Snapshot: 7B Rational Numbers

Today, we reviewed our understanding the categories of real numbers. We discussed inclusion and exclusion of different types of numbers at different points in the framework. We used an analogy about which numbers have access to different categories. For example, natural numbers have the all-access pass and fit into all categories of rational numbers. We expanded our conversation to irrational numbers, imaginary numbers and complex numbers. There was lots of curiosity and questions, but many students ended up "with their brain full!" 

7B: Math Challenge 2 - Cyclic Number

Math challenges are designed to push the students on multiple fronts. They need to decipher the problem; they must identify the tools required to solve the problem; they must use the tools correctly; determine if their solution is reasonable; and then figure out how to communicate their thinking on paper and then translate it for an audience. Whew!

I choose math challenges for different purposes each week. Sometimes it will push their problem-solving skills or it might be difficult to document or both! This was a tough math challenge, but I wanted to see what 7B would do when up against something that was hard and that they might not have all the pieces to figure out. Here is the original problem:

The symbols and representation were a hurdle for most students. Those who were able to translate the information in the problem then struggled to figure out how to glean information from the statements. It was great to have students share what they were able to find out and what they could rule out to be true. Everyone who came up to share added more information to the pool of knowledge. I was really impressed with how students were able to give credit to peers and their efforts, especially those who did not solve the problem, but advanced our understanding of the problem. 

The students who were able to complete the problem shared their strategies and key pieces of information that helped them solve the problem. To quote the students, "My mind is blown!" It was satisfying to see the students who solved the problem be able to answer questions about their work and defend their choices. I was particularly impressed with EB2018's ability to find different ways to answer essentially the same question, multiple times. 

We are starting a new tradition with our math challenges this year. After the sharing phase, students are going to reflect on their process, describe what they learned during sharing, and synthesize their experience in a journal entry. I was pleased with our first go around with the reflections. I believe that this is the next step to developing their skills as problem-solvers and communicators. Here are samples of what was written.

Please ask you child to tell you more about this problem and its solution!  

6C : Four Digit Challenge

Students in 6th grade are working on solidifying their understanding of the order of operations in mathematics. The class explored why it might be important for a mathematical phrase or sentence to have only one solution. They came to realize that without a set of universal rules to follow, communication would be flawed. It would be impossible ensure that the information you are trying to communicate would not be misinterpreted. 

To extend their understanding, the class was given the "Four-Digit Challenge." They were asked make equations that equaled 0 to 50. The requirements were:

• the digits 1, 2, 3, and 4 were required to be in each equation
• each digit could only be used once
• they could use addition, subtraction, and multiplication (no division)
• they could use parenthesis and other grouping symbols
• they could use exponents and square roots

The class was challenged to see if as a group they were able to complete all of the equations from 0 to 50. They broke into groups and set to work. 

I wish you could have been in the room to hear all of the wonderful mathematical thinking that was happening. Here is a small glimpse into the type of collaboration that was happening.

Check back for more on the Four-Digit Challenge!

Population Growth

In 6C, we ended up on a tangent discussing population and population growth. I shared this video with the class because I thought it was a nice illustration of why the population on the planet earth has grown so much. It unearthed questions about history, and where are we headed. They asked that I share this with them, so here it is!

Snapshot: 6 Subtracting Integers

Sixth graders were tasked with figuring out how to subtract integers. Each group of students were given a type of subtraction problem and they were required to figure out how to teach the rest of the class how to solve that. They were required to find at least two ways to solve the type of subtraction problems. The posters were shared and displayed in class. It was great to see the creative ways the students were able to apply what they already know about integers to make sense of subtracting integers. 

Snapshot: 6 Coordinate Plane Designs

The sixth grade is exploring integers. They are looking at the multiple uses of integers and applications of integers. One application we have used extensively are integers on a coordinate plane.  Students have plotted points, read points from a coordinate plane, identified the origin, and identified trends for each of the four quadrants. 

As an extension exercise, the students had to design their own coordinate plane design. They will get feedback from a peer who will complete them for homework. 

Check out the variety of designs!

Snapshot: 7A Four 4's Challenge

The seventh grade kicked off the school year with the Four 4's challenge. They had to use four 4's to make equations for each number between 0 and 50. They could use the operations add, subtract, multiply, divide, parentheses, exponent, and square roots. They were introduced the concept of factorials (4! = 4 x 3 x 2 x 1 = 24). We found patterns to find families of answers and exercised our understanding of order of operations to find solutions. The even numbers were easier to find and we are now left with the challenge of finding solutions for 31, 33, 37, 39, and 41.  

Can you figure out the missing numbers? 

Snapshot: 6 Millet by the Million

The sixth grade took time to explore the meaning of place value and the relative size of large numbers. They worked as a collective to count out a million millet seeds to visual the number one million. We started by individually counting out 10 millet. Each student then counted out 100 millet. Many were surprised by how small one hundred appeared in their Dixie cups.

10 millet

100 millet

One thousand millet was collected by each table. At this point, we realized that this method was going to take all year! So we moved to counting by weight. We weighted the 1000 millet to the nearest hundredth of a gram. We discovered that our numbers varied by almost eight-tenths of a gram! There was great discussion about how to proceed. We agreed that finding an average weight for 1000 was needed but could not decide whether or not to add in the outlier in the data or to discard it. We looked at how much of a difference including the outlier made in our average and we finally settled on discarding the data because it made our 1000 count vary by several hundred millet. From this point, the process went quickly. Each split counted out 333,330 millet. We came together as a grade and ceremonially poured our millet together and added the final 10 millet to make a million! 

It was fun to do a collaborative project with the whole grade. Now, when we talk about millions, we have a point of reference to understand and conceptualize this very large number!