Learning about ratios and proportions

Today Otter explored ratios and proportions using ETA’s Hands-On Math Standards book.

Photograph by Otter!

I handed Otter the bag of plastic square tiles and told him to pretend that each tile measures 1 square foot. I then asked him to build a pretend “porch” in the shape of a rectangle measuring 45 square feet. I told him it takes 3 pints of paint to paint his new porch.

I then asked him to figure out how much paint he would need for just 15 square feet. This is how he found the answer.

Another photo by Otter!

After that I asked him how much paint would he need if the porch measured 75 square feet! He figured he would need 5 pints.

Yep, another picture by Otter

After this activity and a worksheet from the ETA book we talked about changing proportions, like doubling a recipe for cookies. Proportions are now a crystal clear concept instead of a math term to be easily forgotten!

We’ll be doing a lot of hands-on math activities this year to really get ready for algebra next year. You can read about some of the resources I’m using this year in a previous post here.

Making Math Fun with Hands-on Pre-Algebra

It’s not often that Otter asks to do MORE math. However, after incorporating some recent hands-on pre-algebra activities into our summer studies, I’ve been hearing that quite a bit!

Transitioning from concrete math to the abstract can be a little tough for some kids. It doesn’t have to be though!  Below are some of the resources I’ve used to help make pre-algebra not only tangible, but also fun.

Exploring Algebra and Pre-Algebra with Manipulatives

Learning about integers while playing a game!

Exploring Algebra and Pre-Algebra with Manipulatives is one of Otter’s summer favorites. Chock full of lots of activities, this book even comes with tear-out tiles you can use for some of the games. You do need to copy some of the pages though for things like the algebra dominoes, game boards, and activity sheets.

Otter was having trouble solving equations like “40 – 2X = 6”. Looking at rows of problems like that in his math text just made his eyes glaze over. After playing a game with some math dominoes, he was solving these types of problems like a pro and then asking if he could do MORE. After I picked my jaw up off the floor we played for about an additional 45 minutes or so.

Matching up math domino cards with mom

math integers

Learning about integers the easy way

integers game

Playing a game with mom to learn about positive and negative integers

The Hands-On Equations Learning System

 

Another big hit is The Hands-On Equations Learning System. I honestly think this is Otter’s favorite math “program” he’s ever used. Every time I pull it out he’s enthusiastic and his math confidence soars.

Basically the program takes something that is usually thought of as abstract and makes it totally concrete, helping to lay a terrific foundation for algebra. I really wish I had had access to something like this when I was a kid.

UPDATE: You can now get the Hands-On Equations Learning System via a set of apps and save a TON of money:

Hands-On Equations 1

Hands-On Equations 2

Hands-On Equations 3

Hands-on Equations

Learning how to solve a linear equation

Hands-on Equations is so easy to use and understand. In the above picture, Otter is solving the equation 5X – 3X + 2 = X + 5. In this particular lesson he is learning to take away pawns as part of the set-up process. So, the first thing he needs to do is get rid of 3 pawns from the left (that’s the 5X – 3X part). Once he’s done that, he has things set up and is ready to solve the equation.

The next thing he would do is subtract one blue pawn from each side (because it’s a balance whatever you do to one side you must do to the other!). Finally, he would subtract 2 from both sides (get rid of the red 2 cube and replace the 5 cube with a 3) and come up with the final answer of X=3.

Afterwards he has to check his work. He checks it by looking at the original physical setup, NOT the original abstract equation. This way he understands the concrete meaning of the abstract equation.

The program comes with 3 levels of books and each step is spelled out visually to help you easily teach each concept. There is also the option to purchase DVDs, but the books were enough guidance for me.

I also order the Verbal Problems book that goes with the program. Using this book, he’ll be able to solve problems like the following by using hands-on methods that really help make the meaning and problem solving clear:

Dave had one package of cookies in his bag. Ed received 4 cookies from a friend on the bus to add to the 2 packages that his mother had packed for him. Andy did not eat breakfast that morning, so he had already eaten 2 cookies from his one package of cookies. Each package of cookies had the same number of cookies at the start. When the boys were ready to eat the cookies, they counted a total of 10 cookies. How many cookies were originally in each package?

You can purchase Hands-on Equations from Amazon or Rainbow Resource for around 35.00. It’s one of the best supplementary math purchases I’ve made.

Another hands-on pre-algebra resource I bought is ETA’s Hands-On Standards Math Online for grades 7-8.  You can order physical copies, but I found it easier to use the online version which is basically PDFs you can print out as needed.

Hands-On Standards

“Home” screen for ETA’s Hands-On Standards Math Online

Each lesson has full-color lesson pages as well as black and white student pages to print out and work on. You can look at some of the sample lessons online for free. The only downside to the program is that you have to purchase a lot of manipulatives. Fortunately I already had some of the required items, but I had to search all over the ETA website for the rest of the ones I needed and the cost added up pretty quickly (over $100 bucks for the program and the manipulatives!). I also had to put in a special request for a single order of some algebra manipulatives as they only had a classroom sized set listed on the website. Because of this, I would recommend the other two previous resources, if you are looking for something that is inexpensive, quick and easy to implement your math studies. However, if you really need more, the ETA program is well put together with lots of different “things” to play with while you are learning math that help keep the interest level high.

ETA Hands-On Math: Using fraction towers to find percents

ETA Hands-On Math: Using fraction circles to figure out decimals and percents

ETA Hands-On Math: Figuring out decimals, fractions and percents using colored square tiles.

Just because you’ve got a middle schooler or a high schooler doesn’t mean you have to stop using manipulatives! In fact, for some kids (like Otter), they really help foster a true understanding of higher level math. Pre-algebra doesn’t have to be boring and it doesn’t have to be hard!

Siege Tower

I like to include a variety of projects and extras for most of our school subjects. As one mom who recently wrote me put it…it’s the “whipped cream and cherry on top” of our studies! Here’s a recent project Otter made for history:

 

It’s one thing to read about a siege tower. It’s quite another to actually construct one and see how it works first hand. That’s some major whipped cream and cherry action right there.

You can order your own siege tower from Pathfinders here.

We are moving out of the middle ages now and heading into the Renaissance. My Awesome Timeline History Schedule has been a great success and I look forward to continuing with it. If you’d like a copy, send me an email.

Chemistry

Otter is keeping a chemistry notebook. Inside he’s keeping track of some of the experiments we’ve done using this lab report. He’s also doing some notebooking pages, lapbook elements glued onto colored paper and other printables. When he’s done with chemistry, he’ll have a nice notebook to browse through and remember the various projects he completed. Here’s the cover I made to slip into the front:

Chemistry notebook

Here are some of the assignments he’s already entered into it:

This was a project from Christian Kids Explore Chemistry. Otter took a look at the ingredients of various items and wrote them down to see how “chemistry is in our home”. He noticed how some of the items had the same chemicals.

chemistry

In the 2nd week of our study, he learned about chemistry tools, safety and measurement. I made him this lab sheet to record the data from a hands-on activity from C.K.E.C. . Otter learned that when you pour liquid from one container to another, eventually it affects the measurement. He also learned how to measure from the meniscus of the liquid.

Chemistry worksheet

Here’s a cut & paste vocabulary activity I downloaded from middleschoolscience.com.

matter

He also made these lapbook booklets about the scientific method and pasted them onto colored paper:

chemistry lapbook

Here’s another cut & paste activity that helped define solids, liquids and gas:

solid, liquid, gas

I’m also making use of BrainPop, one of our favorite online activities. I found this printable to go with the movie about solids, liquids and gases.

BrainPop

He also did some fun lab safety papers with a Sponge Bob theme. You can find the teacher’s notes here.

Sponge Bob science

Here’s an activity he did examining various compounds and mixtures:

chemistry worksheet

Otter isn’t just learning about chemistry. He’s still exploring other science interests, such as astronomy, on a regular basis. He pulled out this kit we forgot to do when he was studying WinterPromise’s Sea & Sky program and completed it the other day. He looked up the actual positions of the planets from this site, to make sure every planet was in its place.
Woe to the big brother who might move one of them out of the proper orbit!

Solar system kit

 

The other day we read about plasma globes and did some experiments. Here are the pics. Warning: I’m not recommending you do what we did! These experiments could be dangerous and we were referencing websites and videos such as this one. In other words, don’t try this at home.

Otter got a fluorescent light bulb to light up, just by holding it near the plasma globe:

Plasma globe and light bulb

If you put a penny on top and then touch the penny with a nail, you can see a small arc of electricity:

plasma globe

Super close up of the above:

plasma ball

Otter also got an LED light from his Snap Circuits kit to light up just by touching it to the plasma globe:

plasma globe and led

We also recently split water into hydrogen and oxygen. Dad put a lit match to the hydrogen we collected and we all got to hear a POP!

Another experiment Otter did was to figure out how to separate salt from sand:

chemistry

Other recent things we’ve done in chemistry:

  • Learned about hydrogen
  • Distilled salt water
  • Watched an acid reaction
  • Put up a periodic table poster
  • Learned about lab safety with Sponge Bob
  • Learned about controls and variables
  • Went on an elements scavenger hunt
  • Learned about Antoine Lavoisier

I think Otter is in science heaven lately. Chemistry is full of fun experiments and explorations.

For history, Otter made some ancient Greek honey cakes:

Honey cakes

Learning about Egypt

In history we are finally wrapping up ancient Egypt! Here are some pictures of some recent projects:

This papyrus kit was a big hit. You get real bundles of papyrus, a plain sheet of papyrus paper and another sheet with a printed outline on it of an Egyptian scene you can color or paint. The kit comes with instructions on how to make your own sheet of papyrus paper. We ordered ours from Rainbow Resource.
We never did successfully create a piece of paper from the plant fibers, but the kit was still worthwhile to get to look at/feel a sheet of real papyrus paper (which is quite rough and sturdy!) and to see the plant material that makes it.

Papyrus kit

Here’s a map of Egyptian sites on the Nile from Remembering God’s Awesome Acts. I didn’t schedule this book into Otter’s ancient history schedule even though I think it makes a good supplement. We just didn’t have the time or interest to use all of it. If your student really wants to dig into early Biblical history and Egypt, you might want to check it out.

map

This Lift The Lid On Mummies kit comes with lots of mummy making “stuff”. I bought it years ago to use with the “big kids. Now it was Otter’s turn, but he didn’t like it as much as the others had.

Lift the Lid on Mummies

This is a lift the flap Rosetta Stone with a hieroglyphic translation exercise:

Rosetta stone

I’ve been working with Otter on narrating summaries. After I read a selection from our history to him, I ask him questions about it (to help him pick out the “main” facts). Then I have him narrate out loud. After that he writes his narrations down on notebooking pages and files them in his history notebook:

Notebooking pages

For a great article on narration, click here to go to Jimmie’s Squidoo page.

Here is Moses from Famous Figures of Ancient Times: Movable Paper Figures to Cut, Color, and Assemble:

Moses

Otter also painted King Tut. We used a simple lesson from the Art Projects For Kids website. I love some of the art lessons on Kathy’s site and plan to visit again soon for some lesson ideas!

The paint container in the pictures was made from the bottom of a plastic milk jug. It’s perfect- it even has raised areas inside to keep the colors of the paint separate.

How to Draw King Tut

Otter also colored a map of the 12 tribes of Israel instead of the scheduled map lesson in Mystery of History. You can download it for free from Bible History Online.

map

History Pocket Projects

Here are some more pics of Otter’s recent projects for ancient history from History Pockets.

A pop-up Egyptian courtyard :

Pop up

A cut & paste tomb:

Egyptian tomb

A flip-flap booklet of Egyptian gods and goddesses:

Egyptian gods

A pyramid shape book:

pyramid

An ancient Egyptian person
(with sheer “cloth” *cough* -toilet paper- clothing overlay)

egyptian

Otter usually does his History Pocket projects during our read-alouds. It keeps his hands busy and his mind focused on the stories or information that is being read.

After I read to him, I usually ask him questions about what we read and he also often provides a narration that summarizes the material.

One of the books we finished last week is:

A Place in the Sun

A Place in the Sun

This adventure story is about Senmut, a boy in ancient Egypt. After his father is bitten by a Cobra, Senmut attempts to carve a statue of the healer goddess Sekhmet with the hopes it will cure his father. While working, he thoughtlessly tosses a tool and accidentally kills a sacred dove. Senmut is sent to the mines for his crime. Will he survive his harsh sentence? Will he ever see his father alive again?

Read the first chapters at Google Books.

I scheduled this book as a reader, although I actually did it as a read-aloud due to the Egyptian spirituality that is woven throughout the story. I wanted to be on hand to edit out or explain/discuss portions because I didn’t feel comfortable with a lot of it. It’s a worthwhile story though, because it gives a realistic picture of ancient Egyptian beliefs, how lives were ruled by these beliefs, and makes this ancient culture more accessible to young readers.

Otter’s rating: 5 stars

Ancient History Projects

We’ve been really busy lately. Here are some pictures of Otter’s most recent projects:

This project was from the Story of the World Activity book. Otter worked on it while we did one of our read-alouds.

A Mohenjo-Daro house made of “bricks”

Mohenjo-Daro house

You can see some pictures of this ancient city here.

Another thing we did was learn the ancient Egyptian game of Senet. Here is the game board from History Pockets. We also played versions of the game online. Guess who won? It wasn’t me!

Learn how to play Senet

Play senet against a computer

Senet

Here’s a project Otter REALLY loved: making an “ancient” map. We took one of our Mystery of History maps, crumpled it up, dabbed it with wet tea bags and then burned the edges. Just a note for the future: outline the edges of the map areas in permanent marker! Ours “washed” away with the application of the tea bags (duh).

map

I also dug out some pages and lessons from Remembering God’s Awesome Acts. I purchased it in the past for the “big” kids and they completed about half of the workbook. It’s been sitting on the shelf ever since and the last half fits perfectly with what we’re currently studying. The program mixes Bible lessons with history, art, logic, geography, culture and more. One of the lessons was about Egyptian art. Here’s Otter’s picture he drew after looking over the different art elements:

Egyptian art

As far as website news, I designed the “art” for the ancient history section. You can see it here on my rough working page for ancient history books.