Saturday, October 22, 2016

Calling All 5th Graders!

Get Ready to Problem-Solve

One of my favorite strategies I use when problem-solving is to work backwards. So when I think of a problem that almost forces you to work backwards, it gets put into play! This is a volume problem so your students may not be ready yet, but keep it in mind when you're ready to teach volume.

Question: What are the dimensions of the box below?
What we know:

*** The total volume is 54 cubic inches.
*** The box is twice as long as it is wide.


There are several ways students could approach this problem. They could guess and check, which is a great way to plunge in and begin solving a problem! As a teacher, I would be paying attention to what numbers they begin with. After working with multiplication for awhile, we hope that students understand how quickly, or exponentially numbers can grow when multiplying, so smaller numbers are called for here. 
Another strategy might be to divide 54 by 3 and start there. However,  if the length, width, and height are 16 inches each, the resulting volume would be much larger than 54 inches cubed.
I played around with factoring numbers and working with primes, which was fun, but a little beyond 5th grade standards (not that they couldn't do it!). 
As a fifth grade student, I'm pretty sure I would have worked backwards - first thinking of an even number for the length and half of that number for the width. Say, 8 and 4. Then I would see if I could make the height work. 
This particular problem is great because you can substitute so many numbers to make it more difficult, even sneaking in a decimal!
Have fun!

Saturday, September 17, 2016

Should I Go All the Way with Multiplication Facts?

I've been getting a lot of questions from 3rd grade teachers whether they should teach multiplication facts through 9 (Common Core State Standard 3.OA.7; By the end of Grade 3, know from memory all products of two one-digit numbers), or push ahead and work on products involving factors of 10, 11 and 12. 

Most 3rd grade teachers will tell you how difficult it is for students to achieve complete fluency by the end of the year, so piling on more facts is the last thing they want to do!

However, working on strategies to learn double digit multiplication facts is a fantastic opportunity to illustrate, and reinforce key learnings from 3rd grade.

It is essential for 3rd graders to learn how to multiply a single digit by a multiple of 10 as quickly as possible. Aside from being a great preview to the work they will be doing in 4th and 5th grade with base ten, they catch on quickly and this one skill will take them far in the world of multiplication. Think about it; 12 x 5 becomes (10 x 5) + (2 x 5). Students can quickly go from paper and pencil to mental math. After doing this enough times, the answer becomes memorized. 

3rd graders already need to conceptually understand the distributive property of multiplication (Common Core State Standard 3.OA.5). By decomposing 2-digit numbers to multiply easily, they will be using the distributive property over and over again. 

Finally, there is one secret math move I always show 3rd graders once they are confident multiplying by 10. I write 5 x 18 on the board and ask them to solve it different ways. Providing a student doesn't think of this strategy, I write: 10 x 18 = 180 and half of 180 is 90. All of the oohhhs and aaaahhhs are music to my ears!
Math - It Works

Friday, September 2, 2016

Creating an Anxiety-Free Math Classroom

One of my very first math lesson is about making mistakes. I tell my students that I LOVE math mistakes because it is the best way to start discussions, talk about out work, and teach us how to prove and justify our work. I can almost see my students breathe a sigh of relief when they realize I am not expecting them to magically perform perfectly!

The truth is, many students come to math with anxiety. Their beliefs about their abilities are tied to their self-esteem and for some students math can become  something to avoid at all costs. 

There are some things we can do, as math teachers, to alleviate children's math stress and create a safe, and supportive environment for learning math. 

1. Talk about the importance of errors. Students should look at errors as a way to learn. Jo Boaler's new book, Mathematical Mindset addresses how making mistakes grows our brains and is part of the creative process. 

2. Avoid timed tests. Timed tests create huge anxiety for students and many are beginning to rethink how effective these are in getting our students to fluency with their math facts. 

3. Provide opportunities for team work. Students can feel a sense of security when working with the support of others. Building a group consensus can build communication skills and self-confidence. 

Grab the ERROR poster as a Freebie!

Tuesday, April 7, 2015

How I'm getting 3rd Graders ready for Performance Tasks

Last year I began seriously looking at released items from Smarter Balanced, especially the performance tasks. "Wow!" I said to myself. "We've got some work to do!"

Although it is exciting to see that students will be using math seamlessly to solve real-world problems, it is daunting for classroom teachers. We have always focused on the learning of math, rather than the "using" of math

With a colleague of mine, we devised a plan. Every week, for an hour and a half, we would have students work on extended tasks that use multiple standards. We would focus on the process, not so much the answer, and we would praise, praise, praise students for their perseverance. 

Each week we would build a performance task a little harder, and a little longer as students built up their stamina and confidence. We wanted students to use different strategies to solve problems and to feel like although it was hard, it was possible to complete the task. 

Each Friday we worked with students, and each Friday at lunch, we sat and discussed what we had seen, and heard. We pondered why certain things were happening, like why students were using repeated addition for a problem that clearly called for multiplication. We thought about the right type of help to give students so as not to enable them right out of problem solving. 

So, a short recap of what we learned:  1) It is just as much about the process as it is the answer. As students actually see the improvement in "time on task" and their ability to stay focused, they become engaged in the task. 2) These tasks are hard! Our 3rd graders were using a lot of brain power to work through them. Therefore, when students kept using repeated addition until January, we didn't intervene. Repeated addition was comfortable for them, so that is what they used! 3) Scaffold, scaffold, scaffold. When we "threw" in graphs before they had worked with them and we asked them to do difficult tasks with the graphs, it was a disaster. Fast forward to a task after they had worked with graphs during class, and the task was no problem. 4) Celebrate the feeling of accomplishment when finally solving a problem - there is nothing better!

I've started bundling these tasks and putting them in my store. I'm really excited to see how these 3rd graders do on their state test!
                                               Math - It Works

Math - It Works

Friday, January 2, 2015

The Best Place Value Experience for 2nd Graders!

2nd graders need lots of experience decomposing numbers as they work with place value concepts. I often see these guys carefully pulling numbers apart: "167 is one hundred, 6 tens, and 7 ones". They are correct, but are they truly understanding place value with this exercise or just memorizing hundreds, tens and ones?

To check whether students are really thinking things through, I introduce an activity with brown paper bags. Inside the bag are flats (100s), rods (10s) and cubes (1s)

I label the bag with a number and fill the bag with a different combination of base ten blocks. Students are not allowed to open the bag!

They can pick it up to feel the weight, they can shake it up a bit, but they can't look inside. They need to make an educated guess about what combination of blocks are inside the bag. 

The bag labeled 147 can be composed of different combinations:
147 cubes
1 flat, 4 rods and 7 cubes
1 flat, 3 rods and 17 cubes
1 flat, 2 rods and 27 cubes
1 flat, 1 rod and 37 cubes
1 flat, and 47 cubes
14 rods and 7 cubes
and so on...........

It is a lot of fun for students, and as they record their guesses, they begin to really delve deeply into the concept of place value. 

Saturday, November 29, 2014

Volume Within Volume

Students need to be able to think about volume both spatially, and mathematically. They also need to model with mathematics. I recently created some problems around volume that have students determining how many smaller boxes will fit into a larger box.

Students can actually think about it spatially and use manipulatives or mentally determine how many smaller boxes will fit, or they can determine it mathematically by finding the volume of both small and large boxes, then dividing. While I was at it, I created many different problems that have students working with volume in a real-world context. The 5th graders I worked with loved working on these problems and began to notice patterns with multiples and factors. 
Math - It Works
TPT Volume Within Volume

Saturday, November 8, 2014

Free Formative Assessment Idea

As math teachers, we work really hard to assess whether students are learning, how deep their understanding is, and how well they are self-assessing their own learning. Recently I have been trying a new type (well, new to me) of formative assessment. I used large note cards and put a green, yellow and red circle on one side. 

Towards the end of a lesson, I ask my class to hold up the card with their finger over the color that represents their stage of learning. 
Each color is tied to a specific phrase. 

Red means: "I really don't understand. My learning stopped when......."

Yellow means: "I'm starting to get it. I still don't understand ......."

Green means: I understand it well. I would like to know more about......"

These can be used as exit tickets where students have to write out the answers to whatever color they chose. Once students are adept at pinpointing where they are in the learning process, they can begin to verbalize it - making it easier for us to adjust our instruction.

Math - It Works for Common Core Activities, Assessments, Games and More
Teachers Pay Teachers

Premade Blog Design by Delicious Design Studio