brain on math handouts

7/29/2019 Brain on Math Handouts

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1. Reciprocal Teaching/Cooperative Learning

Bag a Problem: Each pair receives an envelope with a word problem

taped to the front. The pair solves the problem and places the solution

in the envelope. When a pair finishes, students find another pair that is

also finished and trade problems. When time is up, pairs open the

envelopes they have in front of them, take the solutions out, andcompare the strategies and solutions. Pairs may share the varied

solutions wit the class.

Think-Write-Pair Share: Ask students to first think about your question; after

a brief think time, ask students to write their answers (e.g., a list of items that

might weigh one pound or a list of polygons). Next, have students combine

their lists with their partners lists. Then provide time for some whole-class

sharing. Writing their own list of answer ensures that all students are engaged

in the task and allows you to monitor their thinking as you move throughout

the classroom. Writing makes their thinking visible! A few suggestions:

What ways could you make 15 cents? What did you learn about fractions today? What can you measure with a meter stick? When might you need to multiply?

Mix and Match: Students are given two sets of index cards: one with answers

and one with questions, or one with words and the other with definitions, orone with equations and the other with solutions. Students work with partners

to match the correct cards. (E.g. pentagon matches a polygon with five sides

and five angles 15 matches 11 +4).

Numbered Heads: Students are grouped in teams of four and are numbered

1,2,3, and 4. The teacher poses a question or problem for the teams to solve.

After work time, the teacher calls a number and that person must explain the

answer or solution to the class. Only students with that number can respond

and earn points for their team. The technique can be uses as a review session

in which teams coach each other to learn material. This technique promotes

collaboration and peer tutoring because team members recognize that all of

them must understand the solution since they do not know who will be chosen

to report for their group.


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Student Questioning:

What are you doing now? Why? Do you know what ___________ is? How did you get ______? Whats the problem asking us to find out? How do you know the answer is correct? How do you explain that? Did you do it differently than me? How did you use that formula? Is there an easier way? Could you draw me a picture to show ____________? How did you get your answer?

Teacher Questioning:

Will Allisons plan work? Do you agree with Jason? Can you summarize what we learned? What are the key ideas? What do you think the answer would be if ________?


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2. Story Telling

Show It: Use manipulatives during demonstrations to provide a visual as you

explain ideas. There are a wide variety of transparent manipulatives that are

perfect for demonstrations on an overhead project. Having them organized and

close to the projector so that they are available for spontaneous

demonstrations is important.

Slow It Down: Allow sufficient wait time (3-5 seconds) after asking questions.

The quality of answers improves and the quantity of students who respond

increases with proper wait time. Be willing to wait for students to formulate

ideas and give them time to finish their thoughts before commenting.

Create Math Story Problems: After reading a literature story, students write

and/or act out math problems tied to the story.

Identify the math Ask the students to put themselves in the positionof the character in the story: What math did the character need to

know? Why?

Act out the story using manipulatives:o Grandfather Tangs Storyby Ann Tomperto Monster Mathby Grace Maccaroneo Alexander Who Used to Be Rich Last Sundayby Judith Viorst

Pose comprehension questions: Continue the investigation:

o Using the stories theme, present students with an investigationto further explore it.

McSquares and the McTrianglesby Marilyn Burns Write a similar story and act it out.


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3. Metaphor/Analogy

Analogies: Simple analogies challenge students to test their thinking.

Posing some analogies and then asking them to discuss their answers with a

partner will give students opportunities to talk about the connections

between words and the subtleties of word meanings.

Addition is to sum as subtraction is to ________________. Five is to pentagon as ________ is to octagon. Inch is to mile as _______ is to kilometer. Degree is to temperature as pound is to ___________.

Use Metaphor to Understand Large Numbers

Draw a line approximately 4 inches long.o Label the left end of the line one million.o Label the right end of the line one trillion.o Mark a mark on the line indicating where 6 billion, 200 million

would fall.

o Give students the following metaphor: If we had 10,000dollar bills and we stacked them one million dollars =

approximately 4 inches. One billion dollars = 300 feet or

about 1 block; One trillion dollars = 63 miles.


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4. Simulations/Role Playing

Body Counts:

As students develop number sense, an important building block is for students

to understand the relative magnitude of numbers. In Body Counts students

use their bodies to express the size of different numbers. This uses many of

their learning modalities, including kinesthetic, auditory, and visual toreinforce learning.

Probability Ties:

Students use situations from the real world and stories/movies to explore

probability on a number line from 0 to 1.

Prior to the lesson, on a large sheets of paper write

the following, one per page:

- 0

- 1

- A tossed penny will land on tails.

- You have type D blood.

- It will rain in Kansas today.

- The average (mean) age in this room is ___.

- A card drawn from a deck is a heart.

- You will live to be 100 years old.

- You will miss a day of school this year.

- The sun will rise in the east tomorrow.- People will eat turkey on Thanksgiving.

Adding On a Number Line:

Students develop the concept of adding and subtracting using a number line.

Once students have a firm understanding of adding and subtracting positive

numbers, older students can experience adding and subtracting integer

numbers. The key is to remember that negative is the opposite of positive.

Yarn Shapes:During this cooperative group exploration, teams of 4 - 6 students use a

concrete object, a piece of string, to explore characteristics and properties of

two-dimensional geometric shapes by making with string the geometric figure

suggested by the teacher. Although naming shapes is important, it is even


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more important for students to observe the characteristics of these shapes.

These attributes should include:

- the number of sides and vertices (corners)

- parallel sides, equal or not equal sides.

Step Right Up:

Give students a set of ordered pairs to represent. When given a card, student

steps right, then up to represent the location of the ordered pair. Give

students many opportunities to practice the physical movement.


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5. Reflect/Write/Review

Word Splash:

After reading a prompt to the class, such as We have been studying geometric

shapes, what are some vocabulary words we have learned?, ask students to

suggest some words that might appear in their written response. Record a few

vocabulary words on the board. As students construct their written responses,they can use the words splashed on the board. This technique helps

students focus on the key vocabulary as they develop their responses.

Is He Right?:

Teacher creates problems in which the answer of a student is also given. The

students goal is to justify/disprove the students answer. This can be done in

writing or in presentation.

Convince Me:

Many times students are asked to justify their math solutions. In doing so,

they must come up with supporting information, math data and or logical

reasoning to prove the correctness of their answers of their thought processes.

Justifications should convince the reader that the answer is correct or that the

method is appropriate. Pose problems for students to solve and ask them to

convince you of their answers. There are tremendous benefits to doing this

orally because all students are able to hear your comments as you ask for more

detail. What is the correct answer to this problem? Convince me! Which is greater 2 feet or 2/3 of a yard? Convince me! Which is greater: the number of sides on a hexagon or the number of

angles on a pentagon? Convince me!

Which is the best buy: 5 CDs for $25, 3 CDs for $10, or 10 CDs for$43? Convince me!

Pinch Cards:

All-pupil review technique in which each student is given and index card that

displays grade-level appropriate operation signs, ABCD, 1234, etc. The teacher

poses a word problem and students pinch the part of the card that indicates

the operation that should be used to solve the problem. This process provides

teachers with a quick check on students understanding.


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Writing Tasks:

Illustrate (and label) a Problem or Concept:

Draw more than 3 kites. Write the number to show how many are inyour picture.

Draw a picture to show 12 + 5 = 17 Illustrate area and perimeter. Draw a picture to show the difference between 3 tens and three

tenths.

Give Examples/Make Lists:

List numbers that are less than 1,000 List things you could measure with a ruler. Give examples of times when you might need to know how to count

money.

List things that are packaged in a cylinder. Make a list of things about 5 cm long.

Write a Word Problem:

Write a story to go with this picture (choose from pictures in a piece ofliterature, a newspaper, or a magazine)

Write a problem that can be solved using this equation: 4 x 12 = 48 Write a problem that can be solved using multiplication.

Predict/Estimate an Answer or Outcome:

Predict how many paper clips will fit from one end to the other end ofyour desk. Why did you predict that number?

Estimate the average (mean) age of children who are 9, 11, 12, 16,and 17. Explain your estimate.

Predict the most frequently used letter of the alphabet. Explain yourprediction.

Describe/Define:

Describe how to find the area of a triangle. What is a pattern? What is surface area?

Explain a Process:

Explain how to tell time. Imagine you are buying new carpeting for your room. Explain how

you will figure out how much carpeting to buy.

Compare/Contrast Concepts, Processes, or Solutions:


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How are fractions and decimals alike? How are they different? Compare/contrast a square and a triangle. How are a penny and a nickel alike? How are the different?

Justify a Process or Solution:

Would a dog be 2 feet tall or 20 feet tall? Justify your answer. Why is repeated subtraction another name for division? Why do we need 0 in the number system? Which problem-solving strategy did you use to solve this problem?

Why did you choose this strategy?

Reflect on Learning:

What was difficult/easy about todays activity? During todays math lesson, I felt What can you do today that you couldnt do yesterday? Today I made this mistake I learned


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6. Rhythm, Rhyme, Music and Rap

Buzz:

This multiplication activity is played aloud with the whole class or in a small

group. The teacher states a number and students begin to count off, each

saying one number; however, they cannot say any number that is a multiple of

the number stated by the teacher. When there is a multiple, the student mustsay buzz (E.g. 1, 2, buzz, 4, 5, buzz, etc.) Students continue in a round robin

format.

Bizz Buzz:

When students are getting proficient at Buzz, the teacher adds another

multiple and students must say bizz for that one. If the number is a

multiple of both, the student would say bizz, buzz.

Writing Music:

There are several patterns in music. In Writing Musicwe use those patterns

to explore, extend, and identify repeating patterns. Students use their own

creative minds to create music that can then be played using musical

instruments.

Ron Brown Math Songs:

http://www.songsforteaching.com/mathsongs.htm

Play appropriate classical, jazz, or another type of calming music as

participants enter the classroom.

Participants march around the room to high-energy, fast-paced music. When

the music stops, each participant recalls one major concept covered in the

minilecture and discusses it with the person standing in close proximity.


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8. Projects and Problem-Based Learning

The Toothpick Problem:

Give each pair of students four toothpicks. Students determine all the different

ways the four toothpicks can be put together. The criteria is that any angles

are right angles and that toothpicks must touch end to end.

2. Give students ample amount of time to find the 16 different ways. Students

record on dot paper all the solutions, one solution per grid.

Group Projects:

http://www.wested.org/pblnet/other_gp.html

http://ozpk.tripod.com/pbl.html

http://web.mac.com/khoneycuttessdack/Kevin/21st_Century_Collabora

tive_Projects.html

http://www.kidshealth.org/kid/feeling/school/group_projects.html

http://kids.discovery.com/

http://www.sustainableliving.com.au/getinvolved/pastwinners

http://www.lhup.edu/dtyson/math_group_project.htm

The Diversity of Cultures in the United States and the Presence of Media

Forces

The project was designed to help students think critically about media,

understand the relationship between media and culture, and identify thecharacteristics of subcultures.

How do members of a given subculture find meaning in life? What are

their values and fears? Given that knowledge, how could government

policy-makers, the media, and advertisers successfully manipulate the

subculture?

Real World Geometry

This is a different way of investigating math - not just with numbers and

facts, but by creating an imaginative, informative, interactive geometry

journal that will give students a new appreciation for the fascinating and

innumerable applications of geometry in the world around them.


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Addresses 7th - 8th grade standards in Geometry, Language Arts, Visual

Arts, Social Science, and Technology.

Student Information CatalogA small hall catalog listing each individual's major, interests, and

personal data may be used to involved the withdrawn or shy students in

hall programs.

"Design a Museum" at your school

This is a favorite activity in many schools that combines research,

history, social studies, and the arts, as well as involving a major public

exhibition element. A particular school-wide theme may be selected for

the year, thus enabling participation across different classes and grades.

This project may be combined with a local history fair, folktales, art,

archeology, dinosaurs, technology, or many other topics.

The Up to Par Project

Students work in groups to design a hold for a miniature golf course. Eachhold had to allow for a hole-in-one, which was constructed using a compass

and the law of reflection. This project takes a hands-on approach to learning by

having students experiment with a ball bouncing off of a wall, make

observations about the rebound of the ball, and formulate a conclusion about

the angle at which the ball leaves.

How can we design a miniature golf course and construct the path for a

hole-in-one using reflections and angle measurements?


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Visuals/Graphic Organizers

Vocabulary Posters (Math Wall):

Students are each assigned a vocabulary word. They are to design aposter using the following guidelines:

o 1. All posters must be done in color no pencil or blue ink.o 2. The vocabulary word must appear correctly spelled on the

front of the poster.

o 3. The dictionary definition of the word may NOT be directlystated on the poster.

o 4. Characters on the poster may be conversing, giving anindirect definition.

o 5. Computer drawings or artwork may be used as well asmagazine and newspaper clippings.

o 6. Posters will be presented orally in front of the class.Word Webs:

In this easy to implement activity, students work in pairs of groups to

brainstorm and record words related to a math term. For example the key

word may be measurement. Younger students might add feet, yards, miles,

pounds, ruler, scale and measuring cup. Older students might add volume,

linear, thermometer, etc. Student then make a word web using the words they

created by grouping and categorizing them.

Word Boxes (Frayer Model):

Students fold a piece of paper into four sections. Label each section: My

definition, A real-world use, An illustration of what it is, and What it is NOT.

Perceptual Judgment Measurement Tasks:

Worthwhile measurement tasks:

Indirect Comparisons: (optical illusions)

Measuring Out: (when you cant imagine what that measurement looks like)

Recipes or constructions (sewing/building)

Broken ruler measurements

Created Rulers used to make objects (giant inch)

Manipulatives (Squares on a Geoboard)

Worthwhile Tasks (tennis can task, wheelchair ramp, measurement

olympics)


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Scale Relationships (student in a doorway, designing a vacation)

Vocabulary Practice (Mental Models, Graphic Organizers)

Derived Formulas

This website is a paid subscription site.http://www.enchantedlearning.com/graphicorganizers/math/


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9. Mnemonics

Mnemonic instruction is a set of strategies designed to help students improve

their memory of new information. It also links new information to prior

knowledge through the use of visual and/or acoustic cues. These strategies

have been proven effective with students at a wide range of ability levels and at

all grade levels. Mnemonics are particularly helpful in teaching students withdifficulties who have difficult recalling verbal and content-area information, as

they are effective with any type of verbal content.

3 Basic Types:

Keyword A keyword is a familiar word that sounds similar to the word or idea

being taught.

Dont Be Mean Fair Share Median Mode most

Pegword Refers to a set of rhyming words that are used to represent

numbers. Helpful when using information that needs to be in a certain order.

Peg Word System to link and recall items in sequential order.

Letter Letter strategies include acronyms and acrostics.

Please Excuse My Dear Aunt SallyWork in groups to create their own acronyms and acrostics, which will assist

them in recalling course content.


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10. Hands-On Activities 11/23/09 5:57 PM

http://michellef.essdack.org/?q=node/6

Just Say No To Worksheets by Michelle Flaming

Be Prepared:Organize group baskets or plastic bags with all the necessary supplies for

the activity. Assign a student in each group to pick up the basket or bag for

the group. This student will also be responsible for returning the materials

to a central classroom location after the activity and may be asked to

inventory materials to be sure all have been returned.

Have a Signal:

Have a zero-noise signal (e.g. the flickering of classroom lights, a clapping

pattern, and odd noise) to quiet students temporarily in case whole-class

discussions or further directions are needed.

Guard Against Mix Ups:

Distribute materials so that students next to each other have different

colors.

Institute a Class Clean Up:

Spend a few minutes at the end of that task having students help putmanipulatives back in proper order for the next use.

Organize It:

Find a system to organize your classroom or school manipulatives so that

they are readily available. Classroom teachers often store manipulatives in

clear plastic bins or clear plastic bags so that the contents can be seen

easily. Small pieces can be stored in tool or sewing boxes that have small

compartments.

Sticky Notes:

Following manipulative tasks, many teachers jot down observations and

ideas regarding manipulative use to guide the next manipulative

investigations. Placing reminder sticky notes in your plan book, teachers


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manual, or manipulative bags or containers will help you remember key

management or activity ideas next time the manipulative is used.


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11. Brainstorming and Discussion

Exploring Ideas:

Conduct a class session with the major purpose of exploring ideas related to

a course topic or having participants offer input into the course objectives

and strategies for implementation. Students come prepared to generate

questions for discussion prior to teacher or participate in dialogue related tothe topic.

Multiple Answers:

Participants are given a question to which there may be multiple answers.

They participate in a brainstorming session generating the multiple ideas.

Class Assignment:

Students work in groups to explain their answers to a class assignment as

well as the method by which their answers derived. When answers very,

students defend their answers until convinced to change them.

Seasonal Partners:

Students make dates with seasonal partners in the classroom; one date for

each season of the year, winter, spring, summer, and fall. At four

appropriate times during the class, partners discuss pertinent course content

with a seasonal partner.

Two Minutes And Counting:

Students are given two minutes to brainstorm as many concepts as they can

remember from a previous class session. They then compare their list with

the list of one of their classmates. Each student receives one point for every

concept recalled that is not on their partners list.


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12. Drawing and Artwork

1/4 x 1/3 =

3 1/2 divided by 3/8 =


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Singapore Math


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13. Fieldtrips


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14. Games


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15. Technology

Computer Resources:

Math Links from my page

http://michellef.essdack.org/?q=links

http://del.icio.us/michellemath

BAIP

http://baip2.elearndesign.org/

Quick and Easy Calculator Activities:

Counting Up or Back:

Have students practice their counting skills by counting forward or backward

from a designated number. Have them record their guess for the next

number and then use the calculator to check the guess. For example:

Start at 24, count by tens. Start at 4,678, count backwards by hundreds.

Mystery Numbers:

To work on patterning and number sense, have students skip-count using

the constant function on the calculator and try to find the mystery number.

Skip count by 30s I am between 130 and 160. My tens digit is 5 Skip count by 300s. I am greater than 4400. I am less than 5000. My hundreds digit is 5.


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16. Maximizing Parent Involvement

Interactive Open House

Parents can be engaged in playing games to review basic facts or use

geoboards or other manipulatives. The activities will be fun and may give

them insight into ways they might work with their children at home.

Family Game Night

Read Math Send home a list of childrens books that support the math

ideas being explored in class. Encourage parents to read with their children

and then discuss the math from the story.

Math Backpacks Develop some take-home kits for students to check out

for parent-child use. Backpacks should contain materials and directions for

a hands-on activity. They might contain a small clock with moveable hands

and some cards with various times for students to show on the clock, or a

ruler and a list of items to estimate and then measure.

Math Interviews Involve students in talking to their parents about the

math they use each day at home and at work. Parents may be surprised at

the many ways they use math, and students will gain insights into the

applicability of the math they are learning.

Math Websites for Parents See technology strategy


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17. Problem Solving As the Focus of Math Instruction

At the fair, there are 36 children in line to ride the roller coaster. The roller

coaster has 10 cars. Each car holds 4 children. How many children can sit 3

to a car, and how many have to sit 4 to a car? Solve in two different ways.


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Personalize Your Problems

CGI is a GREAT strategy for this approachUse real data from newspaper, travel brochures, menus, etc.Do Fewer Problems

Assign fewer problems, but conduct thoughtful discussions. Morediscussion and reflection time is the key to developing problem

solving skills. With less problems to do, students have

opportunities to slow down, think through the situation, discuss

options, and evaluate their thinking.

Problem of the Week

o Assign a problem of the week (POW). On Monday, review theproblem and discuss necessary directions. Throughout the

week students can work on the problem as they have time.

On Friday, the class engages in discussion of the POW with

students sharing various methods. You might chart the

different ways that students solved the problem.


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18. Singapore Math

8 Step Model Drawing

1. Read the entire problem

2. Decide who is involved in the problem.

3. Decide what is involved in the problem.4. Draw unit bars of equal length.

5. Read each sentence, one at a time.

6. Put the question mark in place.

7. Work computation to the side or underneath

8. Answer the question in a complete sentence

Addition Guided Practice:

Kate read 2 books. She also read 3 magazines. How many books and

magazines did she read altogether?

Alicia had $6 more than Bobby. If Bobby had $10, how much did they have

altogether?


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Try one on your Own:

On Friday night my family picked 8 pumpkins. On Saturday we picked 12

more pumpkins. How many pumpkins did our family pick in those two days?

Subtraction Guided Practice:

Mia had 14 baseball cards. She gave 5 away and kept the rest for herself.

How many cards did Mia have left for herself?


Christine has $24 in her piggy bank. If she spends $8 on a gift, how much

money will she have left in her piggy bank?

Multiplication Guided Practice:


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Joe has 3 plates of cupcakes. There are 4 cupcakes on each plate. How

many cupcakes does Joe have?


At lunch recess Karen passed out 3 times as many cookies as Vito did. If

Vito passed out 35 cookies, how many cookies did they pass out altogether?

Guided Practice:

Pedro purchased 5 shirts and 3 pairs of pants at the department store. All

the shirts were the same price, and each pair of pants cost $1.20 more than

each shirt. If Pedro spent $163.60 on all of the shirts and pants, how much

did each shirt cost?


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11/23/09 5:57 PM

brain on math handouts

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