Math Trailblazers Tales Eau Claire Area School District Implementation Year 200304

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MathTrailblazersTalesEau Claire Area School
DistrictImplementation Year 2003-04
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What Does Math Trailblazers Look Like?

• Kindergartners can be seen making motion
  patterns with their bodies. Tap, tap, clap and
  Stomp, nod, stomp, nod are two of the many that
  they created on their own.

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What Does Math Trailblazers Look Like?

• Here students use pattern blocks to figure out
  how to write a number sentence. Students
  commented that using the pattern blocks helped
  them visualize the problems and made it easier to
  solve the problems.

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What Does Math Trailblazers Look Like?

• Fourth graders were doing their first lab and
  finding that height and arm span are related.
  They proved that a persons arm span is within 3
  inches of their height and in some cases exactly
  equal to their height no matter how tall they
  are.
• One aha moment was when the students
  discovered they were doing harder math than their
  parents did in fourth grade and they were going
  to have to train the experts on things like
  numerical and categorical variables!

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What Does Math Trailblazers Look Like?

• The first graders having fun with our Pennies,
  Pockets and Parts unit. The hands-on nature of
  this unit has helped the kids to really SEE how
  we can join numbers together to create a whole.

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What Does Math Trailblazers Look Like?

• Here 2 students work together to solve their
  fraction problems. Students have commented they
  enjoy this new math program because it allows
  them the flexibility to solve problems with
  friends as well as on an individual basis.

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Kindergarten Problem-Solving
What Does Math Trailblazers Look Like?

• Vanessa has 5 blue buttons and 4 red buttons to
  put on her snowman. How many buttons does she
  have all together?

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What Does Math Trailblazers Look Like?

• Kindergarten Problem-Solving, contd
• A Kindergarten child we are very concerned about
  who could not consistently rote count or count
  objects to 10 before vacation gave this solution
  If I have 5 buttons and I count 4 more, that
  makes 8. (She counted on fingers 5, 6, 7, 8.)
  When I went back and questioned her about her
  answer, she went back, recounted on her fingers
  and corrected her answer to 9.

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What Does Math Trailblazers Look Like?

• Kindergarten Problem-Solving, contd
• Another Kindergarten child, a little more
  advanced, said, I know that 5 5 10 and if I
  take 1 away that makes 9. Wow!

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What Does Math Trailblazers Look Like?

• Here students write fractions based on a pattern
  block setup on the overhead. The overhead
  manipulatives are very helpful in demonstrating
  the problems.

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What Does Math Trailblazers Look Like?

• I just noticed something, said Marlon. 5 x 7
  is the same as 7 x 5! This came from a student
  that is absent once a week and has no family
  support. It was great to see him light up!

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Kindergarten Theme Buildings
What Does Math Trailblazers Look Like?

• The kids were actively involved in data
  collection and problem-solving throughout. What
  we did in this particular lesson, Window was to
  have the kindergartners buddy up with the 3rd
  graders to help in the data collection.

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• In these pictures, the kids are working with
  3rd grade buddies to count the windows in the
  building. Each kindergartner had a clipboard
  with the room name they were to report to. The
  3rd graders helped us move threw the building,
  making sure we counted all the windows in the
  room, and recorded the number of windows before
  leaving.

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• We came back and sorted our data according to
  the number of windows in each room. We compared
  and discussed our findings and solved word
  problems related to the data. For example The
  computer lab had 2 windows and the office had 7
  windows. How many windows did we see? or The
  gym had 6 windows and the music room had 3.
  Which room has more windows? How many more?

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• The thinking and questioning that took place
  during this lesson was wonderful. We heard the
  kinders say things like,
• I noticed that 4 rooms we went to had 3
  windows.
• There are more rooms with 3 windows in them than
  any other number.
• I know 4 is more than 3 because there is one
  more window left if we made partners.

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What Does Math Trailblazers Look Like?

• We got ready to start counting down to 100 days
  of school. At number 77 today, I had a student
  tell me it would be 23 days from now.
• When asked how he knew, he said, You go 3 more
  to get to 80 and then 2 tens to get to 100.
• This is a kindergartner who did this
  problem-solving on his own. We then proved it by
  using the links.

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Grade 2
What Do Teachers Say About Math Trailblazers?

• I have noticed a wide range in my own students
  as they progress towards fluency.
• Some are still using fingers
• Others use the 200 hundred chart.
• Some rely on facts they already know
• Others use 10 for a benchmark

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What Does Math Trailblazers Look Like?

• The first graders in our class were taking a
  walk around the playground looking for shapes
  they could notice on the equipment. They found
  lots of circles, rectangles, triangles and
  squares. As the kids took turns sharing the
  shapes they found, Alex said, Hey, look! Heres
  a rhombus! Aha! He really understands!

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What Does Math Trailblazers Look Like?

• Students use white boards to solve math problems
  from our student guides. This allows me to view
  individual workmanship. It was much easier to
  see who understood the problems at hand using
  immediate feedback.

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What Does Math Trailblazers Look Like?

• In third grade they are working on breaking
  apart addends to find sums. Think about the
  problem 8 15 6. The light bulbs have been
  turning on like crazy!
• The kids quickly draw brackets to break 8 into 4
  4. They easily add one of the 4s to the 6 to
  make 10. Putting that new 10 with the 10 from
  the 15 makes 20. The remaining 5 and 4 make 9.
  Add 9 to 20 and the sum is 29.
• Its really amazing to see the kids excited to
  understand and use this great strategy! Check
  out Stevens great work! 14 16 12 ?

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What Does Math Trailblazers Look Like?

• Grade 3 Boo the Blob
• Lets put this half with these fourths to make a
  whole.
• You got 20, Shamiah got 21, and I got 23, so
  lets write down 21.5 thats about the average.

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What Do Teachers Say About Math Trailblazers?

• Boy, this Trailblazers program is really a
  roller coaster! Just when I think Im getting
  it, they throw a more complicated lesson at us!
  It certainly is keeping me on my toes and keeping
  my planning skills sharp! Actually, I like most
  of the lessons. Once Ive taught them, I realize
  it wasnt so bad and I understand better what the
  objective was. It makes me feel like a beginning
  teacher again!

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What Do Teachers Say About Math Trailblazers?
Grade 1

• I am pleased at how independent they are
  becoming in transferring their data to a line
  graph, even when the graphing intervals are in
  units of 5!

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What Do Teachers Say About Math Trailblazers?

• Sometimes I feel overwhelmed because they cover
  so much material in one lesson. For example, in
  one lesson, we did an experiment (lab)--found the
  area, found the median, graphed our results, and
  interpreted them. It lasted several days,
  obviously. It seemed like so much to cover, but
  it was a good application of previous learning.
  (A spiral within the grade level.) Im thinking
  that next year will be easier because they will
  have done those same skills in second grade and
  it wont be so new.

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What Do Teachers Say About Math Trailblazers?

• In my class I am seeing a growth in the new
  math vocabulary. When I couldnt think of the
  word interval the other day, one of the students
  came up with it. I am seeing better and better
  explanations of their thinking on number
  sentences and more general number sense.

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What Do Teachers Say About Math Trailblazers?

• I love the activities at the kindergarten level
  and see a nice growth in the students. I feel
  the teachers in future years will have some very
  advanced students!

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What Do Teachers Say About Math Trailblazers?

• I have been so pleased with the complex math
  thinking that is becoming easier and easier for
  the students as we progress through Trailblazers.
  I asked how much it would cost to buy letters
  for 4 shirts if each shirt had 9 letters and each
  letter cost 10 cents. Very quickly Alex replied,
  3.60 I asked him to explain how he found the
  answer so quickly

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What Do Teachers Say About Math Trailblazers?

• He responded, If each shirt had 10 letters, it
  would cost 4.00, but I subtracted 40 cents since
  each shirt has only 9 letters, so that makes
  3.60.
• Not only did Alex use great thinking skills, but
  the rest of the class nodded in agreement as if
  it made perfect sense to them too. I love
  moments like that!

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What Do Teachers Say About Math Trailblazers?
Grade 1

• The consistent procedure of the labs (draw,
  collect data, graph, discover) is already in
  their heads after only 3 labs!

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What Do Parents Say About Math Trailblazers?

• I was really worried about the new math
  curriculum early in the year because of some
  things that I had heard. I am now pleasantly
  surprised at the math that is coming home and the
  confidence that my child has in math this year.

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What Do Parents Say About Math Trailblazers?

• My child has really struggled at math in years
  past. She really seems to be enjoying it this
  year. She is able to do her homework on her own
  many nights and has a book there to provide
  assistance to us if we need to help her. I am
  happy with the math curriculum so far.

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What Do Parents Say About Math Trailblazers?

• Third grade is solving magic puzzles. One
  parent commented about the Magic Square homework
  saying, I like to see the children challenged
  and thought the math homework was fun.

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What Do Parents Say About Math Trailblazers?

• My child really enjoys math this year. She
  sits down right away when she gets home to work
  on her math homework. This is exciting to see!

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Math Trailblazers and The Facts

• I love the systemic way it has us teach the
  math facts. In other programs, I felt that we
  talked about the fact one day and then expected
  the kids to know them the next day. This program
  really has us pound the facts in.

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Math Trailblazers and The Facts

• One of the games in fourth grade MTB is to draw
  cards from 0-9 and place them in a two or
  three-digit subtraction or addition problem to
  get the largest/smallest possible difference.
  Students in my room love to play this game in
  their free time. They beg to play the game. It
  really reinforces good strategies for math along
  with the facts.

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Math Trailblazers and The Facts

• In Unit 4, students were to make arrays with the
  facts. As I walked around the room I heard lot
  of, Lets try this, No, that wont work, Try
  three in a row, Eleven has only one array,
  Twenty-four has lots of them They really had a
  ball. Its interesting to see how students work
  in groups. Some just sit back and wait for
  someone else to lead others lead even though
  they may not be the best student, theyre used to
  trying hard to figure out a solution and then
  work well going from the known to the unknown in
  groups.

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Math Trailblazers and The Facts

• The DPPs are great. I see the review
  opportunities they give the kids everyday. Other
  teachers have said they like the DPPs because
  they offer good review. I have also seen where a
  child didnt quite get the concept when it was
  taught but then after it was covered in the DPPs
  a few times, it clicks. It was great! They just
  needed the extra practice.

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From a School Newsletter
Math Trailblazers and The Facts

• A balance between understanding concepts of
  number and working problems a set way is best.
• For all operations, standard methods for
  computation are not introduced until students
  have developed solid conceptual and procedural
  understanding. Introducing a way to solve
  additions, subtraction, multiplication or
  division problems (the ones we learned in school)
  too early may short-circuit students common
  sense and natural mathematical thinking.
• This can lead to a lack of understanding and
  confusion. Students may learn to do the
  problems but not understand what the problems
  actually mean.