering

helps children build the understanding they need to

think about a set in relationship to other sets and begin

to make comparisons between numbers. Familiarity with

this idea prepares children to address questions they will

encounter in first grade and beyond, such as

“If Ian has ten crackers and Juanita has 8, how

many more crackers does Ian have?”

Introducing Difficult Language In Natural Contexts

Three children went to the reading corner. The reading corner has 4 pillows.

Each child wants to sit on a pillow. What do you think will happen? Can each child sit on a pillow?

• Are there more pillows or more children?

• How do you know?

• How many extra pillows are there?

Teacher statement: So, there are more pillows than children.

This time, five children went to the reading corner.The reading corner has 4 pillows.

Each child wants to sit on a pillow, what is going to happen? Can they all get a pillow?

• Are there more pillows or more children?

• How do you know?

• How many children won’t get a pillow?

Teacher statement: So, there are fewer pillows than children.

Ms. Hedges asked 6 children to grab a pillow and join her in the math corner.What is going to happen?

Will each child get a pillow?Do we have extra pillows or extra children?Are there more pillows or children?

Opportunities to Practice

Bears and Chairs

Set out 8 chairs and 6 bears.

Each bear wants to sit on a chair.

What do you notice?

Are there more chairs or more bears?

How many chairs are empty?

How many extra chairs do you have?

Bears and Chairs

Set out 7 chairs and 10 bears.

Each bear wants to sit on a chair.

What do you notice?

Are there more chairs or more bears?

How many bears won’t get a chair?

Reflection/Summary

• Summarize some key points and classroom ideas related to the topics or focus standards in this session.

Focus Topics or Standards Summary of Key Points

ClassroomIdeas to Try

MATHEMATICAL CURIOSITYRevisiting Spot It!

What do you recall about the game of Spot It and how the cards were designed?

Today we are going to examine how to make our own set of Spot It cards.

PROBLEM SITUATIONS Types of Story Problem Structures

Learning Intention & Success Criteria

We are learning

• what are the CCSSM expectations around story problem structures.

• that students progress through levels of reasoning as they solve story problems.

• how we might support students’ representations of their thinking.

Unpacking Story Problem Standards: K.OA.1, K.OA.2, 1.OA.1, and 2.OA.1

Count off by 4 at your table.

• 1s read K.OA.1

• 2s read K.OA.2

• 3s read 1.OA.1

• 4s read 2.OA.1

• Read the your assigned standard.

• Divide your whiteboard in half.

• On one side, rephrase this standard and on the

• other side, provide an example.

• Share with your partner.

12/10/2017 24

Part 1 of these standards

• K.OA.2: Solve addition and subtraction word problems…• 1.OA.1: Use addition and subtraction within 20 to solve

word problems involving situations of adding to, taking from, putting together, taking apart, and comparing with unknowns in all positions…

• 2.OA.1: Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing with unknowns in all positions…

What are the addition and subtraction word problems identified by the CCSSM?

“… in the eyes of children, not all addition or subtraction problems are alike. There are important distinctions between different types of addition problems and different types of subtraction problems, which are reflected in the way children think about and solve them.”

-Children’s Mathematics Cognitively Guided Instruction, p.2

CGI Resource:

• Children's Mathematics: Cognitively Guided Instruction by Thomas Carpenter et al.

CGI (Cognitively Guided Instruction): What is it?

A problem-solving approach to teaching the operations (addition, subtraction, multiplication, and division) that promotes the understanding of different ways operations are used in “real world” contexts.

CGI (Cognitively Guided Instruction): Why use it?

• Students will have a better understanding of the operations if they are able to see them at work within a context

• Students extend their understanding of number concepts in ways that make sense to them through connections to what they already understand.

CGI (Cognitively Guided Instruction): How does it fit with CCSS?

• Shift of Rigor: CGI promotes conceptual understanding because it focuses on making sense of the action(s)/context of the problem rather than key words. – Key words should avoid being taught because they do not

always indicate the same operation.• E.g. “In all” usually indicates addition but sometimes indicates

multiplication too.

• Shift of Rigor: At the heart of CGI are word problems –tying mathematical thinking to real world contexts. The primary grade standards call for specific kinds of contextual problem solving in addition and subtraction. – K.OA.1 & 2, 1.OA.1, 2.OA.1

12/10/2017 31

Four kindergartenproblem subtypes

Four 1st Grade problems

Four problems to Experience at 1st grade;

working toward proficiency of all

problem types at 2nd

PRR: Professional Reading & Reflection

OA Progressionsp. 8-10

p. 12-14

p. 18

p. 19

What are some characteristics that distinguish one problem subtype from the other?

Why is it important to understand what seem to be subtle distinctions in word problems?

Kindergarten – stop before “Working within 10”

Grade 1 – stop before “Using Level 2…”

Grade 2 - 1st four paragraphs only

Extensions

Addition & Subtraction Situations

• What are some characteristics that distinguish one problem subtype from the other?

• Why is it important to understand what seem to be subtle distinctions in word problems?

33

Problem Sort

• One person takes a card out of the envelope at a time.

• Read the problem on the card aloud.

• Decide on the problem type and label it with a post it.

• Explain your reasoning using language from the CCSSM, the Progressions.

• Pass the envelope to the person to your right.

34

Problem Sort

How did you make decisions about how to label the problems?

Factors that affect the rigorof a word problem

• Problem Type• Quantities in the problem• Order in which the information is presented

– Quantities presented in the order they are acted upon less challenging

– Quantities presented in a different order more rigorous

• Whether the action is in the future or already passed– “how many more are needed?” less challenging– “how many were given?” more rigorous

• Discrete or continuous quantities – Discrete quantities (pencils, cookies, etc.) can be modeled with

counters– Continuous quantities (pounds, inches) require a more abstract

representation.

Similar and Different

• Silently read the problems on the following slide.

• Turn to your shoulder partner and describe how the problems are similar and different.

• What factors make one problem more challenging than another?

Set A

1. Amy has 9 rocks. How many more rocks would Amy need to get to 13 rocks?

2. Amy had 13 rocks. She gave 9 of them to Mainhia. How many rocks does Amy have now?

Set B

1. Brittany just shared 6 pencils with Ellen. Before she shared those, she had 14 pencils. How many pencils does Brittany have left?

2. Brittany has 14 pencils. Ellen has 6 pencils. How many more pencils does Brittany have than Ellen?

Practice

• Stand up – Find a grade level partner!

• Brainstorm contexts for story problems with a grade level partner.

• With a your table partner, write a word problem for each problem type.

Keep your problem above the dotted line.

Reflection/Summary

• Summarize some key points and classroom ideas related to the topics or focus standards in this session.

Focus Topics or Standards Summary of Key Points

ClassroomIdeas to Try