Tag / math

by Beyond Traditional Math

Writing Clear Learning Targets in Elementary Math

If you missed it, I’ve already lamented about my lack of organization with learning targets. When I started to rethink this whole learning target thing, I knew that teaching in isolation was no longer going to work. This happened to be the same year that we had a new teacher join our six person team. Her joining this team started a transformation, we realized that we should be planning together, and even though our learning targets might be the same, we’d still have our own spin on how we taught it.

So we started with math, because math learning targets seemed manageable. We also started with our text as a resource.  We already had a curriculum/pacing guide set up, but it happened to align with the textbook, and it had been written almost a decade ago.  So we looked at both learning targets, and the pacing of our content at the same time.  It was not easy, but it was some of the best math conversation I’ve ever had with other staff members.

We transformed our learning targets little by little. We did the first unit together, then we split up and trusted one another to do future units.  It was amazing. Our learning targets went from complicated and confusing, to clear and concise.  Most importantly, they became student friendly.

Here is an example:

Writing Clear Learning Targets

We took the long and wordy objective from the book, and converted it to what the student must absolutely be able to do.

What was listed in the book was wordy, long and full of teacher noise.  In this case, this is a HUGE objective, writing and reading numbers that are both 3 and 4 digits, especially when written in various ways (standard form, word form and expanded form). We asked ourselves 2 questions to narrow it down.

  1. What is it that the student must absolutely learn? (What is essential for the next grade level?)
  2. What does the student need to be able to DO as the END goal?

This original learning target:

Students will read and write 3-digit and 4-digit numbers using place value understanding.  Students will use expanded, standard, and word form when working with numbers.

Became the following two targets for two days of instruction:

I can read and write numbers up to 1,000.

I can read and write numbers up to 10,000.

We used this common assessment at the start, middle, and end to find out what they already knew: Number of the Day Quick Check (FREE!)

I will not lie, the process was a little hairy to start. Many of us struggled with the rest of the objective…why aren’t the various forms of numbers included in the target? Why don’t we use the words place value in the new targets? We came to the realization that all of THAT comes into play during your instruction.  Students find out those words as you play with and explore the numbers.  In addition, teachers give them success criteria so that they know what it means to read and write numbers up to 1,000. Once we had that understanding, it became easier and easier to write clear learning targets.

Stay tuned for more on success criteria in my next post.

 

 

Advertisement
by Beyond Traditional Math

Sometimes They Explain It Better Than You

As much as my ego doesn’t like to admit it, often times my student’s explanations of math concepts and processes is WAY more effective than mine.  In the past I would actually make myself a little crazy as I tried to think up 15 different ways to say the same thing to teach a tough concept. Then, one tiny little 8 year old would trot up to the board, say it perfectly, and the light bulbs would go on.

During a response day, when I noticed that students were struggling a bit with perimeter, I made tiered/leveled posters around the room of perimeter tasks.  Leveled posters allow for differentiation, and they are also formative so that you can see who is meeting your learning target vs. who is not.

For example, this learning target was: I can calculate perimeter when a side is missing.

  • Level 2 (basic): all the measurements were labeled on all of the sides of the figure.
  • Level 3 (proficient): one side of the figure had a missing measurement.
  • Level 4 (advanced): more than one side was missing their measurements.
Perimeter Task

Level 3 Poster: The students had to add the two sides that were known, to find the unknown side. (The two in the corner signifies that this is the second problem as they numbered their papers.)

Their goal was to try to get through them all. The problems were numbered, so they simply numbered their half sheet of paper and tried each one.  I tell them ahead of time what it means when they successfully answer each problem.  They knew the levels and consequently tried hard to get all three. (No one got the Level 4 problem, very close, but not quite!)

Perimeter Task

Level 4 Poster: This one perplexed even my accelerated gifted and talented student. He missed the insides of the figure.

My favorite part is the math talk session where they discuss their answers with each other. We move from poster to poster, and students speak up and share their thinking. I don’t have to say a word.  You hear a lot of shouts of understanding and mistake finding as they explain.  Again, it is okay for me to take a backseat. I don’t have to blabber my mouth (for double the time) when very quickly they speak to each other.  When everyone is stuck, that is when I step in.

When students do the talking, they do the learning!

 

by Beyond Traditional Math

Classifying Shapes Using Tangrams

Since our geometry unit is so full of vocabulary, I am always looking for ways to have students apply the vocabulary to new situations. After learning how to make our own tangrams yesterday, we took it to another level today. We decided to sort and classify the shapes that make up the tangrams. Because we’ve spent a few days describing two types of polygons: triangles and quadrilaterals, we had some really nice anchor charts up on the wall.

Their task today was to classify and describe the shapes from their tangrams using sides and angles. This meant that some of their shapes could be described in more than one way. This was a really cool opportunity for students to participate in math talk, and it was even better to see them using the anchor charts we made together:

Classifying Triangles

The student on the right is trying to classify his triangle by looking at angles.  The student on the left quickly realized that he was holding a shape with four sides.

Classifying Quadrilaterals

This student is checking to see if all four of her sides are equal, as well as if there are four right angles in her shape.

There is nothing better in a math class than hearing students argue over whether something is a right angle or not. Hearing words being used authentically was really cool, especially since they could actually touch and manipulate the shapes! I’ve really taken geometry a long way since I started teaching (ahem…I used to use worksheets only…please don’t judge me!), and the terms and vocabulary has started to stick because of it.

by Beyond Traditional Math

Real Life Examples of Geometry

The number of terms that students are expected to learn in geometry is a little crazy.  We counted 30 different new vocabulary words at the end of four days of instruction.  So I checked out an iPad cart and decided to have the students find real life examples of geometry in the world around them. After introducing the symbols, and describing each term’s features…they solidified their understanding of each new word with photos. (We pulled out some of the trickier ones from our minds as well.)

We recorded the findings on a giant chart!

Real Life Examples of Geometry Terms

Students captured real life examples of: point, line segment, line, ray, intersecting lines, perpendicular lines, and parallel lines with iPads.

It was both motivating and fun to use technology, as well as promote math talk in the classroom.

by Beyond Traditional Math

Earth Day Water Pollution Activity: A Cross Curricular Inquiry Study

Today was one of those magical days at school. It was the kind of day that makes me LOVE my job, where all the pieces go together very nicely and the worldview expands for the students in the classroom. Today was one of those “teach like a pirate” days, where we took risks and immersed ourselves fully into an important issue.

We began our Earth Week (not just Earth Day) by learning about the Great Pacific Garbage Patch, something that is largely unknown to the general population.  We read about the issue with a two page informational text today, while responding in writing with our new understandings.

Then we watched this video:

earth-day-activity-great-pacific-garbage-patch-for-kids

 

After lots of important discussion, I asked them a question, “How would you clean it up?”

That led to an awesome water pollution experiment, which ended up both engaging and frustrating the students.  The groups had to try to clean up the water using the least amount of money possible.  They had to write out their plan as a group together, figure out the cost and bring their proposal to my supply table to collect the materials they needed to clean the water. They had to be detailed and precise, use math in a very real way, and had to work under time pressure. Here is a peak into what it looked like:

Earth-Day-Water-Pollution-Activity2

Buckets were prepared with water and biodegradable items like coffee grounds, shredded paper, food that the kitchen hadn’t served but had to throw away, and soil.

Earth-Day-Water-Pollution-Activity6

Reused or recyclable items were for sale for students to use to clean up the water. (I wash out the cups and forks to reuse each year for this experiment! We reuse ziplock bags collected throughout the week.  We recycle other plastics and aluminum foil.)

Earth-Day-Water-Pollution-Activity6

The students cleaned the water after “purchasing” materials.

Earth-Day-Water-Pollution-Activity5

Many methods were used to clean the water.

Earth-Day-Water-Pollution-Activity3

We compared water samples at the end, to see who was most successful. We also compared budgets, to see who was able to keep costs down.

We’ll continue this work for the rest of the week:

  • We’ll be writing a letter to explain what we learned today about the Great Pacific Garbage Patch and the difficulties of cleaning up water.
  • I plan to immerse them in lots of good Earth Day literature like: The Great Kapok Tree by Lynne Cherry, Oil Spill by Melvin Berger, The Lorax by Dr. Seuss, The Wump World by Bill Peet.
  • We’ll be learning about alternative energy to make wind powered cars later in the week, and we’ll even try to harness the sun by measuring and making solar ovens.
  • We’ve also got some tough math problems in the works as part of the Great Pacific Garbage Patch unit to help us think about conserving!

I love Earth Day…Earth Week, and more importantly introducing important issues to our young learners, encouraging critical thinking in meaningful ways.  I’d love to hear what you do in your classroom! The more ideas we have to share, the more we can teach our children to be environmental stewards.

Learn more with these resources and dig deep into the issues:

Earth-Day-Great-Pacific-Garbage-Patch-LessonEarth-day-activity-for-kids

by Beyond Traditional Math

Fraction Tile Strategy: Hide the Labels

I used to tell students WAY too much when introducing new concepts in math, and I neglected to let them discover things on their own.  When students are told what to think, I believe that it limits understanding. I used to stand up in front of my students and talk about fractions by telling them which ones were halves, thirds, quarters, etc. It is embarrassing to admit that I would teach that way, but now at least I can share what I’ve replaced that method with…lots of inquiry based hands on learning.

Today the learning target was: I can use benchmark fractions to estimate. After spending lots of days in a row with tangible real world concreteness, it was a big leap to move to representational models of fractions. We pulled out the fraction tiles (basically harder versions of fraction strips) that came with our new math series.

Fraction Tile Strategy

You’ve seen these, you may even have them, If not there are likely a dozen free ones out there that you can print and cut. Just try a web search for “fraction strips” or “fraction tiles”.

After we took them apart, I had them flip over the entire thing, putting the red whole number 1 at the top.  There were a LOT of confused faces, and even one student said “how will we know what they all are?” I asked them to trust me and luckily they do, so they flipped them over. Then, I asked the same question that the student had just asked. How do you know which one is which? Which one is 1/2, 1/4 or 1/3? A few students right away started to lay them on top of the red whole piece like this:

Fraction Tile Strategy

Flip over the tiles so that the labels are NOT showing.

After a little buzzing with their partner, they all pointed to the pink one immediately for 1/2.  It took them only a few more minutes to identify the 1/3 and 1/4 sections.  When we talked about how they discovered this, there were a couple of cool things they noticed:

  1. “I just counted, if there were two of one color, I knew it was two halves! If there was three, I knew it was thirds.”
  2. “I lined them all up below the whole tile to see how many could “fit” in one whole. Sometimes I didn’t need to fill up the whole thing, because I could just tell.” (Boom! Learning target met!)
  3. “I counted them and stacked them, as I they got smaller, they got taller.” (I really like the size thinking there.)
Fraction Tile Strategy

These students counted and stacked each one to figure out the fraction piece label. Then they noticed the sizes of their fraction tile stacks began to grow!

Giving them time to explore has made fractions way less intimidating. The models came much easier to them when they didn’t have confusing labels staring them in the face.  I am definitely a fan of using fraction tiles/strips with the labels hiding.  What an awesome way to get them to estimate using benchmark fractions.

Tomorrow, we’ll explore equivalent fractions with these same strips, and try to connect it to the real world.  I can’t wait to see their thinking!

by Beyond Traditional Math

3 Hands On Earth Day Activities that Integrate Math

Here are three really amazing Earth Day activities for your elementary classroom that all include math. I’ve done them all and they’ve been memorable, educational, and fun! The best part is they always lead to deep moral and ethical conversations.

1.  Hold a Trash Free Lunch Picnic:  This is a two day project.  The first day, you ask the students to keep track of how many pieces of trash they have as they eat lunch.  For the second day, you send home a note asking parents to pack a trash free lunch, (as trash free as possible) to see if you can cut down on the amount of trash.  On the day of the trash free lunch, you ask the students to count how many pieces.

Earth Day Activity Trash Free Lunch

Here is an example of a student’s trash free lunch.

 

We kept track on a tally chart and realized the impact we can have if we change one simple thing, how we pack our lunches!  Then, the students draw a bar graph or a pie chart to show the results of the tally chart.

Earth Day Activity: Trash Free Lunch

Record the data of a trashy lunch vs. a trash free lunch!

2.  Build a Solar Oven and Bake S’Mores:  Show a tutorial for how to make a solar oven a few days before Earth Day.  Here is one that could be made from a pizza box!

Tell the students to bring their own supplies from home (cardboard boxes, plastic wrap, aluminum foil, tape) and give them time to make them when they first get to school.  It took our class about 2 hours. The math involved is awesome, measurement, measurement and more measurement! I brought the graham crackers, chocolate, and marshmallows and they melted like crazy in the sun. It was super fun! Here are a few photos.

Earth Day Activity: Build a Solar Oven

Students bring in their own materials, but you may want to have some extras on hand.

Earth Day Activity: Build a Solar Oven

This student even put a skewer in the middle of the oven, too bad they decided not to use it in the end.

Earth Day Activity: Build a Solar Oven

Some students learned the hard way that you need to CLOSE the solar oven!

3.  Study an Important Environmental Issue and Act on it: Perhaps the best Earth Day activity we’ve done is something that felt meaningful, like we could make change happen!  We studied the Great Pacific Garbage Patch by watching videos, reading about it, doing some math problems surrounding conservation, and by writing persuasive letters.  We ended the project by doing a water pollution science experiment.

Here is a video about the Great Pacific Garbage Patch if you haven’t heard about it (Depending on the age of your students, you may be able to show it to your class.):

Here are some photos of us trying to “clean” water, so students could find out how truly difficult it was.  As they work, each tool they borrow from me costs them money. They have to keep track of the cost of their clean up.

Earth Day Activity Water Pollution Experiment

Students are trying to clean out a polluted basin of water using different tools (all of which cost different amounts of money). They keep track of their successes and the cost of cleaning out their basin of water.

Earth Day Activity Water Pollution Experiment

A student is trying to remove vegetable oil from their basin of polluted water. NOT easy!

The bottom line, is there are so many things that students can do to learn about alternative energy, and to study current environmental issues. Instead of encouraging them to recycle with a coloring sheet or a worksheet, engaging them in these issues will help them feel an authentic push to do it!

I love Earth Day and the awareness it brings to young people! What kinds of things do you do with your class on Earth Day? Share below in the comments. 🙂

by Beyond Traditional Math

Discovering Numerator and Denominator with a Pan of Brownies

The way to a child’s stomach heart brain is most definitely with sweet treats. While I don’t like to sugar up my students, I do like when they can connect math to the real world.  That was exactly my mission when I brought in a pan of brownies.

Example of Real World Fractions

If all else fails, capture their interest with food!

So far at this point, we had examined the definition of a fraction, and thought about things that come in halves and quarters.  It was time to move into some more new vocabulary, the numerator and denominator of a fraction.

In came the pan of brownies.  I brought it over to a large rectangle table and had them all gather around me.  As they were salivating I asked them how I could split this pan into fractions so that we’d all get an equal amount.  I asked them to draw what that looked like in their math journals knowing that we had 25 students in the room.  This was easier said than done.

For some reason, a bunch of them abandoned the hard work we’ve done with arrays, and started drawing diagonals and squiggly lines all over their papers.  It was like they heard the word “fraction” and felt they needed to abandon everything they knew for this brand new concept.

*Sigh*

Then, I asked them to start sharing solutions, and we started to get somewhere. Arrays popped up on the chalkboard, 2 x 13 arrays (“I didn’t want to leave the teacher out!”), a 5×5 array and a 3 x 10 array.  I asked them which one would get them the best deal.

The settled on the 2 x 13 model so that I could get a brownie (how kind!).  That was when I began cutting.  I handed out the first one and asked them to think about what fraction of the brownie pan they were getting. That was when I introduced the fraction in number form and explained the difference between the numerator and denominator. The numerator was the number of pieces they were going to get to eat, and the denominator was the total pieces in the pan. For example (Hint: This is not the actual pan of brownies I used, since the cuts became VERY small and very messy…they were super gooey! So…I had to whip up another batch tonight for this picture, YUM!):

Real World Examples of Fractions

The numerator and denominator suddenly became clear!

They didn’t REALLY get it though, until the last person got their brownie. At that moment, I gave her my piece, telling her how proud I was that she was so patient to wait and be last. That was when the numerator part really sunk in, because I announced that she was getting 2/26 of the brownie, while everyone else only got 1/26. It was a lesson in patience as well as a lesson in math.

It was a pretty sweet mini lesson!

by Beyond Traditional Math

Third Graders are Googling the Answers to Math Assignments?

My jaw literally dropped when I received this email the other day:

Assign Rigorous Problems

Let me explain two things to give you a little background:

First, I have a “contact me” section on this blog, for anyone who may need to get in touch. I received this email through that form.

Second, I recently put out a free resource called Doggy Dilemma for teachers.  It is an open ended problem that requires a lot of reading, writing and thinking.  There is no immediate answer, and all students would have a different answer in the end.

So…by the powers of observation and inferencing I can only conclude:

  1. This person who contacted me is a child that has received the assignment in class. (I am thinking this due to the lack of punctuation, capitals and misspellings. The “voice” of the writer seems very young, also.)
  2. This person is likely a 3-5th grader (since that is the target age group of the problem).
  3. This person is incredibly resourceful and bold. Not only does she google the problem, but she thinks to contact the author of the problem for an answer!

After I got over the shock of receiving this message I thought to myself, THIS is why I create what I create. No child should be able to google the answers to a great math problem.

What do you think about this?! I would love to know your thoughts.

 

by Beyond Traditional Math

Things That Come in Halves and Quarters: The Real World Connection

Whenever I have connected math to the real world, I’ve seen a boost in achievement in my classroom. Fractions are REALLY important concepts that must be connected to student’s lives. When I first started teaching, I would just plod along in the book. I would hand out worksheets with rectangle boxes that students would just fill in.  They’d write the numbers without really connecting it to much of anything. It was kind of a disaster!

Now, I love to collect real world examples, and put them on an anchor chart.  Because fractions are so abstract, we put this anchor chart together after brainstorming with a partner first:

IMG_8500

 

On the student planner that day, I put an assignment to look for things that come in halves or quarters at home as well. We can always add more! Now, each time we talk about a fraction, we try to picture something from this list.

I am hoping that these concrete examples will really help them understand when I move them into representational symbols and numbers.