Are 3rd Graders Too Young for Proportional Reasoning?

       

     Getting third graders to think proportionally is a fantastic way to encourage modeling, and to “prime the pump” for proportional thinking when working with fractions. Simple proportional thinking can be so clearly seen with models that it is accessible to all students. There are so many real-world contexts relating to proportions that are near and dear to a third graders heart! Think about candy, carnival prizes, field trips and much more.

     An added bonus – math work that lends itself to modeling and is easy to justify with a model. I asked students to examine a small bag of M & Ms. Based on the number of each color in the small bag, students needed to figure out how many of each color would be in a giant bag of M & Ms. Students were busy grabbing their colored pencils and large mat papers before we even answered the last “need more information question”.

     Added, added bonus – many students were able to make a connection to multiples with this activity. Some students began to take shortcuts, which is just really using math in the most efficient way, by using ideas of multiples.

Explore My Store @
https://www.teacherspayteachers.com/Store/Math-It-Works

 

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!

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 Workshttps://www.teacherspayteachers.com/Store/Math-It-Works

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!