Expanded Notation & Number Lines

This week we continued working on composing and decomposing numbers, but to higher place values. The students also learned about expanded notation which they seem to love! Expanded notation is basically just separating the digit from its place value.

Expanded notation example:

12,567= (1x10,000)+(2x1,000)+(5x100)+(6x10)+(7x1)

I created a game where they roll a dice to create a 4 digit, 5 digit, or 6 digit number and then they represent that number in expanded notation. The students have been loving it! Challenge them at home to show you an example and teach you what they learned. 

We also began focusing on number lines. One thing I have noticed is as a whole we struggle with skip counting past 100. For example, the students count by 10s well, but when we get to 100, rather than connecting that the pattern continues to 110,120,130,etc, the students will switch to ...80,90,100,101,102,103,etc. I've been working on trying to build these patterns, but you can help at home too. For example, you can challenge your child to count by 10s from 100-300. (I definitely don't recommend starting at 0 and doing this all the way to 1,000 due to time, but even chunking numbers will help!) This is also helpful past the thousands. Example: Count by hundreds from 1,000-2,000 which would be 1,100, 1,200, 1,300, etc.

We did a number line activity where I passed out numbers and the class had to figure out where they belong on a number line which is easing us into the idea of rounding. We will focus a lot on the number line to help with rounding. For example, 34 is between 30 and 40, but on the number line you can see it is closer to 30 than 40. I like to use the example of miles on the road. If you were driving and your family's car ran out of gas at mile 34. Would you rather walk 4 miles back to the 30 mile exit or 6 miles to the 40 mile exit to get gas? This is a real world connection that seems to help them! We start by placing numbers correctly on a number line simply because that is a prerequisite to eventually be able to round mentally.

*The clothes pin number line collapsed once we finally placed our numbers, so I quickly improvised and threw tape on the ground and we placed them that way. It was pretty funny!

If you have any questions please let me know!

Place Value

This week we have focused on place value and the relationships between two place values. The students have learned a lot of new vocabulary.

Compose - to join sets or numbers

Decompose - to break down sets or numbers into smaller sets or numbers

Value - the amount a digit is worth based on its place in a number

Digit - the symbols used to create a number (0,1,2,3,4,5,6,7,8,9)

At the beginning of the week we composed and decomposed numbers different ways. 

Later in the week we focused on place values past the thousands place. The students learned more about the thousands place, ten thousands place, and hundred thousands place. We even built ten thousands using place value blocks and pictures of place value blocks. We focused on the relationship of place values with their next door neighbor. For example: The tens place is 10 x larger than the ones place because ten ones create a ten. The hundreds place is 10x greater than the tens place and it takes ten tens to create one hundred. We focused on patterns and how to read larger numbers. I'm working on the students not saying the word "and" when they read a number. For example: 12,335 is read as "twelve thousand, three hundred thirty-five," NOT "twelve thousand, three hundred and thirty-five." This will help the students when they learn decimals in 4th grade. 

First, we started by creating ones, tens, hundreds, thousands, and ten-thousands with blocks as a class. 

Then, I sent the students back to their seat to complete their "job." Each student was responsible for cutting it certain place value blocks and then as tables we constructed one thousand. As a class, we created a chart to show ones, tens, hundreds, thousands, and ten thousands. We did not create hundred thousands, but we talked a lot about them! 

This was the end result! I hung it on the wall after and we will use it as an anchor chart the rest of the year. 

It is so helpful to find real world examples of numbers in your every day life and point them out... Especially up to the hundred thousands place. We discussed real world connections, but pointing them out to your child will help make their learning more meaningful. Even sharing your thought process of doing mental math is helpful. For instance, when you go to the grocery store, share how you calculate the amount you are spending, share how you use mental math to find an estimate, etc. If you discuss these with your child encourage them to share what they discovered with me in class! 

Growth Mindset

Today we focused a lot on having a growth mindset when it comes to math. Math can be very frustrating for students because it takes a lot of hard work to master a new skill. Enjoying math is half of the battle when it comes to mastering a new skill. I began by reading a story to the students. As I read, they closed their eyes and pictured themselves in the story. 

We talked about how that would make them feel if their teacher told them they couldn't play on the monkey bars just because they didn't make it the first time. We also talked about how they could make it all the way across with practice and hard work. This lead to a discussion how both students AND teachers should have a growth mindset. We also connected this with learning math. We also discussed the power of the word "yet." We discussed how if math is hard, we don't say "I can't do it!" Instead, we can say "I can't do it YET." If they work hard and have the right mindset it will help them reach success. 

Next, we watched a video on withmathican.org. It is extremely powerful and made many of the students share how they have felt at some point like they weren't good at math or scared to share ideas in class. It was a great open discussion that really built our bond as a class and contributed to creating the positive and safe environment I strive to maintain. Here is the link to the video:

http://youtu.be/sLPFaOvhlKw

Next, we went to the website (withmathican.org) and talked about our class pledge. I created a poster with the pledge and the students personalized their signature to hang around the pledge. After they posted their signature the students held their right hand and we said the pledge together. 

Www.withmathican.org is a great website for resources to build a growth mindset within students. There are tons of resources for not only teachers, but parents as well! I encourage you to take a look and possibly even sign the pledge online with your child. Growth mindset is something I will try to build all year long within my students. It helps the students realize it's okay to make mistakes as long as we learn from them, that all students can be successful with hard work, and to never give up. It helps keep a positive relationship with math. As a teacher that is one of my biggest goals for my students! I want them to LOVE (or at least like) math!

I hope you all have a great week. It was a successful first week of school!! :)

Guess My Number

At the end of the day I love to play "Guess My Number" with my class. The students absolutely love it and they don't even realize the problem solving, number sense, and concept of place value that goes into the process of guessing my number. We started small by guessing between 0-100, then built up to 0-500, and now we are guessing between 0-1,000. The students base their guess based off how many digits are correct, how many are in the correct place, and if my number is greater than, less than, or equal to the number they guessed. It's so much fun!

Graphing

This week we have been learning about graphs! The students started by creating a class pictograph representing their birthdays. We discussed the importance of reading the title, categories (months in this case), and scaled intervals (what the graph is counting by). 

Next, we created a frequency table (new to 3rd grade) using the same information. We emphasized the similarities and differences. It was important for the students to understand that just because they look different doesn't mean we changed the data. 

Then, I passed out a random mixture of graphs to the class. Some were frequency tables, dot plots, and pictographs. I partnered the students up and they shared what they noticed about their graph. Then I turned on music and they walked around the room. When the music stopped they had to freeze and partner with another group closest to them. The students compared their graphs and shared the similarities and differences. We did this a few times.

The last time they rotated to the music they sorted the graphs based on whether they thought it was a dot plot, frequency table, or pictograph. Both classes completed the sort correctly the first attempt! We watched a mini video about each graph after the sort and I gave the students the option each time to make changes to our sort. I didn't reveal if they were correct or incorrect until the end. They had great conversations!!

I encourage you to ask your child what they know about each type of graph. You could also ask them to give you ideas about what data they might represent using each type. A pictograph is a graph using pictures, a frequency table uses tallies, and a dot plot uses dots to represent information. 

We will continue to work with graphs throughout the year. 

Welcome!!!

I am looking forward to being your child's teacher this year. I will be teaching your child math and science. If your child is in my homeroom class then I will be teaching the math, science, AND, social studies. This is a great place for you to see firsthand what your child does in our class and an excellent way to stay "in the loop!" I will post reminders, updates, pictures of our learning, and student work samples. I encourage you to check our blog frequently.