evidence of student learning in educ 364: activity...

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Evidence of Student Learning in EDUC 364: Activity Diary

Table of Contents

Pages 2-3: The description of this assignment provided to students in the course syllabus.

Page 4: The scoring rubric used to assess the Activity Diary. This rubric was made

available to the students at the beginning of the term.

Pages 5-14: The Activity Diary produced by ―Carrie‖ (a pseudonym), followed by the scoring

rubric, score, and my comments on the diary. Carrie‘s diary was of low quality

relative to peers in the class.

Pages 15-25: The Activity Diary produced by ―Bernie‖ (a pseudonym), followed by the scoring

rubric, score, and my comments on the diary. Bernie‘s work was of average

quality relative to classmates.

Pages 26-39: The Activity Diary produced by ―Alice‖ (a pseudonym), followed by the scoring

rubric, score, and my comments on the diary. Alice‘s work was of high quality

relative to classmates.

2 Activity Diary Assignment Description

Assignment Description

The Activity Diary is a brief record you will keep of useful mathematics activities drawn from

your experiences in class, with web-based applets, and from course readings. The diary will

include a brief description of activities you found valuable, an indication of how the activities

connect to the NCTM Process Standards and Curricular Focal Points, and a brief commentary on

how the activity might be used or modified in your own teaching. It is hoped that this diary will

be a useful resource to you as you begin your teaching, and that you will continue to add entries

to it as you progress through your career. Use the ―Activity Diary‖ template which is posted on

Moodle. Diaries should be emailed to the instructor ([email protected]) on or before

each of the dates listed below. The specific requirements of each diary submission are also

indicated below.

Sept. 2: Review some web-based instructional applets, and record the 4 activities you

found most promising in your activity diary. Suggested places to find applets include:

o The National Library of Virtual Manipulatives,

http://nlvm.usu.edu/en/nav/vlibrary.html . Virtual manipulatives, K-12.

o NCTM Illuminaions, http://illuminations.nctm.org . Mathematical applets and

activities organized by grade band.

o Shodor Interactive, http://www.shodor.org/interactivate/activities/ . A collection

of applets designed to illustrate concepts and games designed to add enjoyment to

skills practice.

o Arytech Educational Java Programs, http://arcytech.org/java/ . Manipulate virtual

money, clocks, pattern blocks, Cuisenaire rods, and other stuff.

o Cyberchase Games Central, http://pbskids.org/cyberchase/games.html . A

collection of games involving mathematical problem solving, starring the

characters of the PBS series Cyberchase (appropriate for upper elementary

students)

o Kids and Cookies,

http://www.teacherlink.org/content/math/interactive/flash/kidsandcookies/kidcook

ie.php . Explore division with kids and cookies.

Sept. 16: 4 entries drawn either from in-class activities prior to Sept. 16 or from

activities found in the Van de Walle readings prior to Sept. 16 [7th

edition, chapters 8 &

11; 6th

edition, chapters 9 & 12; 5th

edition, chapters 9 & 12]. Note that AT LEAST

TWO of your entries should be drawn from the Van de Walle text.

Sept. 30: 4 entries drawn either from in-class activities since Sept. 16 or from activities

found in the Van de Walle readings since Sept. 16 [7th

edition, chapters 9 & 15 and pp.

328-341; 6th

edition, chapters 10 & 16 and pp. 333-345; 5th

edition, chapters 10 & 15 and

pp. 280-291]. Note that AT LEAST TWO of your entries should be drawn from the Van

de Walle text.

Oct. 14: 4 entries drawn either from in-class activities since Sept. 30 or from activities

found in the Van de Walle readings since Sept. 30 [7th

edition, chapters 12, 16, & 20 and

pp. 342-345; 6th

edition, chapters 13, 17 & 21 and pp. 346-349; 5th

edition, chapters 13,

http://nlvm.usu.edu/en/nav/vlibrary.html

http://illuminations.nctm.org/

http://www.shodor.org/interactivate/activities/

http://arcytech.org/java/

http://pbskids.org/cyberchase/games.html

http://www.teacherlink.org/content/math/interactive/flash/kidsandcookies/kidcookie.php

http://www.teacherlink.org/content/math/interactive/flash/kidsandcookies/kidcookie.php

3 Activity Diary Assignment Description

16 & 20 and pp. 292-295]. Note that AT LEAST TWO of your entries should be drawn

from the Van de Walle text.

Oct. 28: 4 entries drawn either from in-class activities since Oct. 14 or from activities

found in the Van de Walle readings since Oct. 14 [7th



edition, chapters 19 & 22]. Note that AT LEAST TWO of

your entries should be drawn from the Van de Walle text.

4 Activity Diary Scoring Rubric

Name:

The Activity Diary is a running record which will be kept over the course of the semester. The final diary is

worth 20 points. The diary will have 20 entries, each entry worth 1 point. For each entry, points are earned as

follows:

0.2 points for listing the given activity under an appropriate grade band heading (e.g., Kindergarten, 1st Grade,

etc.)

0.2 points for listing all materials needed for the activity

0.2 points for providing an adequate description of the activity (―adequate‖ meaning that another teacher would

be able to implement the activity based on your description)

0.2 points for listing NCTM Curricular Focal Points which are directly related to the activity

0.2 points for listing NCTM process standards which are directly related to the activity

Name of Activity Score

Earned


Earned

Current Score:

Final Score:

Comments:

5 “Carrie’s” Activity Diary [Relatively Low Quality]

Kindergarten

Name and Location of Activity Materials

Needed

Brief

Description

of Activity

Relevant NCTM

Curricular Focal Point

Relevant

NCTM

Process

Standard(s)

Evaluation/Suggested

Modifications

Color Patterns-NVLM

http://nlvm.usu.edu/en/nav/topic_t_2.html

Online

activity

Program

gives a

pattern using

different

color circles,

and player

must

complete

circle.

Number and

Operations:Representing,

comparing, and ordering

whole numbers and

joining and separating

sets

Problem

solving,

reasoning and

proof

Along with figuring

out the pattern, I

would have students

count how many

different colored

circles there are, and

how many circles in

general.

9/15/09 Real Counting on

Van de Walle p. 129

Cup,

counters,

deck of

cards 1-7, a

die.

Students

draw card

and put that

many

counters in

cup. Then,

students roll

die and put

that many

counters

next to the

cup. Then,

they count

how many

there are in

all.

Number and



whole numbers and


sets

Problem

solving,

communication

Children enjoy this

because it is a ―game.‖

Helps students with

cardinality and

ordinality.

9/15/09 Five-Frame Tell-About Five-frame,

counters

Tell students

to put

numbers

ranging

from 0 to 5

Number and



whole numbers and


Problem

Solving,

reasoning and

proof,

communication

Develops a strong

base-five anchor. In

the long run,

practicing this will

help students


on their

frame. Ask

them, ―What

can you tell

us about x

from

looking at

your map?‖

Focus on

how many

more

counters are

needed to

make five.

Then, do

numbers 5-

10.

sets add/subtract, etc, by

rounding to the nearest

five.

Can do similar activity

with ten-frames.

10/14/09 Longer, Shorter, Same

Van de Walle, p. 273

Various

objects that

are of

different

lengths that

students can

easily move

around.

Make

sorting-by-

length

stations

where

students will

order objects

as shorter,

same, or

longer as

one specific

reference

object. Can

also put

objects in

order of

shortest to

longest.

Measurement: Ordering

objects by measurable

attributes

Problem

solving (if

unfamiliar with

comparing

length of

objects),

reasoning and

proof,

communication

(if asked to

explain how

they got their

answer)

Students who have a

stronger understanding

of length might be

provided with a

challenge by ordering

objects from shortest

to longest because

they must compare

with multiple items

instead of referring to

one reference object.

Students would work

in groups and help

explain their reasoning

(as best as a

kindergartner can) to

other students who

need help.


Grade 1

Name and Location

of Activity

Materials Needed Brief Description of

Activity

Relevant

NCTM

Curricular

Focal Point

Relevant NCTM

Process

Standard(s)


Modifications

Turtle Pond Online Activity Students plot

directions for turtle to

get to pond on a grid.

Number and

Operations and

Algebra:

Developing

understandings of

addition and

subtraction and strategies

for basic addition

facts and related

subtraction facts

Problem Solving,

Reasoning and

Proof,

Communication

Click on the ―exploration‖

section to help guide thinking

and get students to predict

directions and how many

moves the turtle will take to

get to the pond.

Poddle Weigh-In Online Activity Students use different

weights (ranging

from one to four) to

guess the correct

weight of the poddle.

Uses part-whole

relationships.

Number and

Operations and

Algebra:

Developing

understandings of

addition and


for basic addition

facts and related

subtraction facts Number and

Operations and

Algebra:

Problem Solving,

Reasoning and Proof

Stress that there are different

ways of combining numbers

to create a whole. Ex:

1+1+1+4=7, and 2+2+3=7.

9/15/09 Counting in

Groups

Van de Walle p. 193

Anywhere from 25-

100 items that kids

would want to count

The teacher asks

students for different

ways of counting a

large number that‘s

easier than counting

Number and

Operations:

Developing an

understanding

of whole

Problem Solving,

Reasoning and

Proof,

Communication

Engages students by counting

something they‘re interested

in. Allows students to think

critically about different ways

of counting, and can see their


by ones. Try to do

every suggestion.

Asked what worked,

what didn‘t? The goal

is to count by tens.

number

relationships,

including

grouping in

tens and ones

hypothesis tested—gives

value to child‘s opinion,

makes them feel like

mathematicians.

9/30/09 Up and

Down the Line

Van de Walle p. 151

Large number line The teacher lays the

number line on the

floor in front of the

class and has students

move up and down

the number line.

Teacher talks about

movement on the

number line related to

+/-. Demonstrate

more/less in +/-.

Number and

Operations and

Algebra:

Developing

understandings of

addition and


for basic addition

facts and related

subtraction facts

Problem Solving (if

not familiar with +/-

), communication,

representation

Assuming students know

about more/less, this is a good

way to show subtraction gives

you less and addition gives

you more. I would use this to

help correct basic problems

by putting it on the

chalkboard and have students

or myself ―walk out‖ the

problems to find the answer.

10/14/09 Tangram

Areas

Tangrams, outline of

shapes that can be

created by tangrams,

Grandfather Tang’s

Story by Tompert

(optional)

Have students use

tangram pieces to

figure out if shapes

are the same size.

Have them explain

answers. Can read

Grandfather Tang’s

Story for more.

Geometry:

Composing

and

decomposing

geometric

shapes

Problem Solving,

reasoning and proof,

communication

I like the investigative

property this activity has—its

as if students are figuring out

a puzzle. Nice integration

with the story. Students can

work in groups and explain to

group members the reasoning

for their answers.

10/28/09 Pattern

Block Mirror

Symmetry


Plain sheet of paper

with a straight line

through the middle,

pattern blocks, mirror

Students use 6-8

blocks to create a

pattern on one side of

the line (it must also

touch the line). Then,

students try to make a

mirror image on the

other side of the line.

When they are done,

students take a mirror

and place it on the

line so they can see

the reflection of their

Geometry:

Composing and

decomposing

geometric shapes

Connections (to art),

representations (of

transformations)

I would use this as an

integrated lesson for math and

art. I like the idea of being

able to check their work using

the mirror. It also makes the

idea of line symmetry more

concrete.


Grade 2

Name and Location

of Activity


Activity

Relevant

NCTM

Curricular

Focal Point

Relevant NCTM

Process

Standard(s)


Modifications

Clock Wise Online Activity Applet gives a time

on clock face, then

student must enter

said time as fast as

possible.

Measurement:

Developing an

understanding of

linear

measurement

Communication,

Connections, and

Representation

Good to use as

review/practice, but not

necessarily a teaching tool.

9/15/09 Counting

Rows of 10


10x10 dot arrays Put 10x10 array on

projector. Cover up

rows and dots within

a row. Ask ―How

many tens? How

many ones?‖

Number and

Operations:

Developing an

understanding of

the base-ten

numeration

system and place-value

concepts Number and

Operations:

Problem Solving,

Communication,

Representation

Helps develop base-ten

anchor. Shows students an

easy way of counting larger

numbers by grouping in ten

and then adding the ones to

that.

10/14/09 Estimation

Quickie


One object students

are familiar with for

each day

Once a day, estimate

the length, height,

surface area, etc of

one object, such as a

jar, the teacher, a

tissue box, etc.

Measurement:

Developing an

understanding

of linear

measurement

and facility in

measuring

lengths

Communication,

representation

A quick way to give constant

practice to help students

estimate and become familiar

with measurement.

Additionally, after hearing a

few educated guesses, have

students measure the item.

first pattern. They

should see the exact

same image in the

mirror as when they

lift it.


Grade 3

Name and Location

of Activity


Activity

Relevant

NCTM

Curricular

Focal Point

Relevant NCTM

Process

Standard(s)


Modifications

9/30/09 Finding

Factors

Van de Walle p. 158-

9

Counters, grid paper Give numbers that

have several factors.

Ask students to find

as many

multiplication

expressions they can

for that number by

dividing counters

into equal groups.

Or, they can use grid

paper to find

rectangles that

represent that

number. Write down

equation.

Problem

Solving (if

unfamiliar with

factors),

Reasoning and

Proof,

Communication

(using

equation),

Representation

Number and Operations

and Algebra: Developing

understandings of

multiplication and division and strategies for

basic multiplication facts

and related division facts.

Would have students who do

not know factors as well as

others use the counters. For

more accelerated students,

use the grid (less able to

manipulate/visualize). Could

work in pairs and have one

student do one way and vice

versa to see different

representations of the

number.

9/30/09 Who is

Winning?

Van de Walle p. 290

Fraction line Explain that a group

of friends are playing

red light—green

light. Each name has

a fraction next to it,

representing how

much of the distance

they have already

moved (ex: Mary:

¾). Have students

place these friends

on a line to show

where they are.

Problem solving

(if unfamiliar

with fraction

equivalence),

Reasoning and

Proof,

Communication,

Representation

Number and Operations:

Developing an

understanding of fractions

and fraction Equivalence.

Good way to show fraction

equivalence. I would have a

large fraction line at the front

of the class have have

students stand at each spot to

give a better visual of who is

winning.

9/30/09 Zero, One- Set of cards with 10- Have students sort Reasoning and Number and Operations: Can make different sets of

11 “Carrie’s” Activity Diary [Relatively Low Quality] Half, or One 15 fractions cards into three

groups: fractions

close to 0, lose to ½,

and close to 1. Then,

have students take

the close to ½ pile

and sort into more or

less than ½. Have

students explain how

they used the

numerator and

denominator to

decide.

Proof,

Communication

Developing an

understanding of fractions

and fraction Equivalence.

cards for students depending

on their level of

understanding. For example,

can create cards that have

1/20 or 53/10 that are close to

the benchmarks for an easier

set. Can create cards with

fractions that have

denominators less than 20 for

a more difficult set.

10/14/09 LCM Flash

Cards


Flash cards with 2

numbers (no higher

than 16) and least

common multiple on

back

With these practice

flash cards, students

can learn

automaticity of

common LCMs in

order to make

solving fraction

problems faster.

Connections,

representations

(see

modifications

)

Number and

Operations:

Developing an

understanding of

fractions and

fraction

equivalence

To make sure the students

understand the principle of

LCM in relation to fractions,

ask students to create a

problem using ―pie fractions‖

or another representation that

involves the LCMs on the

cards.

10/28/09 Mystery

Definition


Overhead or

whiteboard, multiple

shapes that have

something in

common (1st group),

example of shapes

that do not (2nd

group), a group of

shapes that has some

properties from the

first group, but some

that do not.

In this logic activity,

students identify

variables that all the

shapes share in the

first group that

makes them different

from the shapes in

the second group.

Students will create a

definition of the first

group shapes. Then,

students pick shapes

from the third group

that are like the ones

in the first and justify

their answer.

Problem

Solving,

reasoning and

proof,

communication

Geometry: Describing and

analyzing properties of

two-dimensional shapes

I like this exercise because it

asks students to identify

universal themes in shapes.

This is in concordance with

van Hiele‘s second stage,

informal deduction. Can

make the mystery property

easy or difficult according to

the student‘s level.

12 “Carrie’s” Activity Diary [Relatively Low Quality] 10/28/09 What‘s my

Shape?


Two sets of cut outs

of different shapes,

one set is

individually glued

into a ―secret shape‖

folder

In groups, students

pick a leader. They

look at a secret

shape. The other

students use the

second set of shapes

to figure out which

shape is secret. The

leader can answer

yes or no questions.

Group members must

ask questions about

characteristics or

properties of shapes.

They will slowly

eliminate shapes that

do not have similar

properties until they

reach the mystery

shape.

Problem

solving,

reasoning and

proof (for

leader),

communication




This activity works with level

one of the van Hiele model,

analysis. I like this activity

because students have

concrete examples in front of

them to help see properties of

different shapes. It also gives

the leader an added challenge

about their knowledge of

properties the mystery shape

has. They must be able to

identify if the shape does or

does not have the property

that the group members are

asking about. This is possibly

dipping into the second level

of van Hiele, informal

deduction.

10/28/09 True or

False?

Van de Walle, p.

416-417

A set of four or five

true or false

statements about

shapes that follow ―If

it is a _____,then it is

also a ____.,‖ ―All

____ are _____,‖ and

―Some _____ are

_____.‖ Ex: Some

parallelograms are

rectangles.

Students decide

which statements are

true or false and

provide reasoning for

why they think they

are right. Students

can also create their

own list and

challenge classmates.

Reasoning and

proof,

communication




This activity works for Level

2, informal deduction, of van

Hiele‘s model. I like this

because students reinforce (or

dispel) a theory they had

about a property of a shape.

They need to be able to

communicate proof of why

they are right. I think this

would be a good activity to

do in partners, because it

gives students a better chance

to effectively communicate

their idea.

13 “Carrie’s” Activity Diary Score and Comments

Name: ―Carrie‖



follows:


etc.)







Earned


Earned

Color Patterns 0.8 Who is Winning? 1

Turtle Pond 0.6 Zero, One-Half, or One 1

Poddle Weigh-In 0.8 Longer, Shorter, Same 1

Clock Wise 0.6 Tangram Areas 1

Real Counting On 0.8 Estimation Quickie 1 Five-Frame Tell-About 1 LCM Flash Cards 0.8 Counting in Groups 1 True or False? 1 Counting Rows of 10 0.8 What‘s my Shape? 1 Up and Down the Line 1 Mystery Definition 1

Finding Factors 1 Pattern Block Mirror

Symmetry 1

Final Score: 18.2/20

Comments:

10/28/09

Very good job. I was impressed with the van Hiele connections in the commentary section. You also made

relevant connections to the standards.

10/14/09

Your entries were adequate for the most part, but the descriptions of the activities leaned toward the brief side.

Still, all of the descriptions were clear with the exception of the ―LCM Flash Cards‖ activity. You wrote, ―With

these practice flash cards, students can learn automaticity of common LCMs in order to make solving fraction

problems faster.‖ This sounds great, but what exactly do the students do during this activity, though?

Remember, your descriptions should be clear enough that another teacher could read your description and know

exactly how to implement the activity.

9/30/09

Good. I appreciated how you provided a brief rationale for some of your process standard citations….as noted

in earlier comments (below), it is not always apparent that a particular process standard is present in an activity.

Your comments clarified this.

14 “Carrie’s” Activity Diary Score and Comments

9/16/09

Your descriptions of the activities are still on the brief side, but I felt that this week they were sufficiently clear.

You also did a nice job of connecting them to appropriate focal points.

Keep in mind the meaning of the ―Problem Solving‖ process standard: students are ―problem solving‖ if they

are presented with a situation for which the steps required to solve the problem are NOT known when they first

encounter the problem. Thus, it was inappropriate to list ―Problem Solving‖ as appropriate process standards

for ―Real Counting On‖ or ―Counting Rows of 10‖…both of these activities involved counting; thus, the

students would know exactly how to approach the situation from the outset. Granted, students‘ skills might not

be strong enough to get the correct answer every time, but they do know how to go about approaching the task.

9/2/09

You made some helpful comments in the ―Evaluation/Modification‖ section (e.g., pointing out that a game such

as Clock Wise is best suited for students‘ practice rather than for teachers‘ instruction), and you also

demonstrated a strong understanding of the Process Standards by citing appropriate standards for each activity.

The shortcomings of this submission which resulted in lost points are described below:

The descriptions of all four activities were far too brief. The activities should be described clearly

enough so that another educator (such as a substitute taking over you class for the day or a principal

going over your lesson plans to get a sense of what you are doing the classroom) can implement and

understand the activities themselves simply be reading your description. Your descriptions were too

short to serve this purpose…in the future, please be more descriptive, writing 5 or more sentences per

activity (as clarity demands) rather than 1 or 2. Additionally, with the exception of the Color Patterns

game, you did not indicate where on the web your games were found. Again, another teacher would

need this information if he or she were to implement the activity. Due to the shortcomings of the

descriptions, 0.2 points were deducted from each activity.

For the Color Patterns game, you cited a Focal Point that dealt with counting. I initially found that

unacceptable, but then you explained that you would have students count the colored circles in addition

to recognizing the pattern, so, because of that added explanation, the Focal Point you cited was

appropriate. However, for your future reference, note that there are additional ―sub-focal points‖

displayed in the right-hand column of the Focal Points document…you may cite these Focal Points as

well. So, for this Color Patterns game, the most appropriate Focal Point to cite would have been the

kindergarten ―sub-focal point‖ of Algebra: Children identify, duplicate, and extend simple number patterns and

sequential and growing patterns (e.g., patterns made with shapes) as preparation for creating rules that describe relationships.

Similarly, for the Turtle Pond game, the focal point you listed (dealing with addition and subtraction)

was simply unconnected to this activity. An appropriate focal point would have been the kindergarten

sub-focal point of Geometry: Children integrate their understandings of geometry, measurement, and number. For

example, they understand, discuss, and create simple navigational directions (e.g., “Walk forward 10 steps, turn right, and

walk forward 5 steps”). You might also have cited the ―main‖ 2nd

grade focal point of Measurement:

Developing an understanding of linear measurement and facility in measuring lengths. Either of these

would have been appropriate, but the adding/subtracting focal point was not.

15 “Bernie’s” Activity Diary [Average Quality]

Pre-Kindergarten

Name and Location

of Activity


Activity

Relevant

NCTM

Curricular

Focal Point

Relevant NCTM

Process Standard(s)


Modifications

DigiBlocks, in class

activity

Set of DigiBlocks Ideally each student would

have their own set of

blocks so they can explore.

The set comes apart and

can be broken down into

smaller pieces to show the

relationship of numbers. It

can work on counting and

early recognition of groups

of 10 and the bigger

picture. They are a useful

manipulative to have in the

class.

Developing

understandings of

number and

operations

involving

counting,

cardinality, and

comparison

representation DigiBlocks are a good way to help

students learn to organize numbers.

The arrangement of the pieces into

larger wholes can start to show the

students that there is a relationship. I

like how the cover will not close until

all ten pieces are put into the holder.

That can help students stay organized

.

Kindergarten

Name and Location of

Activity

Materials Needed Brief Description of Activity Relevant

NCTM

Curricular

Focal Point

Relevant

NCTM

Process

Standard(s)


Modifications

16 “Bernie’s” Activity Diary [Average Quality] Bar Graph Sorter:

http://www.shodor.org/interactiva

te/activities/BarGraphSorter/

computer The student first decides to make a

horizontal or vertical bar graph. They can

sort the graph by shapes or color. There are

4 types of shapes that need to be sorted into

the graph. The student will drag the shape

into the correct column and there is a tally

box that keeps track of how many shapes are

in a row. It visually shows a running tally of

the shapes on the side of the graph. This

activity can work on color recognition,

shape identification, and an introduction into

graphs.

Developing

understandings

of geometry

involving

shapes and

space. The

students are

able to identify

and describe a

variety of

shapes and

colors.

Problem

solving

representation

A modification for this

activity would be for the

shapes to be enlarged so the

shapes are easier to identify.

This would ensure that the

student knows what column

to drag the shape into. I think

that this activity is a good

introduction into graphs and

comparing and contrasting. It

could also be used as a review

to make sure the students

know their colors and basic

shapes.

Dot Plate Flash, P. 126 in Walle

Text

Paper plates, markers The teacher will make dot patterns on paper

plates ranging from numbers one to ten. The

teacher will hold up each plate for one to

three seconds and the students will figure

out how many appeared on the plate. There

are easy patterns, as well as some difficult

ones. This can be done as a whole class

(possibly incorporating a parachute) or with

partners on their own.

Developing an

understanding

of number

operations and

algebra by

identifying

patterns (such

as looks like a

dice)

Representation

connections

A modification for this

activity would be to use a big

parachute if there is a gym or

outside space available. The

students would count off

numbers five through eight.

The teacher would hold up a

pattern plate and whatever

number that was shown the

designated person would run

through the parachute to trade

places with another student.

This is a good way to

incorporate movement into

the counting activity.

Longer, Shorter, Same 20.1 on

page 378 in the 6th

Edition of the

Van De Walle text

Assortment of objects

that are shorter, longer,

and the same as a

specified object

The students will go to a station and have to

sort objects as longer, shorter, and the same

as a specified object. The specified object

can change at the different stations. Each

child will have their own objects to sort.

Developing an

understanding

of

measurement

and using

length to solve

problems

through

comparison.

Reasoning and

proof (are able to

see what they

sorted and can

actually measure

to see if the object

is in fact longer,

shorter or the

same)

Problem solving

(figuring out what

the objects are in

relation to others)

This activity provides the

students with a good visual

so they can gain a clearer

understanding of

measurement.


Grade 1


Activity


Activity

Relevant

NCTM

Curricular

Focal Point

Relevant NCTM

Process

Standard(s)


Modifications

Pattern Blocks-exploring shapes

http://arcytech.org/java/patterns/ computer Students can choose from

6 different shapes to place

all over a grid. The shapes

can be placed anywhere,

including inside/overlap

other shapes. Students can

rotate and flip shapes to

create designs and

identify the different

characteristics of each

colorful shape. There is a

broom icon that can be

clicked to clear the grid

and start again.

Developing

understandings of

geometry and

composing and

decomposing

geometric

shapes.

Reasoning and Proof

representation

This activity works well on the

computer but can also be hands on

with different shapes and a large

piece of grid paper. Students can

work in pairs to construct different

designs and shapes.

Groups of 10 Scavenger

Hunt, p. 193 Walle Text

Plastic bags, record

sheets, buttons,

beans, plastic chips

(or whatever type of

small objects you

want to use), pencil

The teacher will first put

the students in pairs. Then

you put bags with

counters around the room

(stations). Each pair have

a record sheet and a pencil

and move around to all

the stations to count the

counters in the bags

around the room, The

counters are grouped in as

many tens possible and

recorded in number word.

Grade 2

Name and Location

of Activity


Activity

Relevant

NCTM

Relevant NCTM

Process


Modifications


Curricular

Focal Point

Standard(s)

Learning to use money:

http://arcytech.org/java/

money/

computer There is a short story problem

involving money presented. In

order to solve it, one must drag the

appropriate bills and coins in the

designated blue box. There is an

assortment of dollar bills and coins.

Once the money is put in the box

there is a button to check if the

answer is correct or not. There are

different ability levels to choose

from as well. Some of the story

problems involved subtraction and

you have to envision yourself

almost as a cashier.

Developing

understanding

s of number

and operations

and algebra.

Problem solving

representation

The bills that are displayed are not

fully shown. Only the top left corner

of each different bill is visible. I

think the activity would be a lot

clearer if the entire bill was shown

so the student would have a better

visual representation of what the

answer should be.

Missing-Part

Subtraction, page 148

of the Van De Walle

text

Counters, piece of

tag board, paper

and pencil

The students will be paired up

and given set amount of

counters and a piece of tag

board. One student will separate

the counters into 2 piles and the

other student covers their eyes.

One of the piles is then covered

with the tag board and only one

pile of counters is showing. The

other child opens their eyes and

has to say the subtraction

sentence (___minus ___is

____,) The covered part is

shown and the addition and

subtraction equations are then

written down on the paper.

Developing

understanding

s of quick

recall of

addition facts

and related

subtraction

facts and

fluency with

multi-digit

addition and

subtraction

Problem solving

(figuring out how

many counters are

covered and

making a

subtraction

sentence)

Representation

Communication

(working with your

partner to figure out

the covered part)

I really like this activity

because it allows the students

to work together and problem

solve. The visual

representation of the

subtraction problem allows

the student to better

understand the concept of

subtraction. This is also a

game that can be played

during free-time, recess, and

even at home.

Incredible Expressions

15.4, page 262 of Van

De Walle 6th Edition

Paper, pencil,

chalkboard/whiteboar

d

Students work on writing addition

and subtraction expressions in a

calendar-time activity. For example

the student would be given a date

such October 28th

and have to write

expressions using any or all of the

operations that equal 28. Students

can get creative and build off their

classmates as well.

Developing

understandings of

recall of addition

and subtraction

facts. They are

also able to

develop and use

efficient methods

to add and

subtract numbers.

Reasoning and proof

Problem solving (trying

to find what numbers

would equal the initial

number and make

expressions)

This activity can allow the teacher

to get creative and choose relevant

dates like Halloween and

Thanksgiving and apply them to

math. This is a creative activity that

really gets the students thinking

about numbers and expressions.

19 “Bernie’s” Activity Diary [Average Quality] Patten Match, 15.9, page

269 of the 6th

Edition of

the Van De Walle text

Overhead projector, six

patterns with different

materials or pictures

The teacher will display a pattern

on the projector and the students

will learn to use an A, B, C method

of pattern reading. Half of the class

will close their eyes and the other

half will read the pattern. Then the

students with their eyes closed will

have to decide which pattern was

recited.

Developing an

understanding of

algebra and using

number patterns

to extend their

knowledge of

properties of

numbers and

operations

Communication

Representation

Problem solving (have

their eyes closed and

have to listen in order

to correctly choose the

pattern)

This is a good activity to involve the

entire class and work on listening

skills. This activity can prompt good

classroom discussion if there are

multiple patterns chosen by the

students.

Grade 3


Activity

Materials Needed Brief Description of Activity Relevant

NCTM

Curricular

Focal Point

Relevant

NCTM

Process

Standard(s)


Modifications

Kids and Cookies:

http://www.teacherlink.org/content/

math/interactive/flash/kidsandcookies

/kidcookie.php

computer First you pick 6 children to share

cookies with. Next you pick

chocolate or oatmeal cookies to

share and how many of each cookie

you want to begin with. Now you

must share the cookies equally

amongst all the children. There is a

cutting board and different sized

cookie cutters to help ensure that

each child has the same amount.

Developing

understandings

of number and

operations

involving

fractions and

equivalence.

Solving

problems using

models that

involve

comparison and

parts of wholes.

Problem

solving

Representation

Reasoning and

proof

This activity can be played

on the computer as well as

directly in front of you

using actual cookies or

dough. The cookies can be

a great manipulative that

will motivate the students

to really problem solve

and make equal parts.

Group the Counters, Find the

Name, page 310 of the Van De

Walle text

Set of counters in

2 different colors,

record sheet and

pencil

The students will start out with a

number of counters in two colors

and the total of both colors is the

whole. The students will need to

group the counters into different

fractional parts of the whole and

come up with fraction names for

both colors. The students can use

arrays and need to record their

groupings and explain how they got

to their answer on the paper.

Developing

understandings

of fractions and

fraction

equivalence and

gain an

understanding

that the size of a

fractional part is

relative to the

size of the

whole.

Representation

Reasoning and

proof (the

students must

record their

fractional parts

and explain how

they got to that

answer)

I think that this is a good

activity for each student to

do at their desk but I feel that

with only one teacher and

twenty something students it

would be hard for the teacher

to help everyone. I can

envision some students

falling behind and not

understanding so it may be

hard to ensure that all

students are learning to their

http://www.teacherlink.org/content/


fullest potential.

Correct Shares, page 297 of the

Van De Walle text

Examples of

shapes divided into

fractional parts

correctly and

incorrectly

I will show the students

examples of shapes that are

correctly and incorrectly divided

into fractional parts. The shapes

will vary in shape and length.

For each shape the students must

explain their reasoning of why

they thought it was or was not

divided into the requested

fractional parts.

Developing

understandings

of fractions

and fraction

equivalence

and

understand

how to use

models to

compare

fractions

Communication

(explain their

reasoning)

representation

I think that this activity

would be even more

effective if each student hade

blocks or some sort of shape

cut outs so they could have a

visual representation at their

desk. This can help them

better see the fractional parts

and really see if the shape is

correct or incorrect. Then

there can be one student who

can come up to the board to

show the class so everyone

cane check their answers.

What‘s My Shape?, page 415

of the 6th

Edition of the Van De

Walle text

A set of 2-D

shapes on paper,

half-sheets of

construction paper,

folders, glue

Students are split into groups, with a

leader who is in charge of the

secret-shape folder. The other

students must find the match that to

the shape in the folder by asking the

leader questions, in which he/she

can only answer with ―yes‖ or ―no‖.

The students must reduce the

possibilities from the shape pile and

test the final shape out when it is

narrowed down.

Developing

understandings

of geometry

and being able

to describe and

analyze the

properties of

2-D shapes

Communication

Problem solving

(not sure what

shape is in the

folder so you

have to guess by

describing

shapes to narrow

the possibilities

and must build

off of what the

leader responded

with a yes and no

I think that this is a good

activity that allows the

students to analyze and

describe the characteristics

of different 2-D shapes. It

also allows the students to

work as a group and use

proper communication in

order to solve the mystery

shape. This activity reminds

me of the children‘s game

Guess Who? , and you must

pay attention to the

responses and questions to

help limit the potential

possibilities.

Shape Sorts, page 409 of the 6th

Edition of the Van De Walle text

Sets of 2-D shapes Students work with a group and

have a set of 2-D shapes. In their

groups the students will choose a

shape and tell two things that are

interesting about their shape. Then

they each choose 2 shapes and find

something that is alike and different

about the shapes. Finally the

students will select one shape as a

Developing

understandings

of geometry

and describing

2-D shapes

Communication

(inform the

group about their

shape)

representation

This can be a good group

building activity and allow

students to share what they

think about different shapes.

Because there is no right or

wrong answer it can make

for easy involvement and

understanding of a variety of


group and find all the other shapes

that are alike. The shapes that relate

to the target shape must follow the

same properties, such as have a

curved side and a straight side.

shapes.

Grade 4

Name and Location

of Activity


Activity

Relevant

NCTM

Curricular

Focal Point

Relevant NCTM

Process Standard(s)


Modifications

Close ―Nice‖

Numbers, page 342 in

the 6th

Edition of Van

De Walle

Chalkboard and large

number line

I would first write a 4 digit

number on the board, such

as 3.0917, and ask if it was

closer to a whole number

like 3 or 4. I would

continue with tenths,

hundredths and

thousandths and challenge

the students to support

their answer by using the

large number line on the

board.

Developing

understandings of

decimals and

understanding the

connection

between fractions

and decimals

representation I think this activity would work

well if there was a large number

line on the board and the numbers

had magnets on them so there is a

good visual representation of the

decimal numbers. I think that the

students should also have a mini-

number line and numbers at their

desk so they can follow along.

This activity is a good way to

spark classroom discussion about

decimals and place value.

Grade 5

Name and Location

of Activity


Activity

Relevant NCTM

Curricular Focal

Point

Relevant

NCTM Process

Standard(s)


Modifications

Letter Multiplication,

example in class on

10/12/09

Paper and pencil The students will be given a

multiplication problem such

as:

Develop

understandings of

number and

Reasoning and

Proof

When we were discussing the

problem afterwards I enjoyed

hearing about the different


EF

X6

=FFF

The main goal of this problem

is to find the number that is

represented by EF. EF is

represented by two different

one-digit numbers and this

number multiplied by 6 must

equal FFF. FFF is a three digit

number.

operations and use

their

understandings of

division to

multiplication to be

able to use efficient

procedures to find

quotients using the

correct way.

Problem Solving strategies that one could go about

to find the answer. I think that it

would be beneficial for the

students to see that there is just

not one way to tackle a problem.

Students think in different ways

and I feel that is necessary for

everyone to acknowledge that.

Bottles and Volume

Graphs 15.20, pg. 288 of

the 6th

Edition of the Van

De Wall text

Pictures or actual

representation of 6

different bottles, and 6

graphs

The students will be shown 6

graphs and 6 bottles. It is assumed

that the bottles are filled at a

constant rate and the height of the

liquid in each of the bottles will

increase more slowly or more

quickly as the bottle becomes

wider or narrower. The students

must match up the graph to the

appropriate bottle.

Developing an

understanding of

geometry and

measurement by

selecting appropriate

strategies to measure

volume and solve the

problem

Problem solving

representation

Grade 7

Name and Location

of Activity


Activity

Relevant

NCTM

Curricular

Focal Point

Relevant NCTM

Process Standard(s)


Modifications

Discovering Pi, page

426 in the 6th Edition of

the Van De Walle text

Circular objects such as:

jar lids, tubes, cans, and

garbage cans, large

marked circles (on the

playground or gym),

rulers/yardsticks, string,

pencil, overhead to

make a scatter plot of

the data

Students will work in

groups to measure the

circumference and

diameter of many different

sized circles. Students will

use string to measure the

circumference and

diameter of circular objects

around the room such as

cans and lids. After the

students complete their

Developing

understandings

of measurement

and geometry by

investigating

similar objects.

They are

applying

proportionality

when using

Communication

(working with group to

measure objects: hold

the string, measure the

length, record the

length)

Representation (using

the objects‘ diameter

and circumference to

This can be a fun activity where

the students can get a chance to

get moving. Walking around the

room or school can be a good

integration of movement and all

the students to make more

connections. I think that the

students would really enjoy going

in to the gym or outside to

measure. It is a fun hands on


measuring the teacher will

collect the many

measurements from all the

groups and make a scatter

plot graph. The class will

then discuss the ratio and

slope of the line on the

graph.

circumference

and diameter of

a circle

help student‘s develop

an understanding that

pi is the ratio of

circumference to

diameter in any circle

activity, but still addresses the

main point of the developing a

greater geometric understanding.

24 “Bernie’s” Activity Diary Score and Comments Name: ―Bernie‖



follows:


etc.)







Earned


Earned Bar Graph Sorter 1 Correct Shares 1 Pattern Blocks 1 Close ―Nice‖ Numbers 0.8 Learning to use money 1 What‘s My Shape? 1 Kids and Cookies 1 Shape Sorts 1 DigiBlocks 1 Letter Multiplication 1 Dot Plate Flash 1 Discovering Pi 1 Groups of 10 Scavenger

Hunt 0.8 Longer, Shorter, Same 0.8

Tens, Ones, and Fingers 1 Incredible Expressions 1 Missing-Part Subtraction 1 Patten Match 0.8 Group the Counters 1 Bottles and Volume 1


Comments:

10/28/09

Very good job overall. Your completed diary has many worthwhile entries, and your latest entries were well

written for the most part. I did have two critiques of the latest entries, which are recorded below:

You listed Problem Solving as a process standard for ―Longer, Shorter, Same,‖ but this didn‘t seem to fit.

Problem solving refers to situations in which students do not know how to approach a problem (e.g., don‘t

know which steps to take) when they first encounter the problem. The approach to the ―Longer, Shorter, Same‖

activity seems pretty straightforward, though, since they have a ―specified object‖ to use for

measuring/comparing.

Part of your description of the ―Pattern Match‖ activity was unclear. You start by writing ―The teacher will

display a pattern on the projector.‖ [emphasis added], and then conclude by noting that the students with their

eyes closed ―would have to decide which pattern was recited.‖ The first phrase suggests that only one pattern

was shown, while the second phrase suggests that multiple patterns are displayed and children must determine

which one of many patterns was recited. There seems to be some missing information here.

10/14/09

Good…well-placed and well-written entries.

25 “Bernie’s” Activity Diary Score and Comments

9/30/09

Good job overall. You definitely listed your activities under appropriate grade bands and connected them to

appropriate curricular focal points. You also did a nice job of connecting them to the process standards,

providing helpful explanations in cases where a particular process standard was not obvious.

The description of ―Close ‗Nice‘ Numbers‖ was a bit confusing. You wrote, ―I would first write a 4 digit

number on the board, such as 3.0917,…‖ First off, that number has 5 digits, but that is a forgivable oversight.

What I found confusing is that later in the description you indicate that students should locate number such as

this on a number line. A number such as ―3.0197‖ would be impossible to pinpoint on a number line, unless it

was some weird number line which ―zoomed in‖ on values between 3.019 and 3.02.‖ Did you intend for

students to indicate roughly where the number appears on the number line?

9/16/09

Nice job once again. Your commentary in the ―Evaluation/Modification‖ section was particularly

thoughtful…you provide some good ideas regarding how each of the activities might be ―tweaked‖ to better

meet the needs of students.

I did deduct some points from the ―Groups of 10 Scavenger Hunt‖ because I didn‘t think that the Problem

Solving process standard should have been listed there. Recall that ―Problem Solving‖ means that students

should not know how to go about solving a problem when they first encounter it…that is, the steps to the

solution are not immediately known. For the ―Groups of 10‖ activity, however, students know that they are

supposed to divide the objects into groups of ten…it is essentially an exercise in counting, and students know

they are supposed to do this from the beginning.

9/2/09

Nice job. You clearly describe each of the activities, and make sensible connections to the NCTM process

standards and focal points. As you probably noticed, it isn‘t always an easy task to map these activities onto the

focal points. For example, with the ―Bar Graph Sorter,‖ I assumed that you would want to connect it to a Focal

Point dealing with organizing data into charts, but you connected it instead to a geometry focal point about

shape recognition. I might have deducted points here, but you clearly described in the activity description how

shape recognition factored into the activity.

26 “Alice’s” Activity Diary [High Quality]

Pre-Kindergarten

Name and Location

of Activity


Activity

Relevant

NCTM

Curricular

Focal Point

Relevant NCTM

Process Standard(s)


Modifications

―Longer, Shorter,

Same‖ Van De Walle

Text

Objects of varying

length, stations set up

at which the objects

are placed

Students will visit

different stations

around the room to

look at the length of

objects. There will be

a reference object at

some stations so that

the students can

compare the objects to

the reference object.

At the stations the

students will sort the

objects as longer,

shorter, or about the

same as a specified

object at the table.

Students can also sort

the objects by shortest

to longest.

Ordering

objects by

measurable

attributes

Problem Solving;

Reasoning and Proof

by setting up the bars

in a specific order;

Representation by

working with and

showing the correct

order from smallest

to largest

After working at the stations

maybe have the students come

up with different objects. This

could range from pencils and

pens to a school bus or a

building and as a class try and

order them from smallest to

largest. With the help and

planning of the teacher, have

the students pick a reference

object to compare the objects

they picked. This way the

students are making the activity

their own.

Kindergarten

Name and Location

of Activity

Materials

Needed

Brief Description of Activity Relevant

NCTM

Curricular

Focal Point

Relevant NCTM

Process

Standard(s)


Modifications

―Five Frame‖ NCTM

Illuminations site

Computer This game has four options to

practice counting by either

Representing,

comparing, and

Representation;

Problem Solving

Designate to the students which

genre you would like them to


playing to build, fill a five

frame, add or ask how many

when filling in a five frame

with circles. The students may

pick a particular genre, or

play all of them at once. The

students move the counters

and enter numbers to find the

correct solutions. When

students think they have the

right answer they click done,

when moving on to another

problem they are to click the

next button.

ordering whole

numbers and

joining and

separating sets.

focus on for the day, otherwise

they may do the wrong activity

and not understand.

Counting On with

Counters, Van de

Walle Text

Counters, Cup Each child is given 10 or 12

small counters, and they line

them up on their desk. Then

tell the kids to cover a certain

amount of counters or put

them in a cup. Have the

students point to their hand

and say how many are under

their hand, then have them

count on continuing from the

number that was under their

hand.

Representing,

comparing, and

ordering whole

numbers and

joining and

separating sets.

Problem Solving;

Representation of

having the

number that is

covered be the

number the

students are

starting off with,

and then the

counters help

them see how

they continue to

count on.

Make this activity into a game

that students can play with one

another. Have one student give

the other a number to cover and

count on from. This way the

activity seems more as a game

than as a task.

Grade 1

Name and Location

of Activity


Activity

Relevant

NCTM

Curricular

Focal Point

Relevant NCTM

Process Standard(s)


Modifications

―How Many Under the

Shell‖ NCTM

Computer Players will select if

they would like

Developing

understandings

Problem Solving Make the game more fun for

children by playing with a

28 “Alice’s” Activity Diary [High Quality] Illuminations site addition, subtraction

or both. The players

will then get a mix of

subtraction or addition

problems. The octopus

will take away or add

some shells, and will

ask the player, ―how

many under the

shell?‖ The player will

then enter the amount

into the keyboard to

check their answer.

of addition and

subtraction and

strategies for

basic addition

facts and

related

subtraction

facts.

partner either together, or

against one another to see how

gets the most problems right.

This could either be a

competitive or a helpful setting.

―Difference War‖,

Van De Walle Text

Cards, Counters Cards are dealt to the

students as they are to

play a regular game of

―war‖, with a pile of

counters prepared on

the side. The player

with the greater

number of dots wins,

and gets the number of

counters that is the

difference between the

two cards that were

played. The players

keep their cards until

the pile of counters

runs out, and the

winner is the player

with the most

counters.

Developing

understandings

of addition and

subtraction and

strategies for

basic addition

facts and

related

subtraction

facts.

Communication;

Representation by

using the counters to

show the difference

between the two

numbers on the cards.

After playing a hand of cards,

have the students further

explain why their number was

bigger, and go through the

process of the subtraction so

that each student knows why

won or lost the hand, and

develop a better understanding

of subtraction.

―Up and Down the

Line‖ Van De Walle

Text

Large number line on

the floor, eraser

In this activity have a

larger number line

either on the floor or

hanging on the

chalkboard tray in the

Developing

understandings

of addition and

subtraction and

strategies for

Problem Solving;

Communication;

Representation by

moving from one

number to another

This activity with the number

line on the floor involves

movement with the math action

so that students can understand

what it means to add or subtract


room. Have a student

walk on the number

line when it is on the

floor, or use the eraser

if it is on the

chalkboard. Talk to

the class about the

movement required for

addition and

subtraction equations.

This creates a mental

image for the meaning

of addition and

subtraction.

basic addition

facts and

related

subtraction

facts.

through the

mathematical action

a number. This will engage

them in the activity and further

enforce their learning. They

can take turns coming up to the

line and creating an equation

for the next student to do. After

each movement it will be

important to discuss why the

student moved that way and

what it means. I really like this

activity for showing the

meaning of addition and

subtraction.

Grade 2

Name and Location

of Activity


Activity

Relevant

NCTM

Curricular

Focal Point

Relevant NCTM

Process Standard(s)


Modifications

―Three Other Ways‖,

Van De Walle Text

Base-ten materials in

Hundreds, tens, and

ones

Students work

together in either

groups or pairs and are

given a number to

represent with their

number strips. Then

they have to find and

record three different

ways to show the same

number.

Developing an

Understanding

of the base-ten

numeration

system and

place-value

concepts

Representation;

Communication;

Problem Solving

In addition to having the

students simply record their

new findings, have them also

discuss and possibly write how

they came up with the new

strategies and what ideas that

had to find the new numbers.

―Base Ten Riddles‖,

Van De Walle Text

Pen, Paper, base-ten

materials

Students are given

riddles such as, ―I

have 23 ones and 4

tens. Who am I?‖ and

Developing an

understanding

of the base-ten

numeration

Representation;

Communication;

Problem Solving

Have the students be creative

with their new riddles and

possibly tell a story. This will

make the math for fun and


are to complete them

with a partner orally or

the partners can use

base ten blocks. After

the partners complete

a list of riddles they

are to then make up

their own riddles to

solve.

system and

place-value

concepts

interesting and integrate

different subjects together for

the activity.

Grade 3

Name and Location

of Activity


Activity

Relevant

NCTM

Curricular

Focal Point

Relevant NCTM

Process Standard(s)


Modifications

―Fractions-

Equivalent‖ The

National Library of

Virtual Manipulatives

Computer The student is given a

fraction and uses the

up and down areas to

create another

identical fraction to

the one presented. The

students can see how

the original fraction

can be changed into a

new and equivalent

fraction

Developing an

understanding

of fraction and

fraction

equivalences.

Problem Solving;

Representations

Have the students guess aloud

before changing the fraction.

Also have an accompanying

worksheet where students look

at how the new fractions

occurred, and what happened to

both the top and bottom

number in order to the new and

equivalent fraction to be

formed.

―Class Fractions‖ Van

De Walle Text

A group of six

students or more.

Have a group of six

students to use as a

whole for this activity.

Then ask the class and

the group what

fraction of the group

have blue shirts,

brown hair, are

wearing certain types

Developing an

understanding

of fraction and

fraction

equivalences.

Problem Solving;

Communication;

Representation of the

students wearing the

appropriate clothing

or trait named.

This is a great activity that

integrates movement of

students that could be used at

the beginning of a lesson.

Having the set of six students

act as a whole is interesting and

relevant to the class and will

grab their attention. For this

activity, you could go one step


of shoes. Be sure to

change the number of

students in the group

to practice more

fractions.

farther by asking the students

to create an equivalent fraction

to one that they came up with

when using the group of

students.

―What‘s My Shape‖

Van De Walle Text

A double set of 2-D

assorted shapes on

cardstock;

Folders

Have students in

group. In each group

assign one student to

be the leader and are

given a secret shape

folder. The others in

the group are to find a

shape that matches the

one in the folder. They

do this by asking yes

or no questions to the

leader. The leader may

only respond with a

yes or no. As they ask

questions the group

eliminates

possibilities. They

must ask questions

that pertain to the

properties of

characteristics of the

shape, and are not

allowed to ask, ―Is it

this one?‖ When the

students think they

have the right shape

they check it against

the one in the secret

folder.

Describing and

Analyzing

properties of

two-

dimensional

shapes.

Communication;

Problem Solving

This activity is great because it

allows students to talk about

the shapes and to test their

knowledge. They work together

to try and discover they correct

shape by asking the correct

questions. Through this activity

they are also learning how to

ask the correct questions and

go about discovering an

answer. I think one way to

modify this activity would be

to give the students a set

amount of time and number of

questions per shape. Then they

will narrow down which

questions work the best and

pertain more to the task at

hand.

―Open Sentences‖

Van De Walle Text

Whiteboard, Marker,

Students need pen and

paper

On a whiteboard or

chalkboard write open

numerical sentences

Developing an

understanding

of

Problem Solving;

Reasoning and Proof;

Representation if a

I think a way to modify this

activity would be to give the

students an option of working


on the board such as 5

+__ = 7. The students

are then to determine

what can be put into

the blank to make the

sentence true. Number

sentences can involve

addition, subtraction,

multiplication and

division. After they

have decided their

answer they are to

provide and

explanation of why the

answer was chosen.

multiplication

and division

strategies for

basic

multiplication

facts and

related division

facts.

manipulative was

used.

with a manipulative. For some

students this would be hard to

understand without seeing it

visually first. Using a

manipulative will allow them to

touch and physically move

around the numbers sentences

to see which number fits in the

missing blank. As students

progress, have them solve the

problems and then check their

answers with a manipulative.

Grade 4

Name and Location

of Activity


Activity

Relevant

NCTM

Curricular

Focal Point

Relevant NCTM

Process Standard(s)


Modifications

―Best Match‖- Van De

Walle Text

Whiteboard or

chalkboard, markers

or chalk.

Write in a scattered

arrangement a list of

five familiar fractions

and five decimals that

are close to the

fractions but are not

the same. Students are

then to pair the

fraction to the decimal

that it matches the best

with.

Developing

and

understanding

of decimals,

including

connections

between

fractions and

decimals.

Problem Solving;

Reasoning in Proof

when deciding which

fraction works best

with a certain

decimal

Have students show why there

is a connection between the

decimal and the fraction. It can

be a picture, or it can be an

algorithm but they have to

show why they picked the

certain pair to match up. Also,

students could work in pairs to

do this activity, and when

finished, think of fractions that

they know that have a decimal

equivalence.

―Rectangle A pair of rectangles Students are given a Developing Problem Solving; After the students have solved

33 “Alice’s” Activity Diary [High Quality] Comparison – Square

Units‖ Van De Walle

Text

that are the same or

close in area; model or

drawing of a single

square unit; ruler

pair of rectangles with

the same area or very

close in area. They are

also given a square

unit and a ruler that

can measure the

square unit. The

students cannot cut out

the rectangles but are

allowed to draw on

them. They are to use

their rules to figure out

whether the rectangles

are the same. To

explain their

conclusions the

students are allowed to

use a variety of

strategies such as

pictures, words, and

numbers. A pair of

rectangles would be:

4 x 10 and 5 x 8

5 x 10 and 7 x 7

and

understanding

of area and

determining

the area of

two-

dimensional

shapes.

Reasoning and Proof

by explaining their

conclusions;

Connections to what

they know about how

to use the square unit

and using

multiplication or

addition to find the

area

the specified rectangles, have

them create pairs of their own

that are either the same area or

close to the same areas. Have

the students work in groups to

brainstorm and discuss why

they chose those dimensions

and provide proof and

reasoning for why they are the

same or close to the same in

area. This way students get to

work with one another and

create their own math

problems.

―Area of a Triangle‖

Van De Walle Text

Two triangles drawn

on grid paper (No

right triangles)

Give students two

triangles that are

drawn on grid paper,

these triangles should

not be right triangles.

Challenge the students

to use their knowledge

of the area of a

parallelogram to find a

method that will work

for finding the area of

a triangle. They should

be able to use their

Developing

and

understanding

of area and

determining

the area of

two-

dimensional

shapes.

Problem Solving;

Connections to their

knowledge of the

area of a

parallelogram;

Reasoning and Proof

by showing that their

method works on

three different

triangles

I really like this activity

because it has students use their

previous knowledge to create

and discover something new. It

allows students a chance to

discover how to find the area of

a triangle rather being taught

by a teacher. By having the

students create a triangle on

their own to test is a great way

for them to test their

conclusions. One adaptation

that I would make is to have


method on the

triangles they were

given, as well as an

additional triangle that

they are to create.

the students work in pairs to

discuss how they came about

their conclusions and to share

answers. The pairs could also

create two different triangles,

one from each student to test

when the pair has their method.

Grade 5

Name and Location

of Activity


Activity

Relevant

NCTM

Curricular

Focal Point

Relevant NCTM

Process Standard(s)


Modifications

―Circle 3‖ – The

National Library of

Virtual Manipulatives

Computer Seven circles are set

up so that they are all

connected by two

others. Each circle has

a decimal number in

one of the three slots.

The player is to make

it so each circle adds

up to a total of three.

The numbers to use

are listed on the side,

and are in decimal

form. When the player

has the right amount,

the circle lights up to

show a correct answer.

The goal is to make

sure all circles add up

to three.

Developing an

understanding

of and fluency

with addition

and subtraction

of fractions and

decimals.

Problem Solving;

Reasoning and Proof

Have the teacher challenge the

kids to set the numbers in place

only once without moving them

to try and get the correct

amount. This will get students

to think ahead and plan what

numbers will go where, and

what will and will not work.

―The Broken Division

Key‖ Van De Walle

Text

Calculator Students work in

groups to find ways of

using a calculator to

Developing

and

understanding

Problem Solving;

Communication;

Reasoning and Proof

This activity will be beneficial

to students when practicing

different methods of how to


solve division

problems without

using the divide key.

The problems may be

put into a story context

and have a discussion

to follow solving the

problem to talk about

the different ways to

obtain the answer.

of and fluency

with the

division of

whole

numbers.

divide whole numbers.

Students may also be able to

make up some questions or

problems themselves to have

other classmates solve. The

students can then discuss and

compare or contrast the

methods that they went about

solving the problems.

―First Estimates‖ Van

De Walle Text

Mini Whiteboards,

Markers or Paper and

Pencil, Overhead

Tell students that they

will be estimating the

sum or difference of

two fractions. They

need to determine is

the answer will be

more or less than one.

Then, show a fraction

problem with either

addition or subtraction

for about 10 seconds.

Then have the students

write on their papers

or whiteboards

whether they think the

answer is more than

one or less than one.

Do a series of

problems and then go

back and discuss how

students estimated on

each of the problems.

Developing an

understanding

of and fluency

with addition

and subtraction

of fractions and

decimals.

Problem Solving;

Communication

when going back

through and

discussing how

students got their

responses.

This activity can be used at the

beginning of a lesson to warm

the kids up when they are about

to work with fractions. A

variation on this activity would

be to let the students work in

groups and pairs to determine

why they guessed the way they

did and to discuss what they

believe is to be the correct

answer. This will allow the kids

to think and expand their ideas

with their peers.

―Discovering Pi‖ Van

De Walle Text

Circular objects to

measure such as jar

lids, tubes, cans,

wastebaskets; Strings;

Rulers or Yard sticks;

Students work in

groups to measure the

circumference of the

circular items

presented in the class.

Describing

three-

dimensional

shapes and

analyzing their

Problem Solving;

Communication;

Representation by

measuring the objects

and showing the

I think that this activity is a

great way to have students

learn about pi. It gives them

concrete examples and they get

the chance to discover pi on


Pencil and Paper;

Computer

They wrap the string

around the outside of

the object, and then

measure the length of

the string. The

students will also find

the diameter of all the

objects and enter their

measurements into a

table. Then using a

program such as

Microsoft excel the

students will construct

a scatter plot with the

x axis representing the

diameter and the y

axis representing the

circumference. The

results should show

that the ratios would

range between 3.1 and

3.2. Then discuss that

the exact ratio is

3.14159, an irrational

number known as pi.

properties,

including

volume and

surface area.

information on the

chart;

Connections by using

math skills such as

making a graph and

using multiplication

and division;

Reasoning and Proof

their own rather than having it

be lectured to them. By

discovering the solution on

their own, they are more likely

to remember the information

and to be actively engaged in

the lesson. The students also

have the opportunity to use

skills they have previously

learned to do this problem.

They work on making charts

and graphs, measuring, and

using division and

multiplication.

Grade 6

Name and Location

of Activity


Activity

Relevant

NCTM

Curricular

Focal Point

Relevant NCTM

Process Standard(s)


Modifications

―Where does the

Decimal Go?

Multiplication‖ Van

Paper and a writing

utensil.

Have the students

compute a

multiplication problem

Developing

and

Understanding

Problem Solving;

Reasoning and Proof

by providing reasons

I think this is a great activity to

get students to understand

decimal placement with

37 “Alice’s” Activity Diary [High Quality] De Walle Text such as 24 x 63. Then

have them give

answers to the

following problems:

0.24 x 6.3

24 x 0.63

2.4 x 63

0.24 x 0.63

After each

computation the

students are to write a

reason for why and

where they put their

decimal points. After

finishing the

problems, they can

check their answers

with a calculator. If

the students found

errors they need to

acknowledge them and

explain how and why

they adjusted their

answer.

of and fluency

with

multiplication

and division of

fractions and

decimals.

why their answers are

right or why their

answers were

incorrect.

multiplication. I think that

having the students work with

their peers and talk about the

answers would further help

them understand why the

decimal is put in a certain

place. I think that if the

students worked in groups or

with another person that they

could discuss reasons and

compare answers to get even

more out of the activity.

38 “Alice’s” Activity Diary Score and Comments Name: ―Alice‖



follows:


etc.)







Earned


Earned

Five Frame 1 Best Match 1 How Many Under the

Shell 1 The Broken Division Key 1

Fractions-Equivalent 1 What‘s My Shape 1

Circle 3 1 First Estimates 1 Counting On with

Counters 1 Discovering Pi 0.8

Difference War 1 Where does the Decimal

Go? 1

Three Other Ways 1 Longer, Shorter, Same 1

Base Ten Riddles 1 Open Sentences 1 Up and Down the Line 1 Rectangle Comparison –

Square Units 1

Class Fractions 1 Area of a Triangle 1


Comments:

10/28/09

Your entire diary is very well done…your last four entries are no exception. You‘ve got a nice range of

activities, including activities you could use in middle school. I was particularly excited about your two area

activities this time. Both of them are great ways to get students thinking about what area actually is (e.g.,

hopefully steer them away from the all-too-common viewpoint that area is a collection of formulas).

10/14/09

Very thorough entries as usual.

Like last time, though, I think you‘re too quick to assign the Problem Solving process standard. Discovering Pi

is a rich activity and very useful to students, but it does have very clear cut directions for students to follow.

Students know what they need to measure and how they should record their results. There is no mystery

regarding how to approach this activity, so ―Problem Solving‖ is not a very good fit here.

9/30/09

39 “Alice’s” Activity Diary Score and Comments Good…this time you listed three activities (Class Fractions, Best Match, and The Broken Division Key) which

could potentially serve you well in middle school classrooms as well as elementary classrooms.

I thought you were a tad generous in listing the Problem Solving process standard in ―Class Fractions‖ and ―Up

and Down the Line.‖ I was likewise generous in my grading, because I chose not to deduct points here. But,

the instructions for both of these activities are fairly explicit….students should know ―what to do‖ as they

approach problems, even if they don‘t necessarily know the answers right away. Remember that this is a key

facet of ―Problem Solving,‖ that the path to the solution is not immediately apparent. I refrained from

deducting points, though, because I could imagine supplementary questions a teacher might ask which would

create problem solving situations. You hinted at something like this in the ―Evaluation/Modification‖ section as

well.

9/16/09

Good job once again. Your descriptions are concise yet clear, and are all connected to appropriate focal points

and process standards. I also appreciate that you explained why you listed certain process standards for certain

activities…the presence of these process standards was not always obvious to me.

9/2/09

Very good. This activity diary meets all of the expectations. You have described each of the activities clearly,

making it easy for another educator to understand what the activities are all about. You also have placed all of

the activities in appropriate grade levels, and connected them to appropriate process standards and focal points.

You have also provided some helpful additional commentary in the ―Evaluation/Modification‖ column,

providing useful suggestions for altering the games to meet the particular needs of students.

evidence of student learning in educ 364: activity...

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