Happy Sixth Week of Summer!

So far we have looked at the chance something could happen in terms of words (e.g. likely, impossible, unlikely, certain). But we can also express the chance that something could happen as a fraction.

For the next example, you spin each spinner once and add the numbers. You are trying to find out all the possible combinations of spins and their totals. The first column is done for you. At the top of the table it shows spinner 1. If you spin 1 on spinner one, the possible totals spinning 1, ,2, 3, 4, or 5 are listed in the first column. There are actually 25 different combinations you can spin believe it or not!

Dice are often used to show the probability of an event happening.


So let's look at the rolls on a die (singular for dice). How many even rolls? How many odd? Well, 2, 4, 6 are even and 1, 3, 5 are odd. So the odds or chance of rolling an even or odd number are equal. We often say "fifty-fifty" chance. The fifty refers to fifty percent of the time. So what's the fraction? It would be 1/2. Half the time you will probably roll an even number and the other half an odd. Remember, this is over time. If you actually rolled a die 10 times you may get 5 even and 5 odd, but it is certainty. If you rolled that die 100 times you would probably get closer to 50 even / 50 odd.

Card games are also good tools to show probability. Dice and cards...... just like they use in a casino. Sadly, probability is what attracts people to gamble. There is the "chance" that they might roll that unlikely roll or be dealt that unlikely card. But you know probability so you can determine that is is probably much more likely to lose than win! Back to math....

It's also important that you understand PROBABILITY TREES (especially in grade 5). All the outcomes are put on a diagram that looks like the branches of a tree. The boxes at the end (top of the tree) are all the possible outcomes. Try one!

The tree diagram tells us the first possible sandwich is whole wheat with lettuce and tuna. The second possible sandwich is whole wheat with lettuce and ham. So there are 8 possible sandwiches. You either have whole wheat or 7 grain / lettuce or tomato/ tuna or ham.

Remember the total possible outcomes is found in the last boxes of your probability tree.

Try this experiment with a parent, sibling or friend. Did you "beat the odds"?

Reminder:
Extra practice on Mathletics!


This is my last post for the summer. Time to get ready for next year. Farewell my Magnificent 4/5 Minions. Enjoy the remainder of the summer and see you in September!

Happy Fifth Week of Summer!

What is Probability? Probability measure how likely something is to happen. Often probability is measured using a scale. Take a look at the following events. What is the probability that they will happen? Probability can also be expressed using fractions or percents (grade 6).

Use the faces of the die to answer the questions below:

Games to practice:
https://mathup.ca/Games/Grade4/WhichisMoreLikely
https://mathup.ca/Games/Grade5/FishingFrenzy/

Your prayers are needed once again for all the people living in areas devastated by forest fires.

Happy Fourth Week of Summer!

Just a bit more review of fractions greater than 1 before we moved onto Probability. You read the fractions below as five halves or two and one half. Don't forget the "and" between the whole number and the fraction.

Remember it is easier to divide rectangles into equal parts than circles. Any shape divided equally into the number of parts given in the denominator are correct. Rectangles are just easier.

To change an improper fraction into a mixed number, divide. The denominator stays the same. The remainder of the division problem is the numerator. If you have difficulty doing this, then draw pictures. Remember the denominator is the number of parts in each shape. The quotient (answer to division problem), is the whole number.

To change a mixed number to an improper fraction multiply denominator by whole number, then add numerator to get the numerator of the improper fraction. The denominator is always the same. Again, if you find this confusing, draw pictures or use a number line.

Simple game to play to practice recognizing equivalent fractions:

Games to play:
https://mathup.ca/Games/Grade4/SortingtoEstimate
https://mathup.ca/uploads/pdf/G5_T6_GP_FractionConcentration.pdf
https://mathup.ca/Games/Grade4/FractionModelMatch
https://mathup.ca/Games/Grade4/FireflyFractions

Hope you're having a fun summer!

Happy Third Week of Summer!

Now back to equivalent fractions, fractions that show the same amount. Fractions that are equivalent or equal to 1/2 are easy. As long as a numerator is half the denominator, then the fraction is 1/2. For example 5/10 is equivalent to 1/2 because 5 is half of 10.

If we divided the pizza into eighths what would be the fraction in eighths equivalent to 1/2?
Sometimes using visuals help. Take a rectangular piece of paper and fold it following the directions below:

Remember, diagrams must be divided into EQUAL PARTS.

I think the student who completed the above answers needs to review his or her understanding of equivalent fractions. The numerator is the number shaded and the denominator is the total number of parts.

 When you use number lines to find equivalent fractions, they must be at EXACTLY the same point on the number line. Use a ruler to make sure they line up perfectly.

To find the pattern, put your equivalent fractions in a line:
1/4 =2/8 = 3/12 = 4/16
How is the numerator increasing? How is the denominator increasing?
Predict equivalent fractions for 1/5 and 1/6. What about fractions equivalent to 3/4?

Don't forget Mathletics assignments.
I came across some interesting videos explaining how to multiply 2-digit by 2-digit numbers. Pretty cool. Check them out....
https://www.youtube.com/watch?v=Rgw9Ik5ZGaY
https://www.youtube.com/watch?v=SV1dC1KAl_U

All the prayers from around the world worked for the soccer team in Thailand. All were rescued safely. Wow, what an inspiring story.

Great World Cup game today!

Happy Second Week of Summer!

When comparing and ordering fractions with the same DENOMINATOR, it's pretty easy. The fraction with the larger numerator is the larger. Remember definitions:

But if the denominators are different, then if becomes a bit more challenging. One way to compare fractions with different denominators is to use fractions strips or a fraction number lines.

Being able to place fractions on a number line is also a very important skill. Sometimes a clear ruler can help you reading fraction number lines. For the first question, put the ruler on 1/2. Is 1/3 to the left or right of 1/2? If it is to the left, then it is less than 1/2. If it is to the right, then it is greater. If the ruler is at the same point for two fractions, then the fractions are EQUIVALENT.

The next set of questions require a bit of thinking. Sometimes the heavy black lines (quarters) are a help, and sometimes you don't use them. Every answer is an EXACT fraction. No estimations! Are you up for the challenge?

In the last problem you have to remember that fractions are not only part of a whole but part of a set. In this set there are 72 coins. If you are trying to find our 1/6 of 72, remember from the first summer post, it's just division (72 divided by 6 = 12). So if 1/6 of 72 is 12, what would 2/6 be? 12 + 12 = 24.

There has been lots of excitement so far this summer. The World Cup has been tremendously entertaining. The France and Belgium semi-final should be a great game, but it would be nice to see the underdogs Croatia or England win. But nothing has been more captivating than the harrowing rescue of more than half of the Thai soccer players trapped deep inside a cave. There are still four players and a coach awaiting rescue. Please take a moment and say a prayer (or two) for them and the heroic divers who are leading them to safety. St. Brendan is the patron saint of divers.