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Math

Teaching with Math Misconceptions

Math
I love using Number Talks and CGI strategies in my math class. We recently had our CGI trainer visit and she mentioned that you can also do Number Talks while clearing up math misconceptions. I loved the idea and decided to give it a try when we were learning subtraction.
With subtraction, one of the misconceptions I noticed, was that students seemed to think when you regrouped you just put the number there. For example, if you were regrouping 100 you just put 100 there and the tens that existed before just went away.  I noticed a few of my students doing this when regrouping with hundreds, tens, and ones so I decided to have a little math misconceptions talk.
I first wrote this problem below on the board. I told students this was the math work from a former student and I wanted them to look at it and see if they think they student got the answer correct or wrong. If they got the answer correct, then you need to figure out how you know that. If they did not get the answer correct, where did they make a mistake in their work. I posed this problem and gave students a few minutes of quiet think time.
After a few minutes of think time, I had the students turn and talk and discuss with their partner what they noticed. I had some students who thought the answer was correct and some who thought it was incorrect. I asked students who felt strongly about both to explain why they thought they were right.  The children who thought it was right were some of my students who were making that same mistake.  As they were explaining why it was right, I asked them – where did the 20 go that was already in the tens spot? I then had many aha’s around the room. I had a child who thought the answer was incorrect walk us through the problem and corrected the original work. I showed this in a different color so we could see the misconception.  See the new work below…

 

This was an amazing class discussion and I plan on having many more Math Misconception Number Talks. I think it’s important for students to always be thinking and observing their work and others when we are sharing out.  This is a great way to go over mistakes that you are seeing and it points it out in a way that doesn’t make the child feel bad.  It empowers them to see the mistake in someone else’s work (I always say a former student and make up a name) and then they are more likely to catch it themselves when they do it.
Do you use Number or Math Talks in your classroom? Comment below…

 

Teaching Repeating Patterns Ideas

Math
We recently worked on patterns in math. In second grade, students work on repeating patterns and growing patterns.
Students have typically been doing repeating patterns for a long time and are able to identify the next shapes or letters so we add more to it in second grade. In addition to identifying the next part of the pattern, students also need to be able to identify the unit, create their own pattern, and identify what the 20th shape would be and so on.  This takes things up a notch and it’s interesting to see the different strategies they use to figure out the 20th shape, 40th shape, 55th shape, etc.
Here is our anchor chart we created as a class.
In addition to small group work and patterns practice on IXL, students also worked on the Repeating Patterns Task Cards. These can be found in my TPT Store (Jordan Johnson).  This includes 20 task cards that ask different types of questions all revolving around repeating patterns.  A recording sheet and answer key are also included. This worked well as an activity during my math rotations, but could also be used in small groups, math stations, or as a review activity.  Check it out in my store…here

IXL

Math

So I don’t know what I did before IXLIXL is an online practice program that has language arts, math skills, and more. My school just purchased it for our grade level and I love it already! The kids also love it too and ask to play it! That is a refreshing change from the groans I used to get when we’d work on some of our other math programs.  We’ve mainly been using IXL for  math so I’m going to share a few of my favorite things about it….

Image result for ixl

  • Differentiation
    • With IXL you have access to multiple grade levels and skills, which allows you to have kids move at their own pace.  I teach second and I can use first grade practice for some of my struggling students and use third grade practice for students who have mastered the second grade skill and need a challenge.
  • Real Time Data
    • This is the best part of IXL.  They have real time data. I can have my students working on IXL in class and/or in study hall and see exactly how they are doing and what they are doing. It lets you know if a student has missed so many and is struggling and needs help.  This instant access to how they are doing is fantastic!
  • Multiple Skills
    • As I mentioned in my differentiation point, there are many skills for each topic. For example, we’ve been working on patterns. It has repeating patterns and growing patterns and different variations of each. I love that there are many options and that it covers so many math and language arts skills.
  • Instant Feedback for Students and Teacher
    • This is why I like using it especially for homework. Feedback is instant. Once the student submits their answer they know right away if they got it correct or if they got it wrong. If they got it wrong it coaches them through some tips to see what they did wrong.
  • Appropriate amounts of practice 
    • I’m not a fan of worksheets and I’ve been saying this for years. I do not think every child needs to be doing 50 problems on a worksheet to show they have mastered something. Some kids do need more problems to demonstrate mastery, but some can demonstrate it in 10 problems instead of 50.  As they get problems right on IXL, it moves them closer to 100 as they get them wrong the lose points. It gives them the practice they need. If a child understands the skill it gives them a few problems to show that and then they are done.  I like that it isn’t drill and kill – a billion problems that many students do not need.
So there you have it – some of the reasons why I love IXL. I’m still learning so I’m sure there are more features, but I am a fan so far!

Ideas for Teaching Rounding

Math
Every year, without fail, rounding has been one of the harder concepts to teach and one of the harder ones for kids to understand. Before starting our unit this year, I did a little research on Pinterest and came across this aha moment and wonderful idea from Mr. Elementary Math – vertical number lines! While yes a horizontal line will work, it’s confusing when we tell kids to round up and down because on a horizontal line you’re really moving left or right.  This is where vertical number lines come in.  You really are rounding up or down and visually it’s much easier for kids to see. Check out Mr. Elementary Math’s ideas for interactive number lines here
Here’s how I started my rounding introduction….
So, we started by creating a list of multiples.To make it easier to figure out the two numbers that it was between, we created a list of multiples of ten and multiples of 100. While yes most kids are quite capable of counting by 10, it’s amazing how when you are talking about rounding some of those common skills go out the window.
Then, we created the anchor chart below and went through a few examples together…  Here you can see the vertical number line in action. The lower number goes on the bottom of the vertical number line and the higher number goes on the top. Then the kids place the number and see which it is closer to.  Then, they literally round down or up depending on where the number is. This made rounding so much easier for so many of my students!
To review – we played this rounding game called Roll It. This game is from Game for Gains and can be found….here….
Want a FREE rounding game to use in your math centers tomorrow? Learn how to play this differentiated Roll It! Rounding Game. You'll even get our free game boards to use!
Hope these tips are helpful for you!  Vertical number lines have changed how I teach rounding and I’m so glad I found it!

Ideas for Teaching Properties of Addition + a FREEBIE

Math
We recently finished up our unit on Properties of Addition. This is always a tough unit for kids.  While they are able to add – being able to identify the properties and figure out missing numbers has always been challenging.
Below is the anchor chart we created together the first day after exploring each property using a balance scale…see below.
I saw the balanced scale idea online.  Using unifix cubes/snap cubes you can show each property and the balance scale is perfect because it shows how things are equal no matter what order they are done in.  The picture below shows the Associative Property.  We had (4+2) + 3 on one side and then (3+2) + 4 on the other. We discussed how both equals 9 and the scale is balanced because it’s the same sum. This then led to the chart discussion about how it doesn’t matter which way you group the numbers you’re adding – the sum will still be the same.
After learning the three properties, I had students practice whole group. I projected my Properties of Addition Practice (a freebie in my TPT store) on the board and students responded to the questions on their individual white boards. 
Below’s slide is asking them to identify which property is shown in the equation…
This slide is asking them to find the missing number that goes in the blank.  We talk a lot about how you want to look and see which numbers are there and which one is missing. Since you see 2 on the other side and not 5 – 5 must be the missing number to make this equation equal.
If Properties of Addition is something you teach – check out my freebie! Great way for kids to practice this skill whole group.

Ideas for Teaching Subtraction

Math
We recently finished up our unit on subtraction and I wanted to share with you a few activities and things that we worked on. I teach second grade and our goal is for students to be able to subtract 2 and 3-digit numbers with and without regrouping. We also use CGI (Cognitively Guided Instruction) at our school so there is more than one strategy that can lead you to the correct answer.
Below is the anchor chart that we created as a class. We worked on a different strategy each day.  Day 1 was place value. I started off with a story problem and then had a student share who had used that strategy. Then, we added it to the chart and practiced whole group and small group. This continued until each strategy was added. After practicing and trying each strategy, students were able to pick the strategy that works best for them.
I use a lot of small group instruction now during math and we have math rotations 3-4 times a week. Here one of my groups is working on a 3-digit subtraction problem. As you can see, everyone is solving it in a way that works for them!
Also during rotations we have game time.  I introduced Subtraction Memory first. Subtraction Memory is a game that focuses on 2-digit subtraction. There are two versions. One version doesn’t have regrouping and the second version has problems with and without regrouping for differentiation.  It can be found in my TPT store…here

 

As the week continued I changed the game up.  Later in the week students worked on Subtraction True/False Sort. This activity is also differentiated to help all learners. Version 1 has 10 problems to sort and the problems are a little simpler. Version 2 has 20 problems to sort and they have more difficulty. This is a great activity for students to practice the different strategies and work together to see if the problem is true or false.  This can also be found in my TPT store…here

Check back later this week for another round of math ideas – this time for Properties of Addition and it will include a FREEBIE!

Story Problem Tip #4

Math
Today I’m sharing with you my last story problem tip for the month! If you missed my past tips, check them out below…
Today’s tip is all about students creating their own story problems. Another way to get buy in and engagement is to let students write their own story problems.  Students love it because it can be about what they like and can be about themselves or their friends. This also offers a chance for differentiation. Some students can write multiplication problems, while some might still be working on addition.  Students can also be working with numbers that fit their comfort level.
The other neat thing you can do is let other kids solve their story problems. In the past, after having kids write their own story problems – I type them up and then have the class work on them.  They loved it!  While it can be “fun” solving the teacher’s problems, it’s even better solving their friends.
If you are interested in this tip, check out my Create Your Own Multiplication Story Problems product on TPT here

Story Problem Tip #3

Math
It’s Tuesday, so I’m back with another tip for using Story Problems in the classroom.
For past tips…
So, today I’m sharing tip #3 with you.  My third tip is to let students share their strategies with each other.
Every Friday in my class we do two story problems. Both story problems are similar – meaning same type, same operation, but different numbers.  I read the first story problem to students and then send them back to their seat to solve it.
While they’re solving, I circle the room and check out what strategies they are using. I then selectively pick a few students to share their strategies with the class.  By selectively, I mean I pick strategies we’re focusing on or efficient strategies that I’m hoping more kids will use. I also pick a variety. I do not typically have the same strategy shared – I choose all different ones.
Then, I have each child that I picked come up one at a time to share their strategy with the class.  The audience is supposed to pay attention and see if they can pick up  new strategies that they could use next time. This is also great for kids who didn’t get the right answer or didn’t know how to solve it. They can now see how their classmates did it and get ideas from them.
I normally use my iPad stand as a doc camera and project their work on the board. The child presenting stands up and explains how they solved it. Some students can explain on their own, while some need some probing questions to get all of the info out.  The pictures below are from a day when technology was not in my favor. I had the students who were picked write on the board how they solved it. While they were writing they explained what they were doing.
This tip is great for many reasons. It lets students teach each other. Students get tired of hearing us all day so it’s nice when they can hear the same thing from someone else. It provides opportunities for math communication, which is a huge part of math nowadays.  It also builds math confidence.
Check back next week for my final story problem tip!

 

Story Problem Tip #2

Math

As I mentioned in my post about Story Problem Tip #1, story problems are a huge part of math. It’s so important that we provide students opportunities to use math with real world situations.  Last week I talked about how students tend to dread word problems. The see words in math and tend to freak out – it’s just supposed to be numbers! That’s why I started this little mini blog series.  You can find tip #1…here

So, for tip #2 to make story problems a little more fun, let the students choose their numbers. A huge part of differentiation is choice.  My example below is from when I taught first grade, but you could change the numbers and story problem skill to fit any grade level.

I often give 3 choices.  One for my struggling students, one for my on-level students, and higher numbers to challenge my kids who are ready.  I let kids pick the numbers. However, I do go around and monitor their choices. If students pick one that is too easy, after they solve it, I suggest they try the larger numbers.  If students pick one too hard for their ability, I suggest they try a different one first and then they can try to go back to that one.

Kids love choice and by giving them choice with story problems we are differentiating for their needs, which will make story problems seem less dreaded and impossible.

 

Story Problem Tip #1

Math

Every Tuesday during the month of September I’ll be sharing tips for using story problems in your classroom. While these story problems are often dreaded for most children, they are such an important part of math and a practical real-world application.  So, it’s important that they practice them and that they hopefully become less dreaded in the process.  Here’s tip #1 for how I make them less dreaded…

Use student’s names in your story problems. Kids love being included. Especially if you can include a hobby or something you know they are interested in.  We do weekly (every Friday) story problems in my class.  I use my student’s names in the story problems. They always get excited to see who the story problem is about! It’s also fun to put in interests and real-life things for them.  The more excited they are to start, the more excited they’ll be to solve it!

Check back next Tuesday for my second story problem tip!