## What do you see? A Freebie?

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!

## How Do You Teach Rounding?

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.

## Using Number Sense with Larger Numbers and a Freebie!

Thanks to the snow day (or shall I say ice day), I finally finished these number charts! Back in the fall I had the idea for this product because I was working with a group of intervention children and they just weren’t able to tell me what 1,000 more or less than a number was when the number had more than four digits. After the second grade standards, there are no standards that have children count past 1,000. I think somewhere, someone who wrote the standards just assumed that children would be able to pick up on these patterns, but many times they aren’t able to see these patterns without explicit teaching. That is what these number charts are meant to help teachers do. In celebration of a snow day (2 snow days now), and over 600 fb followers, I made a free product with charts counting by 500.

Here is the main product that has number charts counting by 100, 500, and 10,000. There are charts that count to 10,000; 100,000; and 1,000,000! These will help students begin to see the patterns of larger numbers and help give you a basis for discussing rounding. Not only that, but they increase in difficulty giving you a way to either scaffold or differentiate for your students! Here is a peek at the complete set of number charts….

You might also be interested in these fill in number charts with smaller numbers:

## This Helped a SPED Kid Learn Subtraction Regrouping!

I posted earlier about a strategy that helped a struggling SPED student add with regrouping. Now, I am sharing the strategy I taught this same child to learn subtraction with and without regrouping.

Thank you to Lovin Lit and Educasong for the clip art!

Above there are two examples. One of the examples is with regrouping and the last one is without regrouping. This strategy will work both ways. I admit I have been using the rhyme that a couple of teachers have gotten from Pinterest…”More on top, no need to stop. More on the floor, go next door, and get ten more.” I have kids recite this first. The rhyme works very well so I use it. Anyhow, I have the kids always circle the number on the bottom in subtraction. The circle represents their head. Then they make dots to count up until they get to the top number. The dots are like their fingers. To get the difference they count how many dots they drew. Simple, easy, and if kids can make the jump to use their fingers, they can go ahead and don’t have to draw dots. I did this because I found some students don’t know how to effectively use their fingers to count up yet.

You may also like Addition Intervention Strategies:

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

(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!

You may also like:

## 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.

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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## Your Kids Aren’t Learning Their Addition Facts ? Try This…(Part 3)

Up to this point if you have been following my previous posts and tried them with your students, you’re students will have learned their bonds of 10, +1 facts, +2 facts, +9 facts, and +10 facts. Now it is time to build on some of that foundational material that you have been working on with your students. With consistent review of what they have already learned students will be ready to move on to using their bonds of ten to find other sums. While allowing them to sit and think, show students these facts side by side and allow them to comment after a few minutes on what they notice. I like to use the Number Talks idea and have students sit and think for a while and when they notice something in the patterns to then respond with a thumbs up on their chest. This allows the other students to think without the over zealous arms dancing in the air with the correct answer. Here even if students say something that isn’t quite what you are looking for, don’t discourage their contributions. For example, if someone says that they all have 11’s respond by agreeing but asking for something more. You might ask, how are the facts on the left like the ones on the right? What are the only numbers changing? How much are they changing by? Only ask these questions if you don’t get much response initially. Allow students time to think and study what you have written.

You may also like these earlier posts about learning addition facts:

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

## Fill In Decimal Number Charts. Could This be the Answer?

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:

## How In the World Do You Teach Rectangular Arrays and Division in 4th Grade?

Well, with large numbers this is something that my fellow colleagues did not feel comfortable teaching. And when that happens…who steps in?? None other than The Mathemagician…ta-da! (which is me of course, but shhh don’t tell anyone!!)…I’ve been off for a few days as I write this, which makes me a little sillier than normal–and probably slightly more interesting! So, on with my lesson! Now just remember when I post these pictures it is not a beautiful, I spent weeks preparing, colorful, lesson. This is a practical lesson anyone could use whether you are savvy with a computer or not. (I may turn this lesson into something more aesthetically pleasing later on.) The part that stumped the teachers was the fact that the standard says “up to 4-digit dividends”.

CCSS.Math.Content.4.NBT.B.6 Find whole-number quotients and remainders **with up to four-digit dividends and one-digit divisors,** using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, **rectangular arrays, and/or area models.**

I had to think myself about how to teach this before I spouted off a lesson idea. (I know I am supposed to be the math expert in my building, but, honestly, I have to look up what exactly common core is expecting before I assume I know what a standard is asking students to do.) I looked at North Carolina Unpacked–my go to document for what common core expects…

*oh so close he*isn’t explicitly saying that there were 24 rows of 12 chairs.

*teacher reflection moment by Ms. K*(soft music playing)

*…*next time I prepare an activity like this, I will make sure that I cover up enough rows so that the only rows that show are a group of 10 rows. This will hopefully push students towards thinking about ladder division.