math Archives - Tanya Yero Teaching

3 AWESOME STEM Challenges To Do In Your Classroom

March 23, 2018

As a math and science teacher, STEM is part of my curriculum. Not only do STEM challenges help me target specific standards, but they also promote problem solving, cooperation, and communication amongst my students. Here are three STEM challenges I do every year in my classroom.

1.) Spaghetti Towers

I always do this STEM challenge the first week of school. It’s a fantastic team-building activity and allows me the opportunity to observe my students in groups. I watch to see who holds back and doesn’t contribute much, who tries to control the situation, and everything else in between. It’s also not an easy challenge, so I observe which groups persevere and which shutdown. I use this data to arrange groups for future challenges.

2.) Rollercoaster Building

These Rollercoaster STEM Kits from Lakeshore Learning are one of the most diverse materials I use in class. My absolute favorite labs included in these kits are the ones for potential and kinetic energy. We start with evaluating how slope effects momentum with the rollercoaster pieces. Next, I introduce a WONDERFUL website where students can digitally create rollercoasters. The website is highly interactive and I have to bribe students to log off the site. For the finale, we spend an afternoon creating rollercoasters with the Lakeshore STEM kits. These kits are a little pricey but I was fortunate enough to receive funding for them from a DonorsChoose grant.

3.) Paper Airplanes

I use this activity after testing. It’s perfect for reviewing converting measurement and I’m usually covering force and motion at this time of the year. I purchased this activity from Lisa Taylor. There are 3 different challenges that include discussion questions and data tracking logs. One of my favorite aspects of this STEM challenge is the small list of materials that are needed; easy prep for me!

STEM education can cover so many standards and critical thinking skills for your students. When my students come back and visit me after they move on to 5th grade they always reminisce about the STEM challenges we did in 4th grade. What’s your favorite STEM challenge to do with your students? Comment below.

Education, Teacher Support

3 Ways to Make Enrichment Easy for You and Your Students

March 12, 2018

Servicing all the levels of ability can be trying on a teacher. You’re one person in a classroom with 20+ little people. During my first few years of teaching I struggled with how to balance the work I gave to my students. I knew I needed to differentiate, but it was hard finding materials and quality work for each group.

Three years after I started teaching I moved to a public school that was full-time gifted, but the need to differentiate was still there. A bell curve of ability exists within any group of students. I needed resources that required little preparation and made enrichment easy for my early finishers. Here are three ways to make enrichment easier in your classroom.

1.) PREP ahead of time…like way ahead of time.

Preparing materials during the summer makes for an easier school year. I print, laminate, and store all my resources in containers from Target. My future self is appreciative of this work later in the year when I’m struggling to stay afloat during testing season, report cards, etc.

2.) Go beyond the curriculum

Puzzlers and brain busters are a great way to challenge your students. Advanced children eat this stuff up. You’re pushing their cognitive abilities and fostering problem solving too. It’s a win-win for everyone.

3.) Set up a system

I like to use resources that have similar directions for students. That way I don’t have to explain new activities throughout the year. My students just grab a bin when they have extra time or looking for a challenge and they know what to do.

My latest line of Enrichment Kits are themed for each month of the year and jammed pack with puzzlers and challengers for your early finishers!

Education, Math

Creating Questions to Promote Productive Struggle

March 12, 2018

Open-ended tasks are a great way to promote productive struggle. I use this type of questioning to drive my math instruction. Designed to have several correct answers, they empower your students to select their own pathways to solutions.

A strong understanding of the curriculum and the standards you are expected to teach is a must for writing conceptual based questions. Standards are multifaceted. Some are deceiving. It’s like looking at abstract art. If you’re just looking at the surface, you’re missing the layers of depth underneath. You also need to identify which standards parallel one another because you can use that to your advantage. Here are 4 tips to use when selecting questions and tasks for your students or when creating questions to promote productive struggle.

1.) Requiring students to work backwards

This a great strategy that brings depth and conversation to any math class. This sort of questioning often produces multiple strategies for solving problems.

2.) Wording

Exclude wording that may provide too much assistance or give students too much information. The triangle activity pictured below was extremely vague. I didn’t specify exactly what I was looking for in each box, nor did I explain what the headers at the top meant. I gave each group a bag of triangles and asked them to complete the first row about equilateral triangles. I wanted to see how far my students could carry themselves first.

3.) Resolving conflict within group discussions

When I was reviewing place value earlier this past school year, I gave my students the following task: “Create a number that has the digit 2 in the place value that is 1/10 less than the 2 in the number 3.628. Next, put a 7 in the hundreds place.” Then, I had each student write his or her answer on the whiteboard. Next, I asked each group to go through the list of answers and agree or disagree with each number. There was a lot of disagreement and justification from groups.

4.) Visual representation

Students providing answers by using diagrams, symbols, models, and/or words – Most students operate procedurally. When tasked with multiplying 2/3 by ¾, they can easily rely on background knowledge to provide the answer. But could they create models showing the operation? Push your students to create visual representations of their work.

Integrating these exercises into your math curriculum will help you create productive struggle. Productive struggle will lead to questioning, discussion, and justification which are the backbone of conceptual understanding.

My line of Power Problems are designed to target conceptual understanding of standards thru productive struggle. They are available for grades 3rd-6th.

Education, Math

How to Step Back as A Teacher To Promote Productive Struggle

March 12, 2018

Teaching conceptually means stepping back. This was incredibly hard for me. By nature, I want to help, hence why I (and you) became an educator. My first few years of teaching involved me rambling in the front of the room. While I was loving every second of my math lessons, I was doing all of the work.

Taking Away the “Think” Component

My early lessons were like the first page of every lesson in a textbook. These mostly involved students inputting numbers into blank spaces with step-by-step instructions provided. I was thinking for them. There was no productive struggle involved. I thought I was doing everything right. I had great standardized test scores, and I felt as though my students left me every year knowing the standards. However, they weren’t problem solvers, and they lacked math grit.

Stepping Back

Through time, I learned that I shouldn’t be doing all of the talking and thinking. In fact, I realized that I should be doing about 30% of the talking and that timing was everything. You need to give your students time to grapple with the task at hand. I like to do this step of the process in groups. Typically you’ll see each group member contemplate the question and then someone finally starts the conversation. It might be quiet at first. It’s okay. Don’t panic. Eventually ideas are tossed around and then the group dynamic starts to grow. This collaboration is important for developing accountable talk. Students are defending and explaining math concepts. They are living the math instead of listening to it.

Here is an example of a task I presented to my students. To kick off our studies on classifying triangles by angles and sides, I gave each group a bag of triangles. They were asked to complete the first row of the chart. I did not explain what each header meant. That was their job to figure out. After some time, I filled in the first row with students’ ideas. If the students did not mention key ideas, such as equilateral triangles always have intersecting lines, then that was my time to intervene and model.

When To Step In

If a group is struggling you need to assist. Give them a hint or ask a question that will spark an idea. What you say or don’t say will affect the group, so be careful not to give away too much information. You don’t want your students to hit high frustrations level daily, but you’re taking away the productive struggle if every time they need help you come running. This process will take time for you and your students to master. The key is careful observations. I walk around all the time during math, watching facial expressions and listening to group discussions. I let the students dictate my level of interaction. When I sense that my students need help, I give them a scaffolding clue. The productive struggle doesn’t have to cease immediately. They need a lifeline to help them advance to the next step, and that next step should never be the answer itself.

You know what they need

We’re trying to build the problem solvers of tomorrow, students that work smarter, not harder. Children that truly conceptualize math. Take it day by day and modify accordingly.

My line of Power Problems are designed to target conceptual understanding of standards thru productive struggle. They are available for grades 3rd-6th.

Uncategorized

Understanding the Difference between Procedural vs. Conceptual Understanding

February 21, 2018

What’s the difference?

Procedural understanding is when students hoard steps and algorithms. They rely on the memorization of these formulas to answer questions, and they rarely make deep connections during instruction.

Conceptual understanding is knowing the procedural steps to solving a problem and understanding why those algorithms and approaches work, similar to a recognition that there is a man hiding behind the giant head in The Wizard of Oz. This level of understanding has students reaching higher depths of knowledge because they are making connections from one skill to another.
As you plan your math lessons, ensure that you are targeting both procedural and conceptual understanding with an unbalanced approach. I use the 80-20 rule. Of the questions I pose to my students, 80% are conceptual-based. This is no easy feat when the majority of textbooks follow a 20-80 rule, where most of the work is procedural-based. We all know those textbooks and workbooks. They have 20+ rote questions for long division on a single page. As educators, we have to go after those meaningful questions.

Examples

Here are examples of questions aligned to the 4.MD.3 standard: Apply the area and perimeter formulas for rectangles in real world and mathematical problems.

This question requires students to perform two simple tasks- to select a formula and input the dimensions. Students have a 50/50 chance of choosing the right algorithm without applying any grit. There is no requirement of deep understanding of area and perimeter in this example.

There are several ways to approach this question. Carefully calculating the direction you take with your students will ensure that you target other standards as well. Acknowledge other ways to solve this question if your students choose different paths. They will feel more respected and open to other complex tasks if they are recognized for being innovative.
Starting with the perimeter, students may plug in different dimensions that total 30 centimeters and then find the correct combination that gives the total area. When I work on this question with my class, I encourage them to start with the area. This encouragement, of course, comes from me after I have let them initially tackle this question independently. Most students start with the ever popular (and easily memorized) math fact of 6 x 6 = 36, but then become frustrated when they realize that 6 + 6 + 6 + 6 does not equal 30 centimeters. Through grit, they eventually come to the conclusion that they have to identify all the factors of 36. Prime/composite numbers and divisibility rules can be revisited or introduced with this question. Select and/or write questions that allow students to make connections with other skills.

Take the time to find materials that require your students to deeply evaluate curriculum. With specific questioning you’ll be able to cross over the threshold from procedural to conceptual understanding.

My line of Power Problems are designed to target conceptual understanding of standards. They are available for grades 3rd-6th.

Check out this preview for a closer look at the Power Problems line.