Comparing and Ordering Numbers

Today we began learning about how to compare and order larger numbers. Before students can really be successful at this skill, they need to have a fairly solid understanding of place value. That is why we teach place value first, before this concept.

The biggest idea that students have to remember about comparing and ordering numbers, and about place value in general, is that as we go further left in a number, the value becomes larger. For example, I would rather have 1 thousand dollars than 9 tens (or 90) dollars. Even though the digit is larger, the value of the 1 is more because it is in the thousands column (it is worth one thousand).

When comparing and ordering numbers, I encourage students to "stack" the numbers on top of each other, paying close attention to keeping the columns lined up. This helps them to clearly see which digit in each column is larger. See the attached presentation for an example. We looked at this presentation in class, and we also did an activity in which students worked in pairs to order the areas of a number of countries from greatest to least. We used place value charts to assist us with the activity. If your child needs to use a place value chart (or the "houses" idea like we did in this post) then that is fine. Students are encouraged to use whatever tools they can to help them understand concepts.

Comparing and Ordering Numbers Grade 6

Homework Helper Place Value Houses

Today we began learning about place value in math. We watched the above video that explains how our place value system works up to the hundred millions. In grade 6, although not part of the formal curriculum, I tend to teach students up to the billions. We learn about each section being called a "house" or a "period", and with each period is a ones, tens and hundreds column. This helps us when we are trying to say larger numbers.



We also learn how to express numbers in 3 ways: standard form, expanded form and word form. Here is an example of each, for the number 234,675,873



Standard form: 234,675,873



Expanded Form:  200,000,000 + 30,000,000+4,000,000+600,000+70,000+5,000+800+70+3



Word form: 234 million, 675 thousand, 873



Finally, we learn to replace values with each column to come up with new numbers, For example, in the above number, what new number might I get if I added 3 more in the hundred thousands column?



First, look at the hundred thousands column, there is a 6, so it is worth 600,000.

Next, add 3 to the 6 = 9 --> but this is in the hundred thousands column, so it is worth 900,000!

Finally, change the number to reflect the new amount: 234,975,873.



We will be continuing to practice this tomorrow as well. Please let me know if your child is having difficulty with this, as it forms a foundation for other concepts.



Later in this unit we will be learning about multiplying and dividing larger numbers, identifying prime and composite numbers, comparing and ordering whole numbers, using the order of operations (BEDMAS), and adding and subtracting larger numbers.

More Patterning Practice!

Today we spent some more time reviewing patterning concepts for our test on Monday. I posted some questions on the Smartboard and students answered them in their notebooks. We took them up together and (hopefully) corrected any misconceptions. Here are the questions we used. Please feel free to use these to review concepts with your child.

Patterning review part 2

Next week we will also be completing a few problems from EQAO and a unit problem to wrap up our assessment of our patterning unit. The next unit we will be working on will be number sense - specifically whole numbers. 

In language next week we will begin learning about procedural writing and identifying what characteristics good procedural writing has. We will look at a number of examples, and give them a level, which we will use to create our Bump It Up wall. Afterwards we will be looking at an example of procedural writing and beginning to explain some procedures on our own. 

Have a great weekend everyone! 

Integers, More Literature circles and Music!

We were introduced to Integers today! We started with a quick definition of what an integer is and related integers (and negative number especially) to a thermometer because it is very common. Then we did an inquiry problem in which students had to use a pattern to find the temperature at the top of a mountain, knowing the starting point and the fact that for every 150m rise in altitude, the temperature would get 1 degree lower. This was a challenge for many students because the increments that started the pattern went up by 300m, not 150m. Afterward, we looked at a presentation that explained a little more about integers. Here is the presentation I showed the class. It explains everything they need to know about integers this year and has some practice problems at the end. It can be an excellent study guide if working with your child to study for a test.

Integers

We will be having a test on Monday for our patterning unit. This week we will be reviewing the material we have studied this unit to ensure we are ready!

In the morning class we also tried to plan out our literature circle work again. I demonstrated to students how to organize themselves to make it easy to assign jobs. All students should have a copy of their jobs for the next 4 weeks in their agendas. It might be a good idea to  post this somewhere visible in the house to remind them! Literature circle books are to be read at home independently, and then students must complete their jobs using Edmodo. See our class website (literature circles link) for more information about how to complete the various jobs. Feel free to download any of the sheets for use at home. They can be used as a template and then copied and pasted into Edmodo if you wish. The first job for Literature circles is due next Monday. If you find that the book your child has chosen is too difficult, please let me know and we can make alternative arrangements. 

In Music, we are learning about the families of instruments in an orchestra. Students are using Chromebooks to learn about the four families and then making a presentation about it to show the class. They are using a website called SFS Kids. Here is the link: sfskids.org.

Solving Equations

Today we learned about what an equation is, and how we solve them. Solving equations can be a challenge for students because this is the first time that unknowns (or variables) are introduced. Sometimes we see them as letters, and sometimes as empty boxes. I try to emphasize to students that it doesn't matter what the variable looks like. It is important to just realize that we don't yet know what that number is, so we use the numbers that we do have. Our job is to figure out the variable so that we can make the equation balance.

Here is a link to a presentation that we looked at today to assist us in figuring out how to solve equations:

Solving Equations

New reading strategy, Number Patterns and Identifying Living Things

In language we are beginning to learn about a new reading strategy called "Self-Monitoring" This simply means asking ourselves if we are understanding as we read, and if not, using strategies to correct ourselves so that we can understand. Here is a chart we developed in class to assist us in understanding what self-monitoring means:

Self Monitoring

In Math, we are continuing to learn about how to find number patterns. Here is a link to the lesson we did today:

Number Patterns

Finding number patterns can be quite challenging for students in grade 6 because they now involve patterns in which there are two operations. For example, the pattern might work by multiplying by 3 then adding 4 more to each term. This can be difficult to discover. The trick to finding the pattern starts by looking at the differences between the terms, and seeing if there is a pattern to them. See the link for a more in-depth explanation.

In science, we are learning about how scientists can tell if something is living. Today we used the chromebooks to research how scientists can tell if something is alive or not, and we discovered that in order to be considered alive, the organism must pass five tests. The answer must be yes to all the tests, or the organism is not considered a living thing. The five questions are;

1. Can it reproduce?
2. Can it grow and develop?
3. Can it react to its environment?
4. Can it use food?
5. Can it make or find food?

We will be continuing to learn more about biodiversity in science, focusing on  classification systems. 

Input/Output Machines

Today we learned about how Input/Output Machines work. In grade 6, we learn about patterns with 2 steps. Click the video below to see what we did in class today briefly.

We also learned that we can work backwards to figure out what the operations are in the machine by looking at the pattern of the output. In the video above, if we look at the output numbers, we can see that they go up by 3 each time. This gives us a hint that the first operation is to multiply by 3. So we try it out! 1 x 3 = 3 .....not 4! So this tells us that we have to add one more. Let's try that throughout the table:

1 x 3 = 3, 3 +1 = 4 check
2 x 3 = 6, 6 + 1 = 7 check
3 x 3 = 9, 9 + 1 = 10 check.

So we can say that the first operation is to multiply by three, then add 1. Here is a link to an interactive website that will let you practice:

Function Machine

How to log into Xtramath

Learning basic facts is an important skill for children in order to be successful in mathematics. It helps them to estimate, perform operations using larger numbers and quickly see patterns in a variety of math situations.

This year, to assist students in memorizing their basic facts, we will be using an excellent program called Xtramath. This website has students answer basic fact questions and "remembers" which facts they seem to know and which they continue to have difficulty with. In order to achieve full mastery in Xtramath, students must answer all the facts with 3 seconds correctly. It starts with addition facts, then subtraction, multiplication and finally division. Students cannot move from addition until they have mastered all the facts. Some students move very quickly through this program, while others can have a difficult time. It is important to work on it daily to improve. The program only lets you work for 5 - 10 minutes and then it asks the student to stop. Practice makes perfect!

To get into Xtramath, students need my email address and a PIN number. They have written down both of these in their agendas. Once in, they just need to follow the program to proceed.

Some students in the past have had difficulty hitting the correct keys on time in order to progress. They know the facts, but can't press the buttons fast enough! If your child has this difficulty, please feel free to have them tell you the answers and you or an older sibling can type the answers in. Encouraging your child to try and enter the numbers on their own is a good idea however, because it will improve their typing skills as well as their recall of basic facts.

If you have any questions about how Xtramath works, please feel free to contact me at school and I will do my best to assist your child in accessing the program. Thank you!