Student Progress Update - due March 9th

2/24/2015

Conjectures!

Please share the mathematical objective you were working on and the conjecture that your class came up with. Reflect on what was challenging about this process and how you addressed any misconceptions the students had. Share any thoughts about using conjectures in your classroom.

19 Comments

Angela Villaluna

2/27/2015 02:14:27 am

We had a great time creating conjectures this week. Fractions is a huge focus of fourth grade math and this week we created conjectures for comparing unit fractions and adding and subtracting like fractions. We started with creating a conjecture for comparing like fractions. At first, it was hard to get the students to share their conjectures. Once one student placed a conjecture up, they thought it was "good enough." I had to encourage a few more students to share their conjectures and then we started to pull elements from each to create one conjecture. That took a bit of time. Once we were done, the students were really happy with the results. Two days later, when asked to make a conjecture for adding and subtracting like fractions, they cheered! It was a bit easier and again, they were responsive with the process and the end result. I liked that the students used the conjectures to help correct Puzzled Penguin problems.

Catherine Nam

3/6/2015 06:25:26 am

I love that they cheered! It sure sounds like your students are growing as mathematicians. Hip Hip Hooray

Lou Ellsworth Yow

2/27/2015 07:42:08 am

Our first grade group is working on "decomposing tens" or "Making Ten's" to help as a strategy when adding within 20. The initial problem on the board was 6 + 4 = ? (How do you solve that? How else can we solve that?)

A couple of students shared their strategy (Counting on & Counting all). They came up to the board proudly and were successful in explaining their strategy. I moved on to 6+5 = ? 4 different students came up and shared two of the same strategies, and then 2 more (Doubles fact (5+5) and Making Tens (6+4) + 1 = 11

I continued with this until I got to 7+4= ?

By then, the class was losing focus and I asked for a conjecture, "What pattern do you see?" One of my top students who stayed focus shared, "The #'s are going up?" She noticed that 8+2=? would be next.

While I don't feel I succeeded with making conjectures for the whole class, there was good discussion and sharing of strategies. More students participated than before and more than I expected. We mainly ran out of steam and I never made a full connection. This is a work in progress and I hope to master this process. It was fruitful, nonetheless.

Michelle Robertson

3/5/2015 06:54:12 am

Today was the second day we worked on a specific conjecture with our classes. (Julie and I both have TK/K combos so we do centers together) Last week she had math, this week I do. Last week she started with manipulatives and showed equations with a number and zero. The conjecture we were trying to get at is that when you add zero to any number it equals that number. Last week they had trouble getting to it. But today we had success with most groups. I put up the equations, they answered quickly. I asked them to discuss with each other why it was so easy and quick to come up with the answers. This led them down the path for a great discussion and conjecture. The lowest group still isn't quite there, but all the other K groups and TK group were able to come up with a conjecture. : ) I have pictures that I'll show in class.

Julie Ramser

3/8/2015 01:17:55 am

To add to Michele's information I gave the students manipulatives and we solved the math problems on the board together. The highest two groups got the two facts that there was a zero in every problem and that there was one number in the problem and the same number was the answer. It was time to rotate before I could ask enough questions for them to get the actual conjecture. I think it was good to shelf the problem and come back to it another day. I am going to try another conjecture this week. I will do all +1 problems. It will be interesting to see if they can come up with the conjecture after having experience with 0.

Mo Prince (First Grade)

3/8/2015 03:32:41 am

The objective for our first grade discourse group this week was the Make a Ten strategy--when adding two addends, decomposing one of the addends to compose a ten with the other.

With the whole class I wrote number strings on two different days. On the second day, after the second number string, I asked students for their conjectures. (On both days, I made an effort to call on the more timid ones if they showed me a one/raised their hands as I wanted to give them a chance to voice their thoughts.)

Although I did not have any misconceptions this time, I could easily see which strategies my students prefer during the number strings activity. Also, the conjectures give the others an opportunity to see the problems in a different way. I could easily do this activity again and maybe even have the students prove or disprove the conjectures!

Hyun Moon

3/8/2015 11:15:13 am

We are slowly opening ourselves to different ways of thinking and solving problems. Each lesson is led carefully with necessary scaffolds provided through the use of visual supports and oral language.

My students have not been exposed to vocabularies widely used in everyday mathematics in addition to lacking practice in expressing how they went about solving questions. Despite all the obstacles in our way, I am amazed how the boys all pick-up one to two strategies or terminologies given time and repeated practice.

We have been working on “decomping a smaller number” to make a ten and adding on. Each student during one-on-one session showed me how they derived at a solution when given 6+4. All students were able to say, “I counted on, “I did it in my head,” or “I used abacus or Touch Math” when probed and given terms to name specific strategies utilized.

I actually showed my students how to break down a smaller addend of the two to make ten and add on knowing their strengths as well as challenges. I hope the boys can solve 7+4 and 8+3 when there is a display of
6+4 = 10 so…
6+5 = 11
^
4+1
once we discuss the new strategy and talk it up during math rotations.

Tom Martin

3/8/2015 02:20:31 pm

Admittedly, with report cards I have not been able to introduce the conjecture concept, but will do so tomorrow. I am very excited to see how my students respond. They are continuing to amaze me in how they are processing math problems, specifically during our Math Journal work.

Tom Martin

3/9/2015 08:00:26 am

Finally taught our Conjecture lesson today and was thrilled by the math talk. The lesson itself went very well as I had them in pairs and they used manipulatives to model the problem. When it cam time to discuss the conjecture, however, most of them were a bit lost. I initially avoided a pair that I knew had a conjecture, to see if someone else might have an idea, however the rest of the group seemed somewhat confused. So I asked the advanced pair and they provided a reasonable conjecture, that the class then used to create a complete conjecture.

Lindsay Henning

3/9/2015 08:06:16 am

Students did very well coming up with conjectures as to how they know when a fraction is more than 1 whole. The way that Everyday Math introduces the students to identifying "the whole" very early on has seem to make everything easier for the students. Everyone in my room can identify the whole. Because of this, even the students that struggled with writing a conjecture were able to have it explained to them by another student. I didn't have to interject or guide at all this time. The other students took over! Very exciting!

Angelina Salyers

3/11/2015 02:32:57 pm

Our adding with 0 conjecture was tough! My class did great figuring out the problems and discussing what they were trying to solve. The biggest concept that they took away from this conjecture was that when we are adding with 0, it means we are adding no more. They didn't come up with the exact conjecture we decided upon as a grade level, but they concluded something that was valuable to them.

Erika Lee

3/18/2015 04:20:55 pm

The mathematical objective we were working on was 0+___=_____

The conjecture that the class came up with was "The answer is always the same as that number." They had a challenging time understanding what I was asking them to do. Ultimately, my question was, "what is the pattern when we add zero to a number? The class was able to do the math and answer the number strings correctly. However, it was challenging for them to explain what it meant in words.

One student had a misconception that 0+7=9 and I asked her to tell me about how she knew that and she wasn't sure. I observed that she was looking at the number line. I had the students use the manipulatives and put the quantity of zero in one hand and the quantity of seven in the other. Then we discussed what they noticed when we combined the two numbers. Next, we played the ball toss game and I focused on 0+ a number. The students were fluently able to add zero to any number I gave them, even 2,000. It really helped to solidify our discussion and reinforce the conjecture.

I think using conjectures in the classroom is a great strategy for older grades because they understand the vocabulary behind the concepts and can choose words to fit their analysis. With kindergarteners, it is challenging because they are struggling to understand what the question and come up with a phrase to explain it.

Lori Hewitt

3/20/2015 09:42:45 am

My third grade class has been working on understanding fractions with a focus on unit fractions. I wanted them to understand that fractions can be decomposed into the sum of unit fractions. We used the cuisenaire rods first, and then a reengagement activity. Unfortunately, the first activity didn't influence the students to think of a conjecture related to this understanding.

After our March 9 class, as a grade level we decided to try a different approach. We decided to have students glue fraction bars to number lines. They labeled the unit fractions on the fraction bars and used them to write the naming fractions on the number lines as well as equations of unit fractions. I did this activity twice before having them create a conjecture. I started writing all their math ideas. One conjecture example was "The denominator is how many equal groups we cut and the numerator is how much we shade". After some prompting a student said this, "Fraction equations are when you take the parts of a fraction and then add them together to make an equation". The next day I emphasized unit fractions and we added it to the conjecture. It could still use some editing, but it is a start.

Since then, we have been creating conjectures daily. I love it! We need to still revise some, but I find them to be a useful reference tool when teaching, whether it is reading the conjecture, revising it, or creating a whole new one. I have now moved on to my third piece of chart paper.

Robin Horenstein

5/5/2015 08:30:54 am

Since we discussed and practiced using conjectures in our math class I find I am asking about conjectures in other subjects besides math. It is a great way to check in with students after they have been working in groups or pairs without much teacher intervention. At first my students were confused because it seemed like a big confusing word but when they realized a conjecture can be about a simple concept, they felt the freedom to simplify a statement to even the most obvious. What I always have to constantly remind myself is that the simplest concept to me might not be to my students, so the verbalization of conjectures adds to the learning and mastering for myself as well as my students.

Janelle McGoldrick

5/6/2015 04:24:19 am

When the class created their first conjecture, I was noticing that students would refer back to the conjecture regarding fractions. I introduced to the class a sneak peek about finding equivalent fractions by looking at the denominator and the numerator. With guidance the class was able to create the following conjectures: is the numerator and denominator are an even number divide by an even number, if the denominator and numerator are odd divide by an odd number, and lastly if the either the numerator or denominator or even or odd divide by a odd number. Some students got the concepts but for some it was over their head.

Brenda Pfeifer

5/9/2015 08:09:27 am

We worked on a conjecture for pi. We were trying to establish the relationship between diameter and circumference. It was the first one we did, so I helped a lot along the way. I wrote on the whiteboard as they dictated to me. Overall, it went okay. The hard part for me was having the students refer back to what we had previously written and come full circle with the work we were showing, what they were telling me, and what I was writing. The vocabulary was also confusing to them (circumference, diameter, and radius), which made it hard for them to connect with what was happening. While coming up with the conjecture was challenging, the best part was the discussion along the way.

Kathy Koford

5/10/2015 08:27:52 am

My students loved learning what a conjecture is, although many of them still are unsure. They do love learning new words!

I had been using teen equations for our ball tosses and was surprised that many of the students still had to count on from 10 to figure out the sum. I was thinking that 10 + 6 should be automatic by now. I wrote some teen equations adding on from 10 and called on people for the answers. I asked them to look at the equations and tell me what they noticed. A couple of my students noticed that the number we were adding to the 10 moved into the spot where the zero had been. I asked them what conjecture they could make about adding a single digit number to a decade number. Many voiced that the single digit would move to where the zero had been. We checked this out with other equations (i.e.: 20+8, 60+4, 90+9).
It really does help them learn something when they have the "aha" moment instead of me just telling them.

Danelle Block

5/10/2015 12:55:57 pm

My students are really enjoying writing conjectures. This last week we've been studying plane shapes. After a good discussion on quadrilaterals, they were able to able to write the following conjecture: All Squares are rectangles. Not all rectangles are squares. I love that they came to this conclusion on their own.

DeMaur Herrera

5/10/2015 04:49:06 pm

This was a huge hit with my third grade students. They love writing conjectures! We worked with fraction and my objective was for students to realize that fractions can be decomposed to unit fraction that equal a whole. I thought this would be a bit of a task, but I was wrong. Once we modeled the decomposed fractions…writing the conjecture was the easy part. The kids were so excited to share their conjectures and post them on the wall. This was a huge success!

Math Discourse - Class Blog

Student Progress Update - due March 9th

Conjectures!

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