Even and Odd

Why do many teachers only teach examples of even and odd numbers, and not properties of even and odd numbers?

What do I mean?  Well, this is what I discussed with a 1st Grade Student when the only thing she could tell me about even and odd numbers was:
Even is 2, 4, 6, 8, and 10
Odd is 1, 3, 5, 7, and 9
And that's all....

First, we built models of the numbers 1 through 10

Then I asked her 2 separate the models into 2 groups that were alike in some way.

This is how she separated the models.  When I asked her what she noticed about the two groups, and she noted this on the models:

"This group doesn't have a partner for each part of the number

and this group does have a partner.  See, how I circled the partners."

Then we discussed how certain numbers can be divided into groups of two, and that we call those numbers Even Numbers.

We went on to talk about odd numbers too.  Since she is in a dual language class, she also wanted to write the Spanish word for even/par and odd/impar on the model.

Next, I asked her to now tell me what she knows about even and odd numbers and she wrote this:

I found it interesting that she put an arrow after the numbers and said "and on and on."  (That put a smile on my face.)

So we talked about how you look at the "on and on numbers" in the ones place to see if they are even numbers or odd numbers. 

I evaluated her knowledge by quickly using a set of teen number cards.

and asked her to classify them as even or odd numbers. 

She was correct, and we even checked our first answer to
 prove that she was correct.

Deborah

 

Developing Number Sense: Plus 1 or 2

   In his book, "Teaching Student-Centered Mathematics," John Van de Walle states "When children count, they have no reason to reflect on the way one number is related to another. The goal is only to match number words with objects until they reach the end of the count. To learn that 6 and 8 are related by the twin relationships of "two more than" and "two less than" requires reflection on these ideas within tasks that permit counting. Counting on  (or back) one or two counts is a useful tool in constructing these ideas."

 

Of course, the development of this skill is also quite useful when adding 2 + 7, or 1 + 9.

 

 There are 36 addition facts that include the addend of 1 or 2. 

 

So I hope this game will help you. 

 Click HERE to take you to my Google Drive where you can download the game board.

 

Deborah

 

 

Exploring Dice-Dot Patterns

The ability to quickly recognize the patterns on a die without counting each dot is important for young children.
 So today I played a game with a First Grader in which we each had 20 counters and 1 die.

The players take turns rolling the die and picking up as many counters as indicated on the die until all of the counters have been picked up. To pick up the last counter, the number on the die must match the number of counters remaining.  The first player that picks up (or slides the counters to the side of their pile) all their 20 counters is the winner.

While playing this game it is easy for the teacher to evaluate:
1) Can the child recognize the pattern on the die at a glance, or is it necessary for the child to count each dot before knowing the amount indicated on the die?
2) When counting their counters do they have one-to-one correspondence, and do they count using the correct sequence?

When we played the game the second time, I counted out my counters by two's instead of by ones. The First Grader followed my lead by counting her counters by two's also. So I learned something new about her again... that not only could she count by two's but she had the ability to utilize that pattern when picking up (or sliding over) her counters. To count out the number of 5, she slid the counters in this way:  2,2,1.

EXTENDING THE LESSON


I told the student that I wanted to know what she already knew about the patterns on dice.  I gave her 6 post-it notes and asked her to draw the pattern for each number on the post-it notes.  This is what she drew:

 

When I looked at  the post-it notes I could tell that the student had internalized the 6 patterns on the die, and could  tell you immediately without counting the value of each pattern.

 

If I was saving evidence of learning, I could save the six post-it notes, or a photo of her work.

 

Deborah



Gosh, I Like that 0-99's Chart!

Last night I started thinking about all the time I spent working with that 100's chart... and I now really  like the 0-99 chart better.  As I researched the 0-99's chart on the web, I came across a post by Jessica Boschen on her blog, What I Have Learned, that featured this idea:

She made the chart make even more sense!!!!!  Look how this 3D Chart illustrates the continuation of the pattern. 

She also made the 0-99's chart forward and backward in 2 different sizes that you can download for free from her blog
http://whatihavelearnedtoo.blogspot.com/2012/10/0-99-chart-freebie.html?showComment=1377762464844#c5607150949739340301


Then I started thinking of making the chart up in two colors to designate even and odd numbers...

That lead me to start thinking about

Maybe this is even better.... because it features the chart extending to 100.... all the way to 109.
This would be a great differentiation tool for that child that is ready for the next step.

By the way, have you seen this trick of using 2 congruent plastic cups and labeling each from 0 - 9?

This is a great manipulative to assist students in seeing that repeating pattern too.

Lastly, I need to stop thinking about numbers and go back to bed as it is 2:40 am  :) Good night.

Deborah

Using the 0 - 99's Chart Instead of the Traditional 100's Chart

In Everyday Math they use a 100's chart to develop number sense.

Yet as I was looking at some Common Core Activities from the Georgia State site, I noticed that they used a 99's chart.

I actually like it better because I believe the way the

 numbers line up would be easier for young children to comprehend.

 

See how the rows begin with the next tens.  Wouldn't it make it easier for students to see the pattern with the new tens place beginning the row instead of ending the previous row?

 

What do you think? 

Deborah

Five Frame Cards

Today I'm sharing a set of five frame cards with you.
I made them for our summer school program with the "almost Kindergartners." As I made them, I was trying to think about how the teachers could cut them out the easiest.

Click here to download the five frame cards.

This is one of the activities that we will do with the students that will utilize the cards.

Five Frame Show    (Materials: large five frame cards)

Show a five frame card to your students and ask them to identify how many dots they see. To challenge students ask them to identify one more or one less than the amount of dots. To extend, have them tell you how many empty spaces there are or how many more are needed to make 5.


Deborah Devine

Adapted Base Ten Blocks Student Kit and 10 Frame

Today I was making these Adapted Base Ten Blocks Kits for a resource room in one of our elementary schools. I thought I would share them with you.
 In the zippered pouch that I bought at "Five and Below" for $1.50, I placed the numbered ten "long" and 20 unit blocks. In the second zippered area, I placed two  numbered 100 blocks with the written portion reading  "10 through 100" by 10's and 10 more longs.

I think these kits will help the teachers in that school utilize the base ten blocks more since they are organized so that they can be handed out to students easier, and the adaptations written on each block will help the students understand that a 100 is made of 10 ten's; and 10 is made of 10 units. I can visualize students using the blocks to practice counting from 1 to 10 or 10-100 by tens. 

So though I don't have a worksheet for you to download, I FREELY share my idea. Now you can print this picture to show your parent helper how you want the materials labeled.

Pouch labled: #5 Adapted Base 10 Blocks



As I was working on my project, my 3 years old granddaughter was busy making a very big circle with Teddy Bear Counters. She started by making a 2 color pattern, but got lost in the glory of creating a big, big, big circle.

This creative environment lead to this idea:

This is a 10 frame sequence drawn on the front and back of a 100's base 10 block.
 I am planning a 20 day Kindergarten Summer School program for students in our district that; 1) are at risk, and 2) have never attended pre school.  I want to use 10 frames to assist them in learning about numbers. I can visualize a very active "Calendar Time" that does alot of singing and choral counting.  These "COUNTING BLOCKS" could be handed out each day to assist the students, and to help them make a visual picture of the numbers value while they are particpating in the choral counting. They will also assist the student as they compare the value of numbers from 1-5. If a child is ready to discuss 6-10...all they do is turn them over to the other side.  No cutting out...no laminating...and teachers will actually use those base 10 blocks that are put away in a closet.

What do you think about this idea?

Deborah Devine

What Common Referents Should Students Understand in Order to See the Relationships between Fractions, Decimals, and Percents?

Since I've been creating all of these fraction, decimal, and percent games recently, I began to think about this question:

What basic fractional measures should all students be able to picture in their minds so that they can compare different fractions, decimals, and percents?

Well, I like to think about a measuring cup set to help me answer that question.

If a student can compare and visualize: 1 whole, 3/4,  2/3, ½, 1/3, and ¼ , then they can use this information to compare other quantities.  For example, if I was trying to make sense out of 5/8, I would think:

•4/8 is the same as 1/2

•5/8 is a little more than 4/8 or 1/2

•So 5/8 is a bit more than 1/2 or 50% or .5

•I bet it is about 60% or .6 something (actual = .625 or 62%)

Now... compare 5/8 and .42.  Could you do it?

Deborah

P.S. This is the perfect reason why you should have your children cooking and measuring with you in the kitchen... building number sense!

Getting To Know You...Fraction, Decimal, and Percent Game

This is the 3rd Game using the Everyday Math Fraction/Decimal/Percent Card Deck. This game would be a great introduction to the study of the number sense idea that all three values represent the same amount.  As you can see on the illustration shown on the game board, all three values of 3/4, .75 and 75% have 75 out of the 100 squares colored in to represent the three amounts.

Why take the class time to play this game?  Many students have difficulty making the connection that the values expressed all represent the same value. By using the same 10 x 10 grid to express all 3 values, that helps the students see the connection too.
  Click here to get a copy of the gameboard.

Please know that you can also create your own fraction/decimal/percent cards in place of those created and sold by Everyday Math.  I'm just highlighting the Everyday Math product because many teachers already have them, but don't utilize them fully in their classrooms.  I found a great internet site that allows you to create your own cards and will discuss it in a future post.

Deborah

100 Number Grid Game Multi-sized

 

My size 7 1/2  shoe gives you an idea of the size of each individual number grid rectangle.

Using this 54 inch by 84 inch 100's Grid enabled the children in a 1/2 Multigrade Bilingual Classroom to have  so much FUN    a rich educational experience while learning how to navigate and understand the 100's grid chart.

Examples of activities we did together.
First, I made sure everyone could navigate around the 100's chart. Everyone took off their shoes and did this activity in their socks (giggle, giggle). Everyone in the class walks on the 100's chart the same way that our eyes travel as we read the 100's chart from 1 to 100. 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, and then all the way back quickly to 11. We continue to walk just like our eyes do all the way to 100.

The class then sat around the chart with their own personal 100's chart to follow along with their finger.  I told the class I only choose students to walk on the mat if I see  them participating 100 % !
So one child is chosen to:

• stand on the number 35, add one more, add one more, add one more...you are now on 38. The class was asked,"What happens when you move to the right on the hundreds chart? YOU ADD ONE MORE TO THE NUMBER YOU ARE STANDING ON.
• (next child) stand on the number 35, one less, one less, one less, one less...you are now on 31. The class was asked "What happens when you move to the left on the hundreds chart? YOU SUBTRACT ONE FROM THE NUMBER YOU ARE STANDING ON.
• (next child) stand on the number 35, step down one row, step down one row,...you are now on 55.  The class was asked "What happens when you move down one row?  YOU ADD 10 MORE TO THE NUMBER YOU ARE STANDING ON.
• (next child) stand on the number 35, step up or backwords one row, one row, one row...you are now on 5. The class was asked "What happens when you move one row up? YOU SUBTRACT 10 FROM THE NUMBER YOU ARE STANDING ON, OR END UP WITH 10 LESS.

• (next child) In order, the children sitting around the chart give a command to the child standing on the chart, "One less, One less, One more, ten more, three more, ten less.... "

• Next, I tell them we will be playing a game that let's them practice using the 100's Chart. It is the Everyday Math Game, "Juego de la cuadricula de numeros" which translates into "Game of the grid of numbers". Perhaps you will recognize the Everyday Math Game called the "Number Grid Game"
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Basicly the game is played like this:

Materials	1 Hundreds Chart 1 die for the First Graders, or 2 dice for the Second Graders a game marker for each player
Number of  Players	two or more players
Directions	Players place their markers at ONE on the number grid. Player A rolls the die and moves 10 spaces if a "1" is thrown, 20 if a "2" is thrown, and the face-value number of spaces for all other throws. Player B follows in turn.
Winner	Play ends when one player gets to 100 or beyond

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 Deborah

Just for Once...Can I Buy It Instead of Making It!

I purchased this colorful, foam set of "Ten Frame Numeration Board" from EAI.  (click to see details about this manipulative)

Some times I just get tired of making student math materials! 
After our linky party about Debbie Diller's "Math Stations", I realized how important it is for students to use materials like 10 frames to develop number sense within the context of ten.  My 5-year old granddaughter and I are having a blast working with them this summer. We are working on adding doubles like 2 + 2 = 4 . Today she noticed that all the answers have a "partner" (even number).

When used in a classroom the magnetic backing will be useful to model to the whole class or a guided math small group.

When I ordered the materials online, I shouted, "Hallelujah, that's done!" My husband asked me what I was doing and  I explained how useful my purchase would be, and how much time I would save. He said that was a great idea since I would be painting 22 shutter "partners" to save $450 that the painters wanted to charge.  So instead of making math materials I am now painting 44 shutters .....