An Alternative to "Add the Opposite" from Nathan Kraft.

We started working on adding integers this week and will move into subtracting integers next week. The past two years, I have introduced it with algebra tiles and taught it as adding the opposite and the students still struggle with what to do when subtracting a negative. His alternative focuses on using number lines. My students have used number lines for adding and subtracting integers, but it has been more of an after thought than a deliberate lesson.

Combining Like Terms from Show Your Thinking

Show Your Thinking shared this MadTv video to introduce students to combining like terms. I like the hook and controversy that it can cause fro students.

Solving Two Step Equations from Jon Orr

I want to revisit this post closer to when I introduce two step equations. A double number line is used to help students determine the value of x.

Flipping Bottles also from Jon Orr

I saw some talk on Twitter about making the flipping bottles fad a math activity and Jon Orr did just that. My students definitely flip bottles more than I would like and this activity would be fun for them.

## Sunday, October 16, 2016

## Friday, October 14, 2016

### Rational Numbers Song

This song has been stuck in my head. When my students learn how to classify numbers, we listen to this song at least once a day. It is a simple song with lyrics that students are easy to remember.

I dare you to listen to it 15 times in a week and not have it stuck in your head!

## Sunday, October 9, 2016

### Posts I Love--Part 7

I love reading math blogs. I like reading what math teachers try in their classroom and reading their reflection on how it went.

Here is a collection of blog posts I love!

Fraction Ordering Activities from Math Fireworks-- The students will be practicing ordering rational numbers this week.This activity from Math Fireworks only talks about fractions, but I would like to expand it to include decimals and percents. I like the ideas of having students share their reasoning and discuss mistakes with each other.

I found this game which is a very basic but necessary beginning practice for graphing in all four quadrants. Stock the Shelves

I Speak Math shared this game. I will have it as a small group station to practice integer operations and absolute value. All I'll need is a deck of cards.

Finally, I love this activity about volume over at No. 2 Pencils. She poses the question "How many starburst can fill our classroom?" and students go about measuring and formulating plans to figure out the answer. Definitely a thing I want to try.

Hopefully you are inspired to try something new!

Here is a collection of blog posts I love!

Fraction Ordering Activities from Math Fireworks-- The students will be practicing ordering rational numbers this week.This activity from Math Fireworks only talks about fractions, but I would like to expand it to include decimals and percents. I like the ideas of having students share their reasoning and discuss mistakes with each other.

I found this game which is a very basic but necessary beginning practice for graphing in all four quadrants. Stock the Shelves

I Speak Math shared this game. I will have it as a small group station to practice integer operations and absolute value. All I'll need is a deck of cards.

Finally, I love this activity about volume over at No. 2 Pencils. She poses the question "How many starburst can fill our classroom?" and students go about measuring and formulating plans to figure out the answer. Definitely a thing I want to try.

Hopefully you are inspired to try something new!

## Saturday, October 1, 2016

### Positive and Negative Situations Vocabulary

This week we started classifying numbers and I introduced integers and the concept of positive and negative numbers.

We started by looking at a thermometer and a table with temperatures decreasing and asking the students what the temperature would be if the decreasing temperatures went below zero.

This would also be a great time to ask students where they have seen/heard about negative numbers so they connect this new knowledge with what they already know.

Then I gave students words to sort into negative, positive or zero. Afterwards we I asked students to give me examples of they words belonged into each category.

It would be "easy" to just skip over this vocabulary as we went into integer operations and word problems. However, I have several LEP students in my classes and just assuming they know these words will make things more difficult in the future.

This sort is available in the Real World Integer Situation Product on TeachersPayTeachers.

## Saturday, September 24, 2016

### Properties of Operations Sort

Properties of Operations is not my favorite thing to teach. I love how numbers work and sharing that with students but I am not a fan of having to memorize names.

So students took notes and they found patterns in equations and describe the rules.

For example, I put the following equations:

1+0=1

0.54+0=0.54

34+0=34

I asked them to find what rule these equations were describing and asked them to find an example of when the rule wouldn't work.

I wanted students to see that they already knew most of these properties, they just didn't now the names.

After they took notes, we did a card sort. Each group got a bag with the names of the properties we discussed and equations to match to the property.

I love card sorts in math and I loved hearing the conversations they had as they disagreed and tried to convince each other. I also loved seeing them refer to their notebooks because my students see to forget that it is there.

So students took notes and they found patterns in equations and describe the rules.

For example, I put the following equations:

1+0=1

0.54+0=0.54

34+0=34

I asked them to find what rule these equations were describing and asked them to find an example of when the rule wouldn't work.

I wanted students to see that they already knew most of these properties, they just didn't now the names.

After they took notes, we did a card sort. Each group got a bag with the names of the properties we discussed and equations to match to the property.

I love card sorts in math and I loved hearing the conversations they had as they disagreed and tried to convince each other. I also loved seeing them refer to their notebooks because my students see to forget that it is there.

If groups finished early, I gave them a dry erase marker and had them write their own equations to show the different properties. I think I will do this part more later. For the few groups that got to it, it was a great way to see if they understood what each property said.

## Tuesday, August 16, 2016

### District Wide Math Training

Here are the links to the handout, activity, and presentation.

Two Truths and a Lie

Handout

Presentation

Two Truths and a Lie

Handout

Presentation

## Friday, August 12, 2016

### Mathematical Mindsets--Jo Boaler

This should be required reading for anyone who teachers math--from PK to College, from teachers to parents. (affiliate link below)

This book will change how I teacher math this year from the very first day of school. I will continue to blog about how things are going in my classroom, but here are a few bullet points of my main takeaways.

- I am going to talk with my kids about brain research--not just once--but several times throughout the year and heavily the first two weeks of school. I have to change their mindset about math and their selves.
- Homework will look extremely different. Jo Boaler says "homework perpetuates inequities in education." She even talks about how her family has two working parents and after everyone is home and fed for the evening, she wants to spend time with her daughters-not in frustration over homework. My homework was very light in the past, but this year it will be more reflections questions and maybe 1 problem to start on that we finish discussing in class.
- "No one is born knowing math, and no one is born lacking the ability to learn math."
- Mistakes are necessary!
- My grading will look different--if mistakes are necessary, I can't punish students for making them.
- Mental Math will improve--I especially want to show students ways to think about numbers to improve their number sense.
- Boaler talks about using tasks that are "low floor, high ceiling." Everyone can access the task and anyone and take it further.

One www.youcubed.org--which is a website Jo Boaler is part of--there are two weeks of inspirational math with videos and activities designed to help students change their mindset about math. What I like most about the activities is they are "low ceiling, high floor" but they also give students practice to work together in math. Math should be a very social subject. I will be using (and blogging about) several about the activities the first two weeks of school.

## Tuesday, August 2, 2016

### CAMT 2016--Jo Boaler

I went to CAMT the first time this year and I presented.

~~I wanted to do a quick run down of my take aways from CAMT. ~~ This turned into a post just about Jo Boaler--everything else will be later.

I have been a fan of Jo Boaler for awhile. I was first introduced to her through her book

__What's math got to do with it?__She advocates for changing math education to reach more students and help more students become successful. Jo Boaler currently runs youcubed.org which focuses on having a growth mindset. Here are some take away from her presentation.- Every child can excel (not just learn) math.
- Schools decide who can and can't do math an an early age (This has always been one of my pet peeves. If a child wants to take an advanced math class and is willing to work, why should we stop him/her!)
- The times we are challenged and struggling are the most beneficial times to learn
- MISTAKES GROW YOUR BRAIN (I think this will be my motto for the coming school year)
- Our message to students should be "I am giving you this feedback because I believe in you."
- Speed, time, and pressure stop the brain from working
- We need to stop associating math with speed--we turn away many students.
- Students think that being good at math means being right
- Students should use their fingers in math (I still use my fingers when I add and subtract.)

I want to take her presentation and really live it as a math teacher this year. I want my students to feel confident that can be successful at math. Math was always my hardest subject and it really wasn't until I took College Algebra that I understood any Algebra or until I had to study to take the GRE that I felt I had any type of number sense. I am still not the best, but I know that I will continue to learn and get better. I try to convey this message to my students every year and hopefully this year I can be more successful at it.

What have you done in your classroom to help more students feel they can successful at math?

## Sunday, July 31, 2016

### Happy Planner

So I bought this planner at Michael's after looking at it for 20 minutes. And I couldn't even see the inside because it was inside a box! Very not normal for me and the fastest I have ever picked out a planner. Also, with a coupon, it was about $25. And it came with stickers, a pen, and a highligher.

It's the My Mind's Eye Happy Planner and they have a bunch of different styles but I went for the teacher one. Here is the cover. It has a plastic cover to keep it safe and a nice message.

Each month has an overview page to write goals, tasks, etc. And it comes with a pocket. Right now my pocket holds the stickers it came with, plus some stickers I bought.

Did you know that planner art is a thing? My instagram is full of pretty pictures of people who have decorated their planner with stickers, washi tape, stamps, gorgeous handwriting, etc. I don't have time/patience/money to take all that on, but I like a few stickers to make my planner more fun.

Each month also has a month at a glance-with dates already filled in. I need the dates already filled in--I make too many mistakes when I do it myself.

Each month also comes with some motivation sayings.

And finally it has some check lists. There are 10 pages here. I am not sure if I will use this because I don't like the idea of writing student names, and I would need at least 12 to get through the year, and I like my current system of just printing an excel spreadsheet with all my student names where I can write out assignments and grades.

So here is my happy planner. It almost gives me the motivation to start planning some stuff--but don't worry. I am still on summer break. You might have noticed I have potty training and moving my toddler to a big girl bed to work on this month--no easy tasks.

## Saturday, July 30, 2016

### Two Truths and a Lie--Writing in Math Class

I had a goal to have my students write more in math class this year, without making writing such a big deal. When students hear that they are writing in math, their responses range from disbelief to outright indignation. "Why are we writing in math?! This isn't English."

So I try to sneak it in their when possible.

I did this activity with my students at the end of the year--really the last few weeks of school, after STAAR testing was over. I was pleasantly surprised how engaged they were and I am excited to try it again next year when summer isn't on everyone's mind.

In this activity, we start by playing Two Truths and a Lie-- the get to know you game. This can work at anytime of the year as students always like sharing things about themselves. I first share two truths and one lie about myself (this is how I announced my pregnancy to my students last year) so students know what to do. Then, I give each student a post-it and ask them to write Two truths and one lie about themselves then they share with their group and the other students guess what is the lie.

I spent about 10 minutes on this part. It gets students talking to each other and excited about class. This way when they go into the activity they are smiling and laughing instead of depressed that they have to writing.

Then I explain we are going to do Two Truths and a Lie-- The Math Version. Each group is given a sheet of paper with a graphic or word problem on it. There are 2-3 students per group, so I will have about 12 different papers distributed around the room. The group is then asked to write two truths and one lie about the graphic or word problem.

I did model this for my students before I passed out the papers. I asked them to dig deep and come up with something profound--not something like there are two dots on this graph. I was happy that some students voluntarily did computation as their truths and then wrote a sentence about it instead of just stating facts they could see without computation.

After all groups had their two truths and a lie written down, I gave each student 4 post-its and asked them to find the lies on 4 other papers. I asked them to write a sentence about why it was a lie instead of just stating "Number 2 is a lie."

In the process, students found that some papers had two lies or that there weren't any lies at all--either students didn't follow instructions, or they had made a mistake.

Here are some students papers after the activity.

This activity can be made easily-- you can take pictures of graphics in textbooks, worksheets, make your own graphics, etc. You can have the whole activity be centered around one concept, or a review of several concepts.

I have a FREE sample of what I used in my classroom--it is appropriate for grade levels 6-8.

Here is my first completed activity focused on one topic--Geometry. This has 21 pages of graphics that will prompt students to write about triangle properties, area of polygons, and volume of rectangular prisms. There are two versions--one with just the graphics and the other with two truths and a lie already written for students to choose from.

## Monday, July 4, 2016

### Excused Absence

If you are looking for my CAMT presentation materials, click here.

I have been MIA for a while on this blog and in life. But my reason is good.

My baby girl is going to be a big sister this December and this pregnancy has taken a toll on me. I have done basically nothing but go to work and then come home and crash for the last two months. I am starting to feel a little better and now I have a short time in summer to prepare for everything I want to get done before school starts and then before baby gets here.

We couldn't be more excited for this new baby.

I attended CAMT in San Antonio and presented and heard lots of interesting ideas. I am planning a post to reflect about all I have learned this week.

I have been MIA for a while on this blog and in life. But my reason is good.

My baby girl is going to be a big sister this December and this pregnancy has taken a toll on me. I have done basically nothing but go to work and then come home and crash for the last two months. I am starting to feel a little better and now I have a short time in summer to prepare for everything I want to get done before school starts and then before baby gets here.

We couldn't be more excited for this new baby.

I attended CAMT in San Antonio and presented and heard lots of interesting ideas. I am planning a post to reflect about all I have learned this week.

## Wednesday, June 29, 2016

### CAMT Presentation Links

Thank you to everyone who attended my session. Hopefully, you feel ready to start getting your students to write about math in your classroom.

As promised, here are the links to the presentation and handouts:

Presentation

Handout

Two Truths and a Lie Activity

You can also follow me on twitter @randi_raquel

As promised, here are the links to the presentation and handouts:

Presentation

Handout

Two Truths and a Lie Activity

You can also follow me on twitter @randi_raquel

## Monday, May 2, 2016

### Teacher Appreciation Sale and Giveaway!

It is Teacher Appreciation Week and Teachers Pay Teachers is having a sale!

The sale starts tomorrow and goes until Wednesday--May 3 and 4.

I am having a sale as well! Visit my store here! You can get 28% off every item in the store--don't forget to enter the code CELEBRATE as you check out to get the full discount.

You can also enter to win one of 2 TeachersPayTeachers $10 gift cards. Follow my store for two entries and then you have a few ways to add more entries. The giveaway will close on May 4 at midnight! Enter now before it's too late. Two winners will be notified on May 5.

## Saturday, April 2, 2016

### Percent Bar Graph

We are right in the middle of our statistics unit. Yesterday we started percent bar graphs.

Here is what I found is the most important thing about bar graphs--use data the students connect to. For this categorical data, I collected it from the students. The day before I had them fill out a google form and for each class I used their data--and a few from the other classes to make it 25 different people. I asked basic questions--favorite color, # of letters in first name, # of pets, # of siblings, etc.

We started with taking these notes I came up with the morning of. I rarely have a full page of notes like this without any foldables/cloze notes for my students with accommodations--but I didn't have time to print something.

HOWEVER, notes like this make me EXTREMELY happy. They are so pretty. Early in my teaching career, I had students just write out notes and every time I would have them admire my/their work.

Here is what I found is the most important thing about bar graphs--use data the students connect to. For this categorical data, I collected it from the students. The day before I had them fill out a google form and for each class I used their data--and a few from the other classes to make it 25 different people. I asked basic questions--favorite color, # of letters in first name, # of pets, # of siblings, etc.

We started with taking these notes I came up with the morning of. I rarely have a full page of notes like this without any foldables/cloze notes for my students with accommodations--but I didn't have time to print something.

HOWEVER, notes like this make me EXTREMELY happy. They are so pretty. Early in my teaching career, I had students just write out notes and every time I would have them admire my/their work.

For the class percent bar graph, we graphed for "How many letters are in your first name?"

After we did it as a class, I gave groups the print out of the data I had collected. They had to choose one question and make a relative frequency table and a percent bar graph. Here are some examples:

The students to that data and tried to find which line was theirs and got so excited about it. Instead of just giving them random numbers to make a graph with, giving them something they can connect to has made the difference. Nobody complained about doing this--the only complaints I got was that they didn't get to help enough.

## Wednesday, March 30, 2016

### Area of Polygons Practice

After the students learned the area of triangles, parallelograms, and trapezoids, they needed to practice.

It would be easy to give them a worksheet with the shapes on it and all the measurements given and they just have to plug the numbers into the formula the solve.

Worksheets can be useful, but when there is a way to not do a worksheet, do it.

I did this activity last year and wish I would have saved all the shapes I made. So I remade them again and laminated them.

I drew 10-12 triangles, parallelograms, and trapezoids each. I spread them around the room and asked the students to find the area of the shapes. They measured everything to the nearest centimeters.

To make them talk to each other about it, I asked them to verify their answers with their classmates. I put a large poster at the front of the room with a table of the shapes. Once students have verified their answers with 3 other classmates, they could start adding the area of the shapes to the poster.

It would be easy to give them a worksheet with the shapes on it and all the measurements given and they just have to plug the numbers into the formula the solve.

Worksheets can be useful, but when there is a way to not do a worksheet, do it.

I did this activity last year and wish I would have saved all the shapes I made. So I remade them again and laminated them.

I drew 10-12 triangles, parallelograms, and trapezoids each. I spread them around the room and asked the students to find the area of the shapes. They measured everything to the nearest centimeters.

To make them talk to each other about it, I asked them to verify their answers with their classmates. I put a large poster at the front of the room with a table of the shapes. Once students have verified their answers with 3 other classmates, they could start adding the area of the shapes to the poster.

Once I made and laminated all the shapes, the activity was easy to put together. I didn't even use any copies! Just notebook paper.

If you dont want to draw your own shapes, you can use this file here. Download it for free.

Here is another way for students to practice finding the area of polygons fro my TpT store.

.

In Texas, 6th graders are to "determine solutions for problems involving the area of rectangles, parallelograms, trapezoids, and triangles and volume of right rectangular prisms where dimensions are positive rational numbers."

## Monday, March 28, 2016

### Decomposing a Trapezoid--Finding the Area

This has been one of my most favorite and wonderful lessons of my entire teaching career. My students pleasant surprised me with how awesome they are.

Students need to be able to explain how shapes can be decomposed into other shapes to find the area--that is how the formulas are derived.

There are several different ways trapezoids can be decomposed and rearranged to make other shapes. Before this lesson, the students had a guided lesson to decompose parallelograms to rectangles and triangles to parallelograms. So they had previous experience with cutting and rearranging shapes.

I wanted to see if they could take what they had done and apply it to trapezoids.

And they did awesome.

I gave them a sheet of trapeziods and a ruler. I asked them to pick any trapezoid and find a way to decompose it, rearrange it, and find the area.

My advanced class found 8 different ways to find the area. My on-level class found 5 different ways.

I don't have the list we made in front of me, but these are some of the ones I remember they were able to find.

Students need to be able to explain how shapes can be decomposed into other shapes to find the area--that is how the formulas are derived.

There are several different ways trapezoids can be decomposed and rearranged to make other shapes. Before this lesson, the students had a guided lesson to decompose parallelograms to rectangles and triangles to parallelograms. So they had previous experience with cutting and rearranging shapes.

I wanted to see if they could take what they had done and apply it to trapezoids.

And they did awesome.

I gave them a sheet of trapeziods and a ruler. I asked them to pick any trapezoid and find a way to decompose it, rearrange it, and find the area.

My advanced class found 8 different ways to find the area. My on-level class found 5 different ways.

I don't have the list we made in front of me, but these are some of the ones I remember they were able to find.

- Cut the trapezoid by the diagonal to make two triangles
- Cut off two triangles at the ends to make one square and one rectangle
- Cut off one triangle and you have a triangle and a rectangle (When one of the sides of the trapezoid is also the height
- Cut the trapezoid by the height, rearrange and make a rectangle
- Double the trapezoid to make a parallelogram
- Cut off one triangle, add to the other side to make a rectangle

After the students spent some time exploring, I had students share what they found. We looked at the measurements of the original trapezoids and of the new shapes they created and found some patterns.

Sometimes, the new base was in between the two original bases(specifically it was the average of the two bases). When you had a triangle, you used the formula 1/2bh and added to the area of the other piece. If you doubled the trapezoid, you would have to half the area of your new shape.

The last step was to write a formula that they could use to find the area of a trapezoid so they wouldn't have to decompose a trapezoid every time they wanted to find the area. I'll need to improve this part of the lesson. Students got the adding something, the multiplying the height and either multiplying by 1/2 or dividing by 2, just not in a way that would work.

It was a fun lesson and I was walking around so excited all day long because they were doing such a good job trying and finding ways to decompose the trapezoids!

If you want pdf of the printable with the trapezoids, you can download it here.

If you want some notebook pages that show decomposing shapes to find the area, I have some in my store.

## Thursday, March 24, 2016

### Measures of Center

We started our unit on Statistics after spring break. It is one of my favorite things to do and teach and it is not easy for students to understand. There are so many little things about that you understand once you've studied statistics for awhile. I took some pretty intense statistics classes in college, so I feel like everyone should learn everything about it--I have to remind myself that my 6th graders need to be gradually introduced to it.

So this is the foldable we created for Mean, Median, Mode, and Range--I let my students use my markers and they loved it--I'll have to pull out markers more often.

I read this book in college and it is so interesting. It's been a few years since I've read it, I might have to pull it out again.

So this is the foldable we created for Mean, Median, Mode, and Range--I let my students use my markers and they loved it--I'll have to pull out markers more often.

I read this book in college and it is so interesting. It's been a few years since I've read it, I might have to pull it out again.

## Sunday, March 20, 2016

### Properties of Operations Pockets

I love little pockets in notebooks. They are also a great way for students to sort things and resort them later to quiz themselves.

This properties of operations page is my favorite.

This properties of operations page is my favorite.

All the cards with 10 different properties of operations is available on Teachers Pay Teachers.

## Wednesday, March 9, 2016

### Classifying Numbers--Nesting Containers

6th grade is the first time students in Texas have to classify numbers. It has been a difficult concept for my students to understand--especially that numbers can "fit" into several different classifications.

I found some "nesting" tupperware to help my students visualize it. I have kept this handy in my classroom so every time we talk about classifying numbers, I pull these out.

I found some "nesting" tupperware to help my students visualize it. I have kept this handy in my classroom so every time we talk about classifying numbers, I pull these out.

So if we classify a number as a natural number, it is also a whole number, integer, and rational numbers since it "fits" into the bother containers.

I have 7 different classifying rational numbers stations available in my store.

## Monday, March 7, 2016

### Triangle Inequality Theorem

This is the second year I have taught the Triangle Inequality Theorem using spaghetti and I love doing it this way.

First I had students copy the table into their notebook and gave them a piece of spaghetti. Their instructions were to break it into three uneven pieces, measure the three pieces, and record their measurements under the columns short side, medium side, and long side. (I asked them to do three uneven pieces because last year too many students broke them into the exact same length and it was more difficult to illustrate the concept)

As the students were measuring, I was walking around the room asking students to write their measurements on the board. I looked for a mixture of those who lengths that would make a triangle and those who did not. I asked a few students to come to the board and share their triangle lengths.

I didn't have the column labeled Short+Medium yet. So with 4/5 columns filled in, I asked the students to look for a pattern. Some classes were able to see that when two small side lengths were more than the large one, there was a triangle.

For the class that did not come to that conclusion, we added the short+medium, then added up those two sides and I asked them to look again.

It is one of my favorite lessons of the year. After we determined what the Triangle Inequality Theorem says, we put this foldable into the student notebooks. My students did really well explaining when a triangle could be formed.

This foldable is now available in my store.

## Saturday, March 5, 2016

### Integer-nary

Integer-nary!

I really liked it and I loved watching them do it. They had some great conversations about what models to use to represent integer operations and it helped me see where they need more help.

I made cards with various integer problems on it like -5+3 and 4*-2 and they had to model the expression and their partner had to write the expression that matched it.

I think this could also work with algebraic expressions and equations--and that will be my next station to try with my students.

I really liked it and I loved watching them do it. They had some great conversations about what models to use to represent integer operations and it helped me see where they need more help.

I made cards with various integer problems on it like -5+3 and 4*-2 and they had to model the expression and their partner had to write the expression that matched it.

I think this could also work with algebraic expressions and equations--and that will be my next station to try with my students.

Subscribe to:
Posts (Atom)