**MathTrailblazersTalesEau Claire Area School** DistrictImplementation Year 2003-04

**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.

**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.

**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 person’s 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!

**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.

**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.

**What Does Math Trailblazers Look Like?** Kindergarten Problem-Solving “Vanessa has 5 blue buttons and 4 red buttons to put on her snowman. How many buttons does she have all together?”

**What Does Math Trailblazers Look Like?** Kindergarten Problem-Solving, cont’d 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.

**What Does Math Trailblazers Look Like? ** Kindergarten Problem-Solving, cont’d Another Kindergarten child, a little more advanced, said, “I know that 5 + 5 = 10 and if I take 1 away that makes 9.” Wow!

**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.

**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!

**What Does Math Trailblazers Look Like?** Kindergarten Theme: Buildings 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.

**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.

** 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?”

** 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.”

**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.

**What Do Teachers Say About Math Trailblazers?** Grade 2 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

**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! Here’s a rhombus!” Aha! He really understands!

**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.

**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 4’s 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. “It’s really amazing to see the kids excited to understand and use this great strategy!” Check out Steven’s great work! 14 + 16 + 12 = ?

**What Does Math Trailblazers Look Like?** Grade 3: Boo the Blob • “Let’s put this half with these fourths to make a whole.” • “You got 20, Shamiah got 21, and I got 23, so let’s write down 21.5; that’s about the average.”

**What Do Teachers Say About Math Trailblazers?** “Boy, this Trailblazers program is really a roller coaster! Just when I think I’m 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 I’ve taught them, I realize it wasn’t so bad and I understand better what the objective was. It makes me feel like a beginning teacher again!”

**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!”

**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.) I’m thinking that next year will be easier because they will have done those same skills in second grade and it won’t be so new.”

**What Do Teachers Say About Math Trailblazers?** “In my class I am seeing a growth in the new math vocabulary. When I couldn’t 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.”

**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!”

**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…”

**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!

**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!”

**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.”

**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.”

**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.”

**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!”

**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.”

**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’.”

**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, “Let’s try this”, “No, that won’t work”, “Try three in a row”, “Eleven has only one array”, “Twenty-four has lots of them” They really had a ball. It’s 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, they’re used to trying hard to figure out a solution and then work well going from the known to the unknown in groups.

**Math Trailblazers and The Facts…** “The DPP’s are great. I see the review opportunities they give the kids everyday. Other teachers have said they like the DPP’s because they offer good review. I have also seen where a child didn’t quite get the concept when it was taught but then after it was covered in the DPP’s a few times, it clicks. It was great! They just needed the extra practice.”

**Math Trailblazers and The Facts…** From a School Newsletter… 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.