I know at this point in the year many of you have already taught expanded form. How do you get your students to maintain their understanding of expanded form? You could leave a reminder up all year long which doesn’t take up much space. Use your classroom number line, and add these special signs to your number line. Ta-da! This is even better than an anchor chart! You can choose from space saving triangular ones…
or longer ones so that the numbers are easier to see from a distance.
If you hang your number line low enough students can help add the cards to the number line, and you can print the signs on card stock. This way students can easily attach and reattach them with velcro onto the number line (great for long term use). Tape works fine too!
You can use your own store bought number line, or you may enjoy using this number line especially created for use with these signs that includes base ten blocks already attached like shown in the instructions above.
You can go here if you are interested in purchasing this product.
Why does this alternative to regrouping work? I have noticed an image similar to this on Pinterest/Facebook.
The comments go something like:
- Cool, I’ve never seen this before!
- How does this work?!
- Why does this work?!
I thought I would take a moment to explain why this works. A simple piece of ribbon gives us a chance to explore this concept. Above I used smaller numbers to demonstrate. 100-88=12, but subtracting one from the minuend and subtrahend gives us the same answer. 99-87=12 also. When moving the ribbon down the number line we can see how the distance on the number line stays the same because we took the same amount from both the numbers. Hence, the ribbon remains the same size because the distance doesn’t change.
The distance = the difference. As long as the distance is constant between the numbers this will work.
Now, you tell me, will this work if, instead of subtracting one, I subtract five from the minuend and subtrahend?
In case you are a Super Teacher Worksheets fan, you may like to know this little secret. On top of the fact that they have eleventy billion fabulous sheets at your fingertips at the click of a button (no losing your files here), they also have a new site for Smart Board lessons! This new site is called Modern Chalkboard. Their Smart Board lessons also are compatible with Smart TVs. It gets better, their Smart Board lessons are also aligned with Common Core Standards! WOW! Imagine saving yourself so much time throughout the school year to have these lessons readily available to you. Here are some of my favorite samples…
If you are willing to pay $5 for all of these resources per month, which in my opinion is totally worth it, then you could invest $50 for all of their high quality Smart Board lessons for $50 a year. I wouldn’t tell you they were high quality if they weren’t, so you might as well get a head start and buy a membership at the beginning of the year so you can have more time for your family ;)! Here are a few free lessons to sample!
Well, I have been scurrying around like a squirrel hiding nuts (and maybe going nuts) these last few days getting ready for our Family Math Night. I usually plan this as close as I can to our 100th day of school, which happens to be this Thursday! While getting ready for this event, I have thought about a game I recently made, which first grade really enjoyed! This game is called Bubble Gum Pop and is centered around adding and subtracting 10’s and 1’s on the hundreds chart. The game is already differentiated and would be wonderful as a take home game for parents to enjoy with their children! There is very little prep to this game other than gathering some game pawns and deciding which way you want to use to make a spinner. There is even an extra engagement factor if you decide to use real bubble gum (flat pieces) for game pawns!
Here is the fun spinner! Kids place five pawns on the board to start with (scroll farther to see the board). Then they move those pawns down one square if they land on +10, up one square if they land on -10, to the right one square if they land on +1, and to the left one square if they land on -1. If students land on the wild space they can move their pawn anywhere on the board.
If students bump into one another, then they automatically knock the other pawn out. Also, if students land outside the perimeter of the chart, their opponent is out. The object of the game is to knock your opponent’s game pawns off of the board. Below you can see a sample game in action.
Here is a look at the game board.
I will be posting pictures of our Family Math Night soon if you are still needing ideas to help plan yours.
I know, I know, I am a little late in my New Year’s greeting! I hope you had a restful time from the normal day to day bustle. I managed to catch up on some family visiting and some cleaning for sure. The cold weather kept me from feeling like super cleaning woman so I refrained in several cleaning areas :)!
I know that many of you are concerned about the upcoming PARCC assessment or similar assessment. For those of you taking the PARCC assessment in paper and pencil, these items are already posted on the website now here.
Further there are now more helpful sites emerging that are helpful for PARCC practice. One of these such sites is Illustrative Mathematics. This site has practice items that are very much like the performance based questions on the PARCC assessment like below.
The best site of all is a practice test site called Ten Marks which gives students digital PARCC like questions with multiple choice and multiple response answer choices. Students can be assigned questions with the click of a common core standard. These assignments can then be taken on the computer or iPad. The results are immediately made available to the teacher. If students miss a question they are given the opportunity to watch a video about what they missed while they are doing the assignment. The program is free and so easy to use however, you must pay a fee for the best version. This is definitely worth taking a look at and the teachers L-O-V-E it.
I hope these few ideas help you get a head start on the upcoming testing season!
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!!!
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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(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.
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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.
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.
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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Maybe I’m a little late to jump on the Math Station band wagon, but when anyone mentioned math stations to me, all I heard was centers. I didn’t feel that math stations were the right thing for our school until I read Debbie Diller’s Math Work Stations book. So began my math workstations journey.
The book completely changed my mind about implementing stations. I LOVE IT!
After reading this book, I decided to experiment with the idea of math stations in a 1st grade and 3rd grade classroom. Right now we are getting them set up–deciding what activities to place in each station, making locations for each station in the room etc. Since it is the end of the year, I knew we could spend time working out kinks with stations so that we could start out full force with math stations next year. I will be writing more about our math stations with photos included coming soon.
I am including a freebie here for now that you may want to use in one of your math stations. This sheet will go with an addition/subtraction station like one of the activities Debbie Diller suggests so that students may mark off the facts they know. Click the blue link to download a copy.
If you are using Debbie Diller’s math stations, I would love to hear about your experiences with what worked and what didn’t. Please comment below. 🙂
Ok! So I won’t lie! I have struggled with the next teacher. Kids just fumble through decimals like there is a missing link. You try to have them do number lines, and they give you blank stares. You give them card sorts. They jumble all the cards up in the wrong order. They tell you the wrong answers almost always. There MUST be another way!! Well, 1 year later, I have finally put the pieces together.
Why can’t kids compare decimals? They are just numbers that follow a pattern with DOTS in them no less!
Have we ever stopped to look at the patterns that are formed when decimals are put in order. Have we stopped to reason about why the zeros drop off the ends of the numbers and they have the same value?
In kindergarten, first, and second grade, we have it somewhat figured out. For three years, students spend time counting and looking at patterns, and building numbers–for THREE YEARS. THEN BOOM! All of a sudden, they are supposed to draw their own conclusions about how to compare and round numbers that are abstract to them in 5th grade. So students CAN build decimals “reasoning about their size”, but where is the repetition that we give students in primary grades so that they can draw their own conclusions about the patterns. There is no counting standard that I can find…but maybe I just missed the standard or maybe I am just going on a rant here.
Anyway, I think students struggle with decimals, because we don’t give kids anything to hang their learning on…they have no foundation! I made some decimal number charts last year, but never really used them in depth. This year I made some fill in charts thinking this would solve the problem of students’ glassy eyed look when learning about decimals–AND NO…I’m not even talking about the kids on meds!! I really think that this is the problem…they need the foundation of counting before they can reason about decimals and move on to comparing, rounding, and ordering.
Because you are reading this, you obviously care about your students. You most likely wouldn’t be on the computer during your down time looking for materials for your kids. I am going to give you a few of the pages I made for FREE just because you care.
More charts are included than this single picture below.
I am also going to tell you about the pack of number charts I made that may help you even further. There are number charts for each section of decimal numbers counting by hundredths and thousandths. There is also a decimal number chart that counts by thousandths that is small enough to glue in students’ journals. Not only that, there are small number charts the same size as a base ten block that will help students put the concrete together with the abstract counting numbers as they place blocks on top of the charts. You can see a bit more below: