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Base Ten Number Line

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Multiplication Tricks

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Telling Time Misconceptions

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Lesson Ideas

Don’t Do This When Teaching Graphs

To enjoy the week before Christmas break, I decided to try out a lesson idea I had about pictographs. I built this lesson around misconceptions that students always have about keys with numbers larger than one. The day before I taught this lesson, I was asked to teach math at a moment’s notice in another third grade class. When this third grade class interpreted a pictograph with a key of four, I noticed that this was really way too easy for these smart students. I decided to change my planned lesson idea into something more challenging. This is how the lesson went…

First, I did a quick lesson for understanding. I surveyed the class about their favorite ice cream: vanilla, chocolate, or strawberry. I then made a frequency table with this information on the board. With some yellow circle die-cuts with one circle to represent two children’s votes, I asked the class how many votes needed to stand for each flavor. Students did this very well even if this required half of a circle for one person. Then I had each flavor group stand in a different area of the room and I passed out the number of circles the children told me to each group. When I passed out the circles to each group and instructed the students to write their name on a circle, some disequilibrium arose. Students said they didn’t get a circle. I told them to talk to their group and they finally understood that they would need two names on each circle. I couldn’t have been more proud of this part of the lesson and the mathematical practices that arose from their discussion. Then came the next part of the lesson…

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I previously gathered real life data about students’ favorite Christmas candy.

  • I chose four types of candy: fudge, candy canes, M&M’s, and chocolate Santa’s. I gave three third grade classes each a roll list with a blank beside it for the students to write their favorite candy on. I collected these vote (data) sheets right before the lesson (mistake #1 don’t do this). I made six copies of the data sheets for each of the groups.
  • In the lesson I presented the children with the data and told them to create a tally chart/frequency table with the data. Students waded through this for a long time without consistent results. I should have counted the data before I passed it out even though I had estimated the results to around a total of 66 students. I ended up having to total it up while the students were counting (mistake #2 don’t do this). Have your data counted before you pass it out, so you know when your students are way off. (But, hey, in my defense, I have been pulled in all directions lately, substitute, fill in secretary, test coordinator, you name it.)
  • I made one student in each group of four responsible to count each class’s data since there were three classes and one student to record the data on a table. This worked very well to keep every child involved in the group.
  • We stopped the lesson to ensure the children had the correct data before we proceeded with graphing. I wanted to be respectful of the teacher’s time while I was in her room, but I may have had them check to see if their data was correct in a different way, such as, compare your data with a different group and see if you agree before I just revealed the correct answers.

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Next, I told students their key had to be 5 or more (I really had 6 in mind), but the teacher was concerned that it wouldn’t come out evenly for the students. The data had to be slightly altered for the die-cut circles to come out with wholes and halves. She didn’t want the students to have to deal with smaller fractional parts. I was actually okay with the students having the data not come out evenly because I wanted this to be a challenge for them to grapple with. In the real world, data doesn’t come out all nice and clean. Third graders had already proven themselves with a key of four, and I felt like they needed a challenge. I wanted them to discuss how much of a circle to cut apart. Again, I wanted to be respectful of this teacher’s time, so I allowed this and the students’ graphs all turned out pretty much perfectly. No fun :/ There was no argument over how much of a circle to cut apart. (mistake #3, don’t make your data work out perfectly). Needless to say here, I had many reflections after this lesson. This was definitely not my best moment as a math coach (I am at a new school this year). BUUUUUT!!! I loved this lesson, it was so great, even though it wasn’t! I know exactly what to do next time to make it better, and it would be an exceptional lesson with lots of mathematical practices involved! Next steps for students after this lesson–ask students what would have happened if the key was 5 or 6 to at least get them to think about this.

Are You Taller Than a Third Grader?

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With the combination of special programs and snow days, our time to teach all of the standards before our 3rd graders’ PARCC test is running out.  With this in mind, I made a graph to help third grade out using the data from the whole 3rd grade with a fraction line plot.  This type of  graph and fractions are not as familiar to third graders because they haven’t been exposed to line plots in earlier grade levels.  I put the graph in a central location where other grade levels could see it.  That way other students could experience measurement and interpreting graphs as well.

 

I started out with an area by the water fountains for repeated exposure to student traffic.

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Next I put up a strip of this amazing ruler like tape that I got at Office Depot when they had all of their special masking tape at back-to-school time.  The tape counts every 12 inches.  So in the picture below, I marked off every twelve inches with little triangles that mentioned that each 12 inches was 1 foot.  Next, I marked off the fractions of an inch with stickers.  I marked off the halves, thirds, and fourths so that students could easily see the relationship between the graph and the tape measure.Tape

Then I had students come a few at a time and measure themselves to the closest fraction of a foot.  Students recorded their X’s on sticky notes.  The only reason I had them record their X’s on sticky notes is because this ensured having them all the same size.  Line plots can make data look skewed if students don’t draw their X’s the same size.  Plus on the PARCC assessment when students drag X’s on the line plot graph questions, students drag the X’s into little boxes which makes test question boxes resemble sticky notes.  Students got to initial their X.  Also, if students in the least bit chuckled about anyone else’s height because they were short, I immediately told them they wouldn’t even get to put an X on the graph.  After I graphed most of the students from two classes, I only had two students who didn’t get to put their X on the graph because of this reason.

Here is the whole picture of everything with a more than willing model :)…Slide5

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Your Kids Aren’t Learning Their Addition Facts?…Try This (Part 7)

After using doubles and tens facts to learn one more and two more than all of those sums, that only leaves students with two facts to learn!!!Slide1

I allow students to tell me ways that these two facts can be easy to learn for them.  Most students say that 3+6 is 9 so it is close to a ten fact.  Some may be more comfortable with 3 +5, but after spending time talking about patterns with students, they will easily be able to discuss a way to get to this fact using a known fact.   The thing that is uncomfortable about using 6+4 is that students have to go backwards and it is uncomfortable for them to go backwards in counting.   Students favor going forward…cause more is better (like the commercial! :))  Also, 8+5 to me is an oddball.  I can think of no easy way to get to this fact, but most students will say that 8 + 5 is close to 8+4 which is 12 so they know that 8+5 makes 13.  Other students will say they know 8+2 is 10 so they can count up 3 more.  I really don’t like that they have to count up 3 more, but at least it is better than counting up 5 from eight.

I will have to say that after working with intervention groups with all of these fact strategies, their answers aren’t as immediate as I would like, and at times they still use their fingers.  I believe they still use their fingers because it is comfortable to them—more comfortable than thinking.  After a strategy is learned it is imperative that they still practice with flash cards so that the facts remain fresh in their minds.  I don’t work with a student population that readily has parents practicing with them at home on flashcards so the only extra practice they get is with me.

I plan on posting some of the materials I used to practice facts with the kids soon.

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Your Kids Aren’t Learning Their Addition Facts? Try This…Part 6

If you have been following the previous posts, then you will see the progression of teaching number facts strategies.  Nearly the last part of teaching addition facts focuses around doubles and doubles plus 2.  I think this is one of the hardest strategies because kids may not readily see the double when it is two numbers away. With a little thinking and prodding, however, they will see the fact without using their fingers.  Line the numbers up side by side so that students can see examples of both sets of numbers–the helping fact and the double plus 2.

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Again, when having students recognize patterns and see relationships, I like to write them out of order so that students don’t say that the numbers are counting by 2’s etc.  If students struggle to see the patterns, underline numbers to help them focus on what you want them to see such as underlining the second addends on both sets of equations.  Then underline the sums on both sets of equations.  Step back for a few moments and let the prolonged silence aid students in thinking about the relationships in the two sets of numbers.  Give students time enough to generalize about how doubles can be a helping fact.  * Note that students have already learned sums of 10 and 10s plus 2 more so they have strategies for 5+7, 4+6, and 6+8.

After this, students only have a few more facts to learn!!

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Thank you Erin Cobb!  Frames Courtesy of Lovin Lit.

You’re Kids Aren’t Learning Their Addition Facts? Try This…Part 5

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(Thank you Erin Cobb from Lovin’ Lit for the pretty border!)

Now after I have taught everything that I previously blogged about in Parts 1, 2, 3, and 4, which includes tens and tens plus one.  Learning the sums/bonds of 10 is the foundation for this discussion.  One of the tens plus 2 will already have been learned because it is a double, but there is no harm in learning multiple strategies to reach one fact.  Also, doubles plus two facts will be learned later and doubles plus two will also give students a strategy to reach 7+5=12 and 5+7=12.  Allow students to recognize this on their own when you reach that lesson.  The more ownership students can have of the strategies without you telling it to them, the more they will remember the strategies and feel smarter for being able to discuss the strategies.

Again when you introduce these facts write them out of order on the board.  Step back, wait, have children quietly look at the number facts and find relationships or patterns in their head.  I use the Number Talks strategy and have them put their thumb on their chest when they find a pattern.  This keeps everyone attentively looking for more patterns without the dramatic hand raisers flailing their arms in the air.  If students say that they see lots of tens and twelves acknowledge this and then ask students to look for more.  Eventually you will get what you are looking for if you have the foundation built from the previous lessons.  If no students say that one of the addends goes up by 2 and the sum goes up by two, offer a hint by underlining these numbers so that they are focusing their attention there.  Follow this up by fact (flashcards if you prefer) practice over the sums they have just discovered a strategy for and over previously learned facts.

Happy Thanksgiving!

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Your Kids Aren’t Learning Their Addition Facts? Try This…Part 4

So far if you have followed my previous posts, students will have learned their bonds of 10, their +1, +2, +9, +10, and adding one more to their bonds of 10 facts.  Next, I like to focus my students’ attention on learning their doubles.  Most of the time students are already comfortable with their doubles up to 5+5 since they easily see these doubles on their fingers, on dice, and in other real world examples.  At least when working with my intervention groups, this is the case.  The doubles kids most often struggle with are 7+7, 8+8, and 9+9.   When writing the doubles on the board, kids can easily see that the sums of double numbers turn out to be even numbers or the numbers that count by 2’s.

Slide1 I also like to use videos and games to help kids remember their doubles.  Here is one of the videos that I like to use.

This is only a preview of the video.  The other part used to be free but is no longer free.  The video costs $2.49 to download the 6-10 doubles, but is worth the purchase in my opinion.

After kids have learned their doubles, show them these doubles plus one more.  Don’t tell them that they are doubles plus one more, but let them see the pattern and tell you about them.

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 Allow the kids to notice the pattern in the doubles and doubles plus one and express to you how the numbers change when one is added.  Kids will excitedly see the relationship between the double and how it goes up by one more.  After discussing the patterns from the previous posts, students will more readily see this pattern and relationship.  Then when using flashcards to follow up, students will sometimes think out loud about their strategy, and you will hear them thinking about the relationships they see to get to a new sum.  When you hear this you know you have taught them well!

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Your Kids Aren’t Learning Addition Facts? Try This…(Part 2)

So, once the kids have learned the initial easy facts like I posted about before (+1, +10, and +9), I focus on getting them to learn their bonds of ten.  Now since we had already learned the +1 and +9 facts, I focus on these foundational facts to help us build other facts later on.  Most often kids know that 5 +5 makes 10 because they have 5 fingers on one hand and 5 fingers on the other hand to make 10 fingers.  After we talk about these, I make them practice these other three facts over and over (4+6, 3 +7, and 2+8) by writing them and saying them.  I don’t let them participate in any other activities in my group time until they can tell me these three facts that make ten.

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I give them these facts to practice for homework as well before we use them as a foundation for anything else because I want them to be solid in this.

Then I leave the bonds of ten facts for a little while to practice the +2 facts.  These are easy.  All the while we are recalling what makes 10 often (in review) to keep these facts fresh in their mind.  After the kids see the number facts with the answers that are adding 2, I ask the students how they can always find the answer to a +2 fact easily.  Sometimes I write the +1 facts right beside the +2 facts to prompt their thinking.  Eventually they tell me that you just count 2 more numbers to get the sum/answer.

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*Thank you Erin Cobb: Frames courtesy of Lovin’Lit.

Do You Need Some More Math Activities for Math Night?

Take a look at these exciting photos of our recent Family Math Night.  Originally we had scheduled Family Math Night on the 100th Day of school to build more momentum for the event, but we had to reschedule Math Night due to weather.  I’m mainly including activities that we hadn’t done before, and I will include links to former math nights so you can get even MORE ideas!

To start, tables with parent information were set up in the hallway.  The more inviting and fun student tables were set up inside the cafeteria.

Since many parents are unfamiliar with ten frames (I had never heard of them until I had started teaching), we had a table informing them of how ten frames work.

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Then we had an information table showing the parents of 2nd and 3rd graders addition and subtraction strategies.  Parents even had an opportunity to see how base ten blocks were used to do regrouping.

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Here is a station explaining to parents how Reflex Math works.  We had a laptop set up to show parents Reflex Math from a kid’s perspective.MathNight2014Blog-43

One teacher put together game packets for parents to play math games with their children at home.

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Now it’s time for the fun stuff!

Below you will see beach balls with math facts written all over them using Sharpie permanent markers.  When someone catches the ball, the right thumb’s landing spot determines the math fact that must be answered.   We had large beach balls for the kids to play with and small ones for them to take home.  We ordered the beach balls from Oriental Trading Company.

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How many books will it take for YOU to weigh 100 pounds?  That is the question that students had to answer when they stopped at this station.  Students estimated how many heavy encyclopedias it would take for them to weigh 100 pounds.  Having experiences with measurement is the best way for students to make reasonable estimates with measurement.

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Uh-oh!  Looks like he picked up too many books, but he’s close!

Fractions beckoned to students’ interests under the guise of a messy pudding party.  Students had to measure out two cups of milk without using a 1 cup measuring cup.  They had to use ½, ⅓, or ¼  measuring cup .  Doing so made them repeat these measurements until they had milk equivalent to 2 cups.MathNight2014Blog-4

What is Math Night without estimation stations?

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I have done estimation stations every year we have had Math Night, but I wanted to do a little something different this year.

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Instead of just having the estimation jar, ziploc baggies were placed in front of the jars with 10 of the candy item inside.  This helped students make more precise estimates.  I also had a wild idea about gluing base ten blocks together to see who could come the closest to estimating the total of the blocks in a base ten tower.

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How many are in this base ten structure?  Can you guess?

(above) I know the tower looks more like the leaning tower of Pisa than anything of mathematical value–it looks like a hot mess–a hot glue gun mess ;).   What can I say…I think I should pose like one of Charlie’s Angels with my hot glue gun!

(below) Making 10 groups of 10 was a kid favorite last year and remained a kid favorite this year.  Kids took small food items and grouped them on a mat.  They got to eat their 10 groups of 10/100 items when they had filled up their mat! Yummy!

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(below) Where did Freddy the Frog land on the hundred’s chart?  These kids played Toss and Guess, a game with a giant hundreds chart grid and a beanbag–in this case a bean bag frog.  The idea for the grid and the Toss and Guess game came from The Learning Carpet.  Kids received prizes when they guessed where the frog landed correctly.

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Below is my absolute favorite booth of all booths!  How many hulas can you hoop?  Students hula hooped until they could hula no more.  Then they counted their hulas and wrote the total of their hulas on a piece of paper.   They stuck this paper to the wall so other students could compete with the highest total.  The two hula hoopers with the greatest number of hulas won a hula hoop!

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The following made the evening worth while.  This parent solved math problems with her Pre-K student.  She helped him count on her fingers!  This embodied the goal of the whole evening–helping parents connect to their children through mathematical thinking!

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 If you liked this post about Math Night, you might also like Math Night from 2012 and 2013…

2012

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 I hope these posts inspire you to make your math night fun!

Teaching Coordinate Grids? Try These Great Resources!

A fabulous fifth grade teacher I work with started using these coordinate grid mystery pictures with her class from Super Teacher Worksheets.  She said that her kids who struggled with everything else in math, loved these and were so engaged in finding the coordinates.  There are many different mystery pictures that you have to pay for on their site, but I want to call your attention to a Santa Clause mystery picture that is absolutely free 🙂 especially since this is the week before Christmas!  We all know how kids are the week before Christmas break–ahem–let’s just say they need something super engaging!

Santa Coordinate Graphing Activity from Super Teacher Worksheets

 

I also just finished revising a coordinate grid activity that I made a while back.  Students must locate buried treasure on a coordinate grid using geometry and graphing terms.  Our fifth graders are enjoying this activity right now, too!  This activity packet is available on TeachersPayTeachers.

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Social studies can be discussed with this activity since the grid has a map behind it.  I like to discuss coordinate graphing on the same days I am teaching map skills in social studies because the two are so similar.  This activity doesn’t explicitly teach social studies, but there is definitely room for some discussion about the maps and what part (or state) the treasure is probably in.

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Save Time Teaching Time! (and two freebies!)

I have to share what I have been working on with you all!  I have been working at home on this for months.  I finally finished my Telling Clock Time Lesson Plans and Activities Unit!  I’ve been putting together all of the lessons I have used to teach time that have been tried by the fire of struggling learners.  I will have to say by far it is the best thing I have posted on Teachers Pay Teachers yet!  This is definitely the product for you if you are busy and teaching 2nd or 3rd graders about time.

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Many of the lessons have links to videos or book suggestions…

Lesson Plan Time Unit

There are 3 differentiated levels of small time booklets for students to fill out.  There are lots of other differentiated lessons, too!

Clock Booklet

To teach elapsed time, there are directions for building a linear clock.  You can read more about the linear clock here.
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There are card sorts, games, and center activities.  This card sort is a freebie!

A.M. P.M. Card Sort

AM PM Sort Blog Freebie

There are suggestions of ways to teach that will help steer students away from misconceptions about clock time.  

MIsconceptions

And there are clock labels for your classroom clock…

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Clock Labels Freebie

And so much more!

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And that’s not even all that’s included!

You can find out more about the time unit here.

I am putting this unit on sale for two days–Monday, November 11th through Tuesday, November 12th–at half price…so scoop it up while the sale lasts!

 

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