Math Integers: Give Me a Clue

March 11, 2009

TITLE: Math Integers

GRADE: 6 – 8

MATERIALS/TIME REQUIRED:  Prepared clue cards – make your own or contact us for prepared examples.  20 minutes

PROVIDE FOR INCLUSION – A You Question, Energizer, or Linking Strategy:


Content Standard: Develop meaning for integers and represent and compare quantities with them.

Collaborative: Solve problems, participate fully, work on tasks together

Personal: Practice cooperation and tolerance

IDENTIFY THE STRATEGY: Give Me a Clue – contact us for prepared expamples.  p.255 Tribes… p. 276 Discovering Gifts… p. 358 Engaging All…High School…

Students use clues to determine the integer, or sum or difference or product or dividend…

Use the prepared materials (contact us) or prepare you own (clues can even be orally given); then have students develop their own and exchange between partners.


Content: What is most confusing about integers?

How does a number line help decipher the clues? What do you know now that you didn’t know before? Which was easier, solving the clues or making your own? Why?

Collaborative: What role did you play in your group?

Personal: What was your level of participation?

PROVIDE AN OPPORTUNITY FOR APPRECIATION: Invite statements among pairs or groups

AUTHENTIC ASSESSMENT: Students develop own clues and solve one another’s. Have each pair hand in their best effort. (Give extra credit points for any student who can stump the teacher?)


· Group Development Process

►Cognitive Theory

· Multiple Intelligences

►Cooperative Learning


· Reflective Practice

· Authentic Assessment


1. Use problems or equations and develop clues.

2. Have students, in pairs or groups develop clues in a “round table”, each simultaneously developing a following clue that makes sense, or use a “placemat” design where each student write a set of clues and the “placemat” rotates so that each in the group can assess and solve. (Grade 6 and higher)

3. Use only numbers for clues. (Example: Instead of ‘greater than 76’, write >76 – or instead of ‘greater than 76, write >(4×19)

Math – fractions: People Hunt

March 11, 2009

TITLE: Math fractions


MATERIALS/TIME REQUIRED: Fraction Hunt reproducible – contact us if you want this!  25 minutes

PROVIDE FOR INCLUSION – A You Question, Energizer, or Linking Strategy:

Ask: How many of you think fractions can be fun?

(Assure them that they will like something about this strategy, and put students in groups of four, no more. If there are groups of three, then students will have the opportunity to imagine a fourth member, as well as his/her answers.


Content Standard: Students will explain different interpretations of fractions and explain equivalents of fractions.

Collaborative: Students will work on tasks together, participate fully, and value diversity.

Personal: Students will reflect on personal strengths / skills.


Students are in groups of four. (If in groups of three, then take turns making the imaginary fourth person’s answers.)

For each statement, the group has a brief conversation and writes the answer asa fraction.

The denominator will always be. . .?

It is possible to have a fraction of 0/4.

Do NOT reduce any fractions…that comes later!

EXAMPLE: Model these for the whole class before they begin the group fraction hunt.

___ I like playing computer games.

___ I’ve never been on an airplane.

___ I would rather listen to my music than watch TV.

(When your answer is “sometimes”, count that as a “YES”)


Have students begin. When finished, have them:

Cross out all fractions that can be reduced, and write the reduced fraction next to what you crossed out.

Choose an answer of ¾ and make it a fraction with a denominator of 12 and write a sentence at the bottom of your page that explains how you did that.

Is this correct? 2/4 = 15/30  Explain why, on the back of the page.

Check for understanding.

Review agreements.

Pass out the “Fraction Hunt” handout and have students begin.


Content: How did this activity make fractions easy to understand?

What was difficult? How could you make it more difficult?

Collaborative: Describe how you worked together to answer the statements.

Personal: The objective was for you (students) to get to know one another better while

practicing or learning fractions. Explain how it worked for you.

PROVIDE AN OPPORTUNITY FOR APPRECIATION: Invite statements that address the experience (You stated earlier that you had a way to make fractions fun?! Invite statements that acknowledge positive practices, behavior, students.

AUTHENTIC ASSESSMENT: Tell students you are going to choose any fraction that has been reduced, a fraction changed to a denominator of 12, and the two explanation statements (that must be sentences). Allow them to check their work, and collect.


►Group Development Process

· Cognitive Theory

· Multiple Intelligences

►Cooperative Learning

· Constructivism

· Reflective Practice

· Authentic Assessment

Fraction Hunt

Extend/Modify: Have students add, subtract, multiply or divide fractions, either within their groups or by sharing with other groups.

Examples: Add your fractions for #2 and #6. Reduce.


Multiply #3 and #10, then subtract #4.

Note: Less can be more! If you are extending, have students complete only one or two of your problems; then have them make up their own. Be sure to have students designate an area on their paper which is easy for them to write in and you to find for evaluation/assessment. Be very clear about your expectations for learning.

Persuasive writing understanding through M.I.

November 20, 2008


5 – 8


poster paper, 50 – 75 minutes

PROVIDE FOR INCLUSION – A You Question, Energizer, or Linking Strategy:

  • Initiate student groups of 4 or 5.  Use a grouping strategy, or have a plan for random group membership; do not make the mistake of allowing students to group themselves, unless they have had frequent opportunities to work with anyone and everyone in the class.
  • Review class rules or expectations or agreements for expected behavior.
  • Have students share with one another:  What is something that you might need to persuade your parents to do…or let you do?


Content Standard: Understand how to write a persuasive composition.

Collaborative: Reflect on experience, think constructively

Personal: Develop personal strengths, explore challenges


IDENTIFY THE STRATEGY: Circular Curriculum (from the Artistry for Learning)

Use Direct Instruction to teach/review the components and steps for writing an effective persuasive paragraph or essay.

Students should be familiar with Multiple Intelligence theory, as well as their own Multiple Intelligence inventory results.

The task is for students in each group to collectively create a poster with all Intelligences represented.  Students can work together on different aspects, or take individual accountability and each contribute his/her own representation.  Students sign their name to the elements of the poster to which they contributed.  I may be helpful to require that students work on at least three different intelligences; they may work in pairs within the group. Be sure to have students sign their names to the appropriate parts (intelligences) represented on the poster.

*After students have success both with the group effort, and with exploring and developing multiple intelligences, you can use the circular curriculum for individual works (utilizing three or more intelligences).

Here is a suggested example of demonstrations of understanding, based on the multiple intelligences (also the student handout):



Logical/Mathematical: Make a timeline of steps, events leading up to convincing someone to try a new type of vegetable.

Linguistic/Verbal: Write a letter to a lawmaker, convincing him/her to lower the driving age to ____.

Musical/Rhythmic: Write a rap that outlines the components of a persuasive argument or develop a rhyme that has a beat to which one can recite the components of a persuasive argument.

Verbal/Spatial: Create a 4 – 6 frame comic strip that portrays a persuasive interaction.

Body/Kinesthetic: Role play a good persuasive argument and an ineffective persuasive argument.

Intrapersonal: Choose a real or hypothetical situation and write (or act out) your feelings of effectual or ineffectual persuasiveness

Interpersonal (Really, intra and inter-personal rely on and/or incorporate the other intelligences): Something like a sequence, where each person takes a step or provides an example…or just the fact that two or more people work on the task together…and take responsibility for presenting as a team/tribe

Naturalist: Choose two objects from nature that do not grow, interact, depend, etc. on one another…or one from nature and one that is man-made, and develop a scenario (written, acted, etc.) where one convinces the other or its importance and/or superiority.


Content: How did you choose your “intelligence” entries…based on your strengths, or based on your challenges? How was this demonstration of understanding more or less demanding than the traditional or usual summary or book report?

Collaborative: What did you enjoy about being able to work with someone else on any part of this project? How did you handle any disagreement?

Personal: Why is it important to recognize multiple intelligences? How can this influence you…in anything in life?


Invite statements after each presentation…or, if possible, use the strategy “Gallery Walk” to share and appreciate. Have students write to you (teacher) what they liked about this “demonstration of learning” experience.



Have students develop a rubric (they will need some experience here) and grade their own work (really helps if they view each others work first). Eventually, students can actually make up the specific “intelligence” suggestions and develop their own responses. (I actually got to the point where I could say “Give me three examples, using three different multiple intelligences, that demonstrates your knowledge of_____.”)



  • Group Development Process
  • Multiple Intelligences
  • Reflective Practice
  • Authentic Assessment


Tribes on the go…

November 19, 2008

Come November and December, time seems to disappear and the list of things to accomplish grows exponentially…

Here are some quick, effective, and thematic Tribes strategies that will keep your momentum without impacting your schedule.

I’m thankful for…

I’m thankful for…” a reflection done in community circle, or at the end of the day, or on a slip of paper dropped in a can to be read later, or a transition to line up for recess.

That’s ME!…

The always useful “That’s ME!…” with reflection questions designed for content (see Learning Experiences on this site) or to begin your Monday mornings, with questions designed to share the weekend and/or communicate frame of mind.

Slip Game (see page 334 in your Tribes Learning Communities book)

Reflecting with some specific learning content questions, as well as some appropriate time of year topics. Once the questions are made (ask your students to help with this by giving each a slip of paper to write a good question), store the slip questions in a can to pull out and use a few at a time during transitions, as writing prompts, in community circle, for centers, or at the end of the day.

Thumbs Up…and 1-2-3 (see page 355 and 293 in your Tribes Learning Communities book)

Have a little reflective moment and use questions that are content rich or questions that pertain to classroom management or group development process. Here’s is an example of how to integrate the strategies and content and behavior:

Thumbs up if you can explain what {content} “the difference between smooth and rough is”…”what [characters from the story] have in common”…”the factors of 24″…

Would you rather… (1) write 3 example test questions and exchange with another student and answer, (2) work on a study guide, or (3) develop a summary paragraph

Thumbs up if you gave more statements of appreciation or encouragement than bossy directions on the playground at recess today

When you are in the halls are you (1) the same responsible student you can be in this class, (2) someone your parent[s] would be concerned about, (3) a ‘micro-manager’

Five Tribbles (see page 246 in your Tribes Learning Communities book)

Have these ready for any reflection, or create your own, with appropriate characters. Use for content or personal reflection.

Something Good (see page 337 in your Tribes Learning Communities book)

Reflecting in community circle, or at the end of the day, or on a slip of paper as an informal survey [what is something good about the way we do things in this classroom…about the way I teach…about the way we treat each other…]  remember, this is always good to use on those not-so-good days or moments; end on the positive.

The Honeymoon is Over?!

September 24, 2008

By now, you may be noticing some behaviors starting to settle in…some good, some on the not-so-good or challenging side.  Here are some strategies for meaningful participation, transition Inclusion-to-Influence stage, and useful classroom management practice.


Setting an expectation (behavior, achievement), asking a question, or stating the desired outcome before the lesson, strategy, or activity can be just as effective as reflecting at the end.  The more you (and your students) reflect, the more you learn.  Reflection is the difference between good teaching and real learning. Remember to ask content/academic, collaborative/social, and personal feeling/emotional questions for every learning experience.

I-Messages (Snowball I-Messages p. 336)

The sooner you teach your students, and model I-messages yourself, the sooner you can set that positive expectation that an I-message is part of the communication when there is conflict, misunderstanding, or need for a specific behavior to start or stop.  Use characters in literature, role-playing, and/or have students watch a sitcom segment and insert I-messages for some good practice.

Paraphrase Passport (p. 302)

Not only does this strategy promote attentive listening, it also supports understanding and tolerance when students paraphrase different views or opinions.  Even teachers may come to understand their students better with a little paraphrase passport?!

What We Need From Each Other (from Discovering Gifts in Middle School)

At the end of one of those days…pre-plan for the next episode with a bit of communication and negotiation.  Small steps at first, and then more long-term (weekly) goals can be put forth.

Something Good (p.  337 )

Use this strategy at the end of a bad day, class, week, etc.  This strategy can also be a “ticket out the door”, in written form…maybe as an informal evaluation…sort of a “how am I doing?” check in with your students.  Ask students to write something good about your teaching style, classroom practices (including management) or the topic that day.

Suggestion Circle (p. 344)

You might be surprised with the effective and logical ideas your students have for solving some of the behaviors that push your buttons…like “what should I do with students who repeatedly refuse to do homework?”  Run the strategy full group, or begin with something like the old-fashioned “suggestion box”.  You will likely get some good input.

The “Take Home” Quiz

Prepare a short quiz (5 questions) for students to take home.  The quiz will only be accepted back if it is in the parent’s handwriting…which means that the parent will have to ask the student for help in answering, since he/she wasn’t there.  Ask questions like, “What is [teacher name’s] signal for attentive listening?”  “Why are I-Messages a good practice?”  What was the discussion about in Social Studies today?”  This is a nice way to involve parents without a conference.


If you aren’t getting the response you had hoped for in the strategies listed above, what might you change to encourage more participation, thoughtfulness, and consideration?  Remember the old phrase, “you get what you give”.

Tribes Learning Experiences for the First Two Weeks of School.

August 5, 2008

These are some suggested strategies to use each day, throughout the day.  Page numbers are provided (DG = Discovering Gifts in Middle School, EA = Engaging All by Creating High School Learning Communities)

Several strategies are suggested for each day; they provide for inclusion on a personal level as well as an opportunity to use some academic content.  This is just a suggested line-up; feel free to mix around, repeat, or look in your book for other options.  The strategies suggested are both inclusion and influence-based.

Not all strategies are in all three books.  Use the “Contact CenterSource” box for more information.

REFLECTION is essential!  If you start the year with a personable, enjoyable experience for your students, you must also be consistent with reflection on each strategy.  Otherwise, you are just playing games or doing fun stuff.  Make it your goal to ask a content (learning), a collaborative (agreements), and a personal question in your reflection.  For the energizers suggested in the following tables, the opportunity to reflect (tell) to the students how well they solved problems, honored agreements, were totally focused on the task, etc. is noted.

The first two weeks of school Learning Experience is available in PDF format by clicking on the link below.

  first-2-weeks-of-school_copy.pdf (70.0 KiB, 2,993 hits)

Writing a Paragraph

June 30, 2008




Hand outline

20-25 minutes

PROVIDE FOR INCLUSION – A You Question, Energizer, or Linking Strategy

Use the energizer “That’s Me” and ask students to stand, raise hands, call out, etc. if they can say “yes” to the following statements:

  • I like to learn about animals.
  • I know a lot about some animals.
  • I like to eat certain foods.
  • I don’t like to eat certain foods.
  • I can give more than one reason why I like (or don’t like) certain foods.
  • I like to play.
  • I like to play specific types of games.


Content Standard: Create a single paragraph: Develop a topic sentence. Include simple supporting facts and details.

Collaborative: Think constructively, Assess improvement

Personal: Share personal characteristics and appreciate others



Have students trace their hand, or teacher prepares an outline of a hand. Have students use their own hands to show and move fingers as follows (teacher should model as well as write on a hand outline for all to see):

  1. Touch your thumb and little finger together – this is the beginning and end of the paragraph – a topic sentence (thumb up) and a conclusion (little finger up). Put them together (touching again) because these sentences can be almost the same; they can restate one another.
  2. Index finger up – This is your first reason, or supporting sentence. Have students remember “That’s Me” – “Who knows a lot about a type of animal?…This (index finger up) would be one of the things you know about that animal.”
  3. (Keep index finger up [very important!!]) Show index and middle finger (“two”) – this is the second reason or supporting sentence.
  4. Add the ring finger (“three”) – This is the third reason or supporting sentence.
  5. Now just the little finger up – This is the concluding sentence; it can restate the topic sentence.

EXAMPLE: (Teacher can write these sentences on the hand outline as they are constructed…with students’ help!)

  • Thumb – I love to eat vegetables.
  • Index finger – Vegetables are healthy foods.
  • Middle finger – They are low in sugar.
  • Ring finger – Spinach is my favorite.
  • Little finger – I eat a lot of vegetables.

Now have students construct their own sentences, on their own hand outlines. Follow the strategy plan in the book for sharing.


Content: How did using your fingers help you to remember the parts of a paragraph? Which sentence was most difficult to write? Why?

Collaborative: How did sharing with others help you to improve your writing? What changes did you make after sharing?

Personal: How did it feel to share something about yourself? How did it feel to share your writing?


Invite statements (model if necessary). Or, ask students to write the name of someone who helped, followed directions, had good sentences, etc on the bottom of the hand outline page.


Now, using the hand outline, have students write the paragraph on a separate piece of paper. Staple the hand outline to the written paragraph and collect and evaluate. Be clear on WHAT is being evaluated…order of sentences? Conventions? Grammar? Paragraph structure? You get the picture.


  • Group Development Process
  • Cognitive Theory
  • Multiple Intelligences
  • Cooperative Learning
  • Constructivism
  • Reflective Practice
  • Authentic Assessment
  • Writing a Paragraph Outline


For paragraphs with supporting details, use the “fingernail” for the reasons or supporting sentence and the body of the finger for the detail>

EXAMPLE: Spinach is my favorite. It can be eaten raw or cooked.

Another modification would be to use a shape or outline other than a hand – any type of graphic organizer or foldable paper design to help students organize and complete the essential parts of a paragraph.

Two-Step (or Multi-Step) Equations

June 30, 2008


7 – 9  (see modification for lower grades in the strategy description below)


20 min. Prepared colored slips with one color the equations and the other color the second step for each equation

PROVIDE FOR INCLUSION – A You Question, Energizer, or Linking Strategy

Tell students you will say a word or phrase and they will need to finish it…ask some personal, fun riddles to get students interested and involved. Review agreements! Establish whether you want them to call out or raise hands – your call.

Example: apples and ________


Content Standard: Algebra and Functions: solve two-step and multi-step linear equations

Collaborative: Work on tasks together, participate fully, assess improvement

Personal: Connect to prior learning experience


Viewpoint (from Discovering Gifts in Middle School training)

Pass out prepared colored strips – one color is the first step in the equations, the other color is the “match” (the second step in the equation).  Have students mill around, sharing what is on their strip until they find a match that makes sense.  When pairs are found, have those students return to their seats and solve the equation.  Have an extension acticity ready for students who are seated (like more problems, or making up their own two steps on the back of the strips of paper).  When all students are seated, have pairs share to make sure they solved correctly.

For younger (lower) grades, use equivalent equations or properties for the paired color slips. (Examples: 4+6 and 6+4, or 2(8+6) and (2×8)+(2×6), or 1 divided by 2 and 1/2)


Content: Which questions were most difficult? Which do you prefer, developing questions or answering questions? (Which was more difficult? Why?) How did this help you to better understand, or review, key concepts?

Collaborative: What was your level of participation?

Personal: What did you learn about your classmates? What did you learn about yourself?


Invite statements, both personal and content related.


Give each student a slip of paper and have each student develop a question for the “next time”; have students sign names to papers for accountability. Collect as the “ticket out” at the door at the end of class.


  • Group Development Process
  • Cognitive Theory
  • Multiple Intelligences
  • Cooperative Learning
  • Constructivism
  • Reflective Practice
  • Authentic Assessment

Syllabication Rules

June 30, 2008


2 – 4


15-20 minutes

PROVIDE FOR INCLUSION – A You Question, Energizer, or Linking Strategy

Model the strategy with your own name. (see below)


Content Standard: Apply knowledge of basic syllabication rules.

Collaborative: Think constructively, assess improvement, reflect on experience

Personal:  Respect and appreciate correct pronounciation of names


Two Truths and a Lie (for this it will be One truth and 1-2 Lies)

Students should be familiar with the rules for syllabication, or taught these rules with examples before using the strategy Two Truths and a Lie.

Rule #1: Every syllable has one vowel sound.

Rule #2: The number of vowel sounds in a word equals the number of syllables.

Rule #3: A one syllable word is never divided.

Rule #4: Consonant blends and digraphs are never separated.

Rule #5: When a word has a “ck” or an “x” in it, it is usually divided after the “ck” or the “x”.

Rule #6: Divide after a vowel if the vowel sound is long.

Rule #7: Divide after the consonant following the vowel if the vowel sound is short.

Rule #8: Divide between two middle consonants.

Now have each student, on a sheet of paper, write his/her name (or the teacher can prepare ahead of time). Students can use first, middle and/or last names, depending on grade level. You may need to turn one syllable names into two syllable names, like “Tom” becomes “Thomas” or “Tommy”.

After each student has this paper and they know which name(s) they are dividing…have them divide the name at least two ways, (one truth and one lie) or three ways (one truth and two lies)

Example: Ma-ry Mar-y M-ary

Now students can determine which is correct by exchanging papers and discussing with a partner. Then switch back and review/correct full group.


Content: How does dividing your own name help you to remember the rules for syllabication?

Collaborative: How did you practice the agreements when you exchanged papers…especially if you disagreed or need to make corrections?



Have students give a statement to their partners.


For the rest of the day…or a couple more times throughout the week…have students write their names (on a paper to be turned in to you) their name divided into syllables.


  • Group Development Process
  • Cognitive Theory
  • Multiple Intelligences
  • Cooperative Learning
  • Constructivism
  • Reflective Practice
  • Authentic Assessment

Note: This lesson tends to go very quickly; students are either anxious to try dividing their name a variety of ways, or, dividing their name is way too easy! Have a backup name ready for a challenge.

Download Presentation

Social Studies Project: California Missions – Multiple Intelligences

June 30, 2008

**note: students must know something about multiple intelligences, including their own.


4 (California History- but could be modified for other topics)


Variable – allow at least one week

PROVIDE FOR INCLUSION – A You Question, Energizer, or Linking Strategy

Tell students they are about to work on an individual project. Have them share their strongest and weakest intelligence with a partner, group, or in class.


Content Standard: People, places, and environments

Collaborative: Think constructively, celebrate achievement

Personal:  Develop and showcase Multiple Intelligences


Circular Curriculum (from the Artistry for Learning)

After you teach the concept, invite students, working in tribes or individually, to choose one to three of the following demonstrations of learning.

Here is an example of demonstrations of understanding, based on the multiple intelligences (also the student handout):

Verbal / Linguistic

Write three sentences about 10 California missions, including:

a) Location

b) Date established

c) Interesting (unique) fact

Musical / Rhythmic

Write a poem that includes 10 California missions, and rhymes!

Mathematical / Logical

Draw a map of California that includes:

a) All 21 missions

b) Each mission’s name

c) A simple outline of what the mission looks like

d) Distance in time or miles from each, in numerical order


Construct a diorama of a mission, with emphasis on the physical / geographical surroundings and identify how these environmental elements contributed to the success of the mission

Body / Kinesthetic

Build a mission replica of an actual mission and label materials used, both original, and those used to replicate


Write a diary of a missionary and a diary of an Indian for a particular mission. The diaries should begin with the establishment of the mission and have three entries about development of the mission, ending with an entry about what results from the mission being there….

Visual / Spatial

Create a Power Point, Publisher, or Inspiration creation that demonstrates your understanding of California missions

Interpersonal (required)

Be prepared to demonstrate your mission project with the class, on some level…


Content: While projects are being shared/presented, have students write comments on grid (see student handouts).

Collaborative: How would you rate your ideas – original, or influenced? Explain.
If someone uses your idea, but changes it to his/her own interpretation, it is copying?

Personal: What did you like about this project and all it’s choices? What didn’t you like?


After each presentation, applause or invite statements.


Have each student grade himself/herself on several levels. For example: accuracy of information, presentation, effort involved, compared to others, etc.


  • Group Development Process
  • Cognitive Theory
  • Multiple Intelligences
  • Cooperative Learning
  • Constructivism
  • Reflective Practice
  • Authentic Assessment

Download the Handout

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