Cypher IV Mathematics Leadership Project

Teaching Student-Centered Math Book Study K-3 Group Session 3

Developing Meaning For The Operations & Solving Story

Problems

(Re)Introductions Kim Ramsay (Gr. 2

Teacher, Whitehorse) Cathy Hines (Gr. 3

Teacher, Whitehorse) Kathryn Lewis (K

Teacher, Old Crow) Shari Heal (Grade 3

French Immersion Teacher, Whitehorse)

Tammy Stoneman (Learning Assistance Teacher, Teslin)

Tina Moody Curran (Gr. 1-2 Teacher, Teslin)

Bernadette Roy (French Gr. 3 Teacher, Whitehorse)

Kathleen Evans (K Teacher, Faro, YT)

Jenna Sawkins (Gr. K&1 Teacher, Dease Lake)

Nita Connolly (Grades K-2 Teacher, Atlin)

Dana Caljouw (K-3 Teacher, Telegraph Creek)

Group Norms Be Responsible For

How & What You Learn Everyone brings prior

experience & knowledge. Take ownership of your learning by being on time and staying, doing the reading & reflection to prepare for discussion, and be willing to try out new ideas in your classroom.

Encourage Risk-Taking and Accept All Ideas When learning and

discussing, everyone needs to feel safe& that ideas will be respected, even if there is disagreement. Discussion of new ideas allows everyone to ? their own beliefs & discover new ways of thinking – an essential focus of this book study.

Group Norms - cont’d Be Your Own

Watchdog Monitor and manage

your participation to prevent contributing too much or too little.

Be An Attentive Listener Listen to each other

during the discussion. Turn off your e-mail and refrain from surfing the net during the sessions.

Homework Review (Small Group) Based on the homework

assigned in the previous session, discuss the following questions in a small group: What have you tried in your

classroom as a result of the last session?

What role did you play in the teaching and learning of math?

What role did the students play in their learning?

What discoveries did you and your students make?

What misconceptions, if any, surfaced about the topic? How did you redirect the students?

What suggestions do you have for others when they try this?

Objectives Focus on the Big Ideas of operation sense Define addition and subtraction Explore problem structures for addition,

subtraction, multiplication, and division Work with models for addition, subtraction,

multiplication, and division Discuss important issues related to solving

story problems

Materials Counters (Create

counters as you need them on the whiteboard in the breakout room screens.)

Square tiles or snap cubes (Create as needed on breakout room screens.)

Grid Paper (Will be provided within the breakout rooms.)

Evaluation Form (Sent at the beginning of the session.)

How Bear Got A Short Tail Materials (Problem Structures) are within the slide show.

Before

Teaching Through Problem Solving Divide into smaller

groups for 10 minutes.

What does it mean to teach through problem solving as opposed to teaching problem solving?

Ideas:

During - Big Ideas Review the Big

Ideas for this chapter (p. 65) on your own for 2 min.

Discuss these ideas with a partner in a breakout room for 8 min. by sharing examples from your teaching that illustrate each of these ideas.

Defining Addition & Subtraction The typical definitions

for addition and subtraction describe addition as “putting together” & subtraction as “taking away.” These definitions can be misleading.

Read the problems in the + and - section on p. 65 and do the first Stop & Reflect box (p. 66).

When you are done, read the 2 paragraphs following the Stop and Reflect box. Put your hand up when you are done.

Prepare to discuss the following question with the group: How does this info

change the way that you think about addition and subtraction?

Problem Structures for + & - + & - problems can be

categorized based on the kinds of relationships involved. The four categories of problems are: Join (Room 1) Separate (Room 2) Part-Part-Whole (Room

3) Compare (Room 4)

Task Review the section of the

text you chose Define the category Create examples of each

type of problem Show how counters

could be used to model and solve the problem (use the whiteboard tools)

Be prepared to present to the large group in 15 min.

Cognitively Guided Instruction: Problem Types For Addition/ Subtraction For __ _ _ _ _ _ _ _ _ _ _ _ __ _ _ _ _ _ _ _ _ _ __ _ _ _ _ _ _ _ _ _ _ _ __ _ _ _ _ _ _ _ _ _ __ _ _ _ _ _ _ _ _ _ _

Join

(Resu lt Un known) (Chang e U nknow n) (Start Unknow n)

Separate

(Resu lt Un known) (Chang e U nknow n) (Start Unknow n)

Compare

(D ifferen ce Un known) (Quant ity Unknown) (Refer e nt U nknown)

Part-Part

Whole

(Who le Unknow n) (Part U nknown)

Cognitively Guided Instruction: Problem Types For Addition/ Subtraction For How Bear Got A Short Tail

Join

(Resu lt Un known) *

€

5+4=x Bear went fis hing. He ca ught 5 fish a nd the n h e caug h t 4 more. How ma ny f is h d id Bear catch? (5, 4 ) (16 , 23 ) ( 46, 4 5 )

(Chang e U nknow n)

€

5+x=9 In t he morn ing Bear cau ght 5 fish. By t he e nd of th e day, he had caugh t 9 fish. How man y fish did Bear catc h in the afternoon? H e d id not cat ch fish in th e e ven ing. (5, 9 ) (16 , 39 ) ( 46, 9 1 )

(Start Unkno wn)

€

x+4=9 Bear caught som e sa lmon . Fox gave Bear 4 more sa lmon . The n Bear had 9 sa lmon . How man y sa lmo n d id Bear h a ve before Fox ga ve him any? (4, 9 ) (23 , 39 ) ( 45, 9 1 )

Separate

(Resu lt Un known) *

€

7−4=x Bear caught 7 fis h. He ga ve 4 fish to a fr iend. Now how man y f ish does Bear h a ve? (7, 4 ) (18 , 6 ) (33 , 27)

(Chang e U nknow n)

€

7−x=3 7 f ish wer e sw im m in g by Bear in the river. Some sw a m aw a y. The there were 3 f ish sw imm ing by Bear. How m a n y fish sw a m aw a y? ( 7, 3 ) (12 , 8 ) (33 , 6)

(Start Unknow n)

€

x−4=3 Bear has some s al mon. He gave 4 to Fox. Now Bear has 3 sa lmon left. How m a n y sa lmo n d id Bear hav e before he ga ve any t o Fox? (4, 3 ) (12 , 6 ) (27 , 6)

Compare

(D ifferen ce Un known)

€

10−7=x or 7+x=10 Fox has 10 fish . Bear has 7 fish. How m a ny more fish does Fox h a ve tha n Bear? (10, 7 ) ( 18, 1 2 ) (42, 3 4 )

(Quant ity Unknown )

€

7+3=x Bear has 7 fish . Fox has 3 more f is h th a n Bear. Ho w man y f ish does Fox h a ve? (7, 3 ) (12 , 6 ) (34 , 8)

( Refer e nt U nknown )

€

10−3=x or x+3=10 Fox has 10 fish . H e has 3 more fish tha n Bear. How man y fish does Bear have? (10, 3 ) ( 18, 6 ) ( 42, 8)

Part-Part

Whole

(Who le Unknow n) *

€

4+6=x There are 4 sa lmon an d 6 trout sw imm ing near Bear’s f ish ing spot. How m a n y f ish are sw imm ing a ltogether? (4, 6 ) (22 , 15 ) ( 37, 2 9 )

(Part U nknown )

€

2+x=7 or x=7−2 Bear caught 7 fish. 2 were trout. The re st were sa lmon. How ma ny sa lmon d id Bear cat ch? (7, 2 ) (26 , 7 ) (33 , 22)

Problem Structures for x & ÷ x & ÷ problems can also

be categorized according to the types of relationships involved. The two most common structures are: Equal-group problems

(Rooms 1 & 2) Multiplicative comparison

problems (Room 3 & 4)

After reviewing the sections of the text on Equal-Group Problems (p. 78) & Comparison Problems (p. 79), get into pairs or 3 to solve the problems in the text as directed in the Stop & Reflect box (p. 79).

Create 1 of each type of problem with your partner(s) for 18 min.

Cognitively Guided Instruction: Problem Types For Multiplication/Div ision For __ _ _ _ _ _ _ _ _ _ __ _ _ _ _ _ _ _ _ _ _ _ __ _ _ _ _ _ _ _ _ _ _ _ __ _ _ _ _ _ _ _ _ _ __ _ _ _ _ _ _ _ _ _ __

Equal Groups

(Who le Unknow n)

(S ize of Groups Unknown) (Partiti v e Division, Part ition Division, Fair - Sharing)

(Nu mber of Groups Unknown) (Measureme n t Divisio n or Repeated Su btraction)

Comparison

(Product U nknown) (Set S ize U nknow n) (Partition D ivisio n )

(Mu lt ipli er Un known)

Cognitively Guided Instruction: Problem Types For Multiplication/Div ision For How Bear Got A Short Tail

Equal Groups

(Who le Unknow n)

€

3×4=x Bear has 3 fis hing spots. He caught 4 fish a t ea ch spot. How ma ny f is h d id Bear cat ch? (3, 4 ) (4, 10 ) (7, 20)

(S ize of Groups Unknown) (Called Par t it ive Divisio n on the w ebsite. )

€

12=3×x or 12÷3=x Bear shared 12 fis h w ith h is 3 fr iends. Ea ch fr iend go t th e same number of f ish. Ho w man y f ish d id each fr ien d get? (12, 3 ) ( 40, 4 ) ( 140, 7 )

(Numbe r of Groups Unknown) (Called Measurem e nt Divisio n on th e websi te.)

€

12=x×4 or 12÷4=x Bear gave 1 2 f ish to some fr iends. He ga ve 4 to ea ch fr iend. Ho w ma ny fr iends go t fish? (12, 4 ) ( 40,3) (140 , 20)

Comparison

(Product U nknown )

€

3×5=x Fox has 3 sa lmon. Bear ha s 5 t ime s as m a ny s al mon a s Fox. How ma ny sa lmon does Bear have? (3, 5 ) (4, 6) (7, 20)

(Set S ize U nknow n)

€

15÷5=x or 15=x×5 Bear has 1 5 sa lmon. H e has 5 t ime s as m a ny a s Fox. How man y sa lmo n does Fox have? (15, 5 ) ( 24, 6 ) ( 140, 2 0 )

(Mu lt ipli er Un known )

€

15÷3=x or 15=3×x Bear has 1 5 sa lmo n and Fox has 3 s al mon. How m a ny t ime s more sa lm on does Bear have compared to Fox? (15, 3 ) ( 24, 4 ) ( 140, 7 )

Using Models For x & ÷ An important model

for multiplication and division is the array. An array is any

arrangement of things in rows and columns, such as a rectangle of square tiles or blocks.

In pairs, Represent the factors of

30 using arrays. Record your arrays on

graph paper and write the multiplication expression that the array represents beside it.

Be prepared to share.

QuickTime™ and a decompressor

are needed to see this picture.

Using Models For x & ÷ (p. 82) How and why do

arrays support students in their understanding of multiplication?

How could arrays be used to support students in their understanding of division?

Solving Story Problems Review, More

Thoughts About Children Solving Story Problems (pp. 86-89).

Why is is important to avoid using key words as a strategy, encourage problem analysis, and require explanations?

Why is is important to avoid using key words as a strategy, encourage problem analysis, and require explanations?

Avoid Key Words Encourage Problem Analysis

Require Explanations

After What does it mean to

think through problem solving as opposed to teaching problem solving? Discuss how learning

about the various problem structures in this session will help you to teach through problem solving.

Evaluation & Self-Assessment Form

Homework Try several story

problems with some students. Use problems from the chapter, problems that were created in this session, or your own. Fax student samples to 867-393-6339 by the Mon. prior to the next session to share with the group.

Read Chapter 4