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.
“Miss _______ (insert your name here), how do you spell ________(insert your number word of choice here)?” I always have students ask how to spell different number words, only to tell students, “The best way you can.” Now you will never have to tell students again how to spell number words. Simply point to your number line. You can now have access to word cards for you number line right here:
There are smaller triangular size cards to save space. There are also larger/longer cards that can be seen more easily from a distance.
That’s not ALL folks! We have a giveaway this week! I am teaming up with Erin from A Library and Garden to offer a $50 Amazon gift card give away! This giveaway is on until Friday, October 21, 2016 so hurry and enter below now!
Tell everyone you know about this great new free animated website iknowit.com that helps elementary kids practice math skills by playing games. This site will remain FREE for at least the next year while improvements and more lessons are added. Iknowit was built by the makers of Super Teacher Worksheets and Modern Chalkboard, a SMART board lesson site.
The lessons give children immediate feedback so that they know if they have answered each question correctly or incorrectly. There are drill lessons for basic math facts–addition, subtraction, multiplication, and division. These lessons are timed. Then there are lessons based on progress in which students answer a certain amount of questions. Right now the lesson topics include addition, multiplication, division, time, money, fractions, and there are many more to come!
In the future as a teacher, you can log in and set up a class roster. You will be able to assign lessons, monitor student scores, and track their progress. You will also be able to adjust the number of hints children are allowed to have on each problem. Teachers will be able to set the amount of time students practice drills and set the number of questions a student must answer for a lesson.
Because this small business was set up by teachers, they value teacher’s and student’s constructive feedback as they venture forward with improvements to this site. You can follow them on Facebook, Instagram, or Twitter to give your input. Just imagine a website built with your feedback in mind
You know the guys who easily multiply in their head who leave you picking your jaw up off of the floor? Well, these folks have special strategies. I am going to teach you one of these so that you can teach your students!
First, let’s look at this example with fractions. If you double ½ you get one. Instead of going through all of the steps it takes to multiply fractions, why not simply double the fraction and multiply? In the case of one half or any other fraction with an even denominator, this process is simple. ½ becomes 1. Then multiplying by 1 is super simple.
In the case of a denominator such as ¼, in the second example, you can double the number twice and halve the other number until you find a factor that is easy to multiply. ¼ doubled becomes ½ and ½ doubled becomes 1. As long as the other factor is easy to halve, this works great!
This may be done with mixed numbers as well. As long as one of the numbers is even, you can double the other.
Now let’s look at examples with whole numbers. Again, double one factor and halve the other. Hmmmm 6 x 24. I don’t know that in my head, but I do know that I can easily double 6 to 12 and halve 24 to 12. Wow! I do know 12 x 12! 144!
I will skip the next two examples (12 x15 and 25 x 16) because these are self-explanatory.
Let’s look at 6 x 32. If we double 6 and halve 32, we get 12 x 16. Still not an easy fact. Ok, I will try to double and halve again, and I get 24 x 8. Hmm, again I don’t know that one. Let’s try another time. We get 48 x 4. Whew! Still difficult. One more time. Ok, 96 x 2. To solve this problem, I will use a combination of strategies. First I know that 96 is 4 away from 100. If I have two groups of 4 away from 100, then I know that I will be 8 away from 200 because 96 is almost 100. If I take 8 away from 200, this gives me 192. Teach children through number talks etc. to think flexibly about numbers and ways to solve problems. By teaching children these strategies, you will become stronger at solving math problems in your head as well!
When students struggle with ladder division, many times it is because they learned a procedure and haven’t made sense of the procedure for themselves. In this case students haven’t had enough experiences with division problems that are near friendly numbers so that they can reason about the numbers. Try giving students some problems that are near friendly numbers first if you notice that they aren’t using number sense to form partial quotients. For example, if students continue to subtract only small groups of ten and aren’t able to estimate a larger number for partial quotients, then try giving students numbers that are easier with which to estimate, like in the picture below. In the above picture, I started with some students in intervention who started solving the problem using groups of ten. 2499 divided by 25 is obviously close to 2500. Why not start with 100 groups and reason about taking away one group so that the quotient isn’t too large. When students look at how they could estimate to solve this problem, they have a lightbulb moment. Give them other examples like this to get students in the habit of solving problems with reasoning and number sense as opposed to a procedure.
I have worked with children from 2nd grade on up to help them learn their addition facts. One common denominator exists among all of these students. That is THEY DON”T SEE PATTERNS! I remember having a difficult time learning my 9’s facts when I was growing up. To help myself, I just took one off of the number I was adding to 9 in the ones place. I noticed this pattern. No one taught me this. When I was growing up, learning facts was like, “Ok, Class, let’s learn all our 8s facts, let’s learn all our 6s facts and so on.” This is not effective for students who don’t recognize patterns on their own. Now with the common core mathematical practices, we should be teaching children to explore patterns through thoughtful placement of number facts to help them recognize these patterns. Giving students opportunities to see the patterns will result in more students who are fluent in their facts. I have shown examples of this before such as in this post about using 10s to help with adding 9s.
But now I have actually put all of my work with struggling learners into a packet which could be used whole group for grades 1 or 2. At the 3-5 level this could be used for students in intervention or as part of the RTI process. Here is a look at the packet that I have put together to help students become fluent with all of their addition math facts. It is on TPT !
You can also try out a little sample of this product for FREE here.
Are you teaching your firsties to add ten, subtract ten, add 1 and subtract 1? The week before Christmas we added this game to one of the selections in the students’ math stations. This game is called “Bubble Gum Pop”. The kids absolutely LOVE it!!!
Students move “bubble gum balls” (bingo chips) up and down the 100’s chart mat according to the spinner. The game is differentiated for students who need more of a challenge so that they can use a mat that counts to numbers past 100 or they can use a bubble gum spinner that allows them to even add or subtract multiples of up to 20.
In this photo above, students are tied with both having an equal number of chips on the board. The one who knocks the other student’s chips off the board first is the winner. What makes this game fun is that there is an element of chance when students land on the pictures, their chips are out. Also, the game requires children to know which direction to move on the board to add or subtract 10s and 1’s so they are learning at the same time.
The game is also available in color. I copied it in second grade however on colored paper, but ended up liking the black and white better because I felt the students could see the chips and numbers better on the board. The color definitely did make the game happier though.
I have been missing in action from my blog lately. Hopefully this will make it up to all of you faithful followers 🙂 ! I have been working on this packet of addition fact lessons that I used with intervention groups all last year with much success. The lower students really seemed to enjoy the thinking aspect of these lessons. I have been working on putting this into a format that is cute enough to post. Because I have been working on the whole packet for months, I thought I would give you a free preview sample in the meantime. I will be posting the whole packet soon for sale. Without further adieu, here is the Freebie! I hope you enjoy using it!
Thanks to Winchester Lambourne for the spooky eyes clip art!
To teach rounding I take several approaches.
The first method I use is to teach rounding with a sentence strip number line. I have students build a number line on sentence strips with whatever numbers we are working on. If they are working on the nearest 1,000 and nearest 10,000 for example, I may double side the number line sentence strip. If we are working on nearest 10 and 100 then I would double side the sentence strip counting by those two numbers. Here is how I have students build their sentence strip without much fuss.
First, I have them put a finger space down with one finger and make a mark. We put a zero here. I also have them leave a finger space before the end. They put the last number here such as 10,000 in this case since we were rounding to the nearest thousand.
Then, I have them fold the strip in half so that students can at least find a mid point. They put a mark at the mid point.
I have them put four fingers down to hold the space to make the next mark. Students repeat this four finger spacing until they get to the midpoint and then repeat the four finger spacing after the midpoint. This gets a fairly even number line if students do this. IT ISN’T Perfect, but it’s close enough to reasonable spaces give or take the size of the students hands.
Next, students label the numbers underneath the marks.
This will give students the numbers they need to use when making a number line sketch such as in the rounding roller coaster model I like to use. Before actually talking about rounding. I like to pose a number such as 8,456 and ask students where this number would fall on the number line. I have them place their finger where they think the number would go and I do a quick sweep around the room to look for understanding.
Here is how you can progress to the rounding roller coaster. Whichever numbers the students’ fingers are pointing between on the number strip go on the end of their roller coaster. For example with 8,456. The numbers would be 8,000 and 9,000.
Next, have students put the midpoint number in between the numbers on the two ends of the roller coaster. Then have them put a dot where the number they are rounding actually is. Explain that when a roller coaster is on top of the hill at the midpoint it will coast all the way to the end. If the roller coaster isn’t all the way at the midpoint then it will coast back down to the beginning. Whichever side it coasts to is the answer.
Now of course in the midst of all this, I have students learn the rhyme “4 or less let it rest, 5 or more raise the score” so that students have another rounding strategy to fall back on.
Now the rhyme and the roller coaster I cannot take credit for. I either learned it on the internet somewhere or from another teacher. I can’t remember, but both of these strategies support students’ understanding. These are my preferred ways of teaching rounding. Now, of course you will have students who don’t understand the above because they cannot count that high or have understanding of numbers that high. That is when I give them some counting practice using these number charts:
This is free in my TPT store:
And you can get these which count to larger numbers and they cost $4:
Or these count by smaller numbers up to 1,200 and are $7. I use these a lot with kids at school. They are great for up to grade 3 or as an intervention for older kids.
Now here is what I do with students who are seriously struggling. I don’t like teaching rounding this way because it really takes the number sense out of what they are doing, but some students just need to know how to get the right answer and do not have the number sense to build on to be able to round with understanding.
I showed the method above to a group of 5 struggling learners and all were really getting correct answers by the end except a resource student. Being able to write something down on their paper before they did much thinking really helped the students. To know that they could go ahead and fill in the zeros and fill in the beginning really helped them. However, like I said this isn’t the best way to teach for understanding.