I hope everyone had a fantastic week – I can’t believe it went by so quickly. It feels like yesterday was Tuesday morning!
A reminder that our math test is on Monday for our ratios and rates unit.
A message from Ms. Hayward...
A few quick reminders:
· Monday is a Day 2.
· The hot lunch site is now open for November! The special this month is chicken stir fry, which is available every Friday. Please DO NOT order lunch for Thursday, November 21st as we are going on a field trip that day! The lunch site will close October 30th at 3:00 p.m. and payments will be due by November 6th.
· Aftercare invoices for the month of September have come out and were due Tuesday, October 15th, 2019. Any questions can be directed to Ms. Chiappetta at echiappetta@stjudesacademy.com
· Casual day forms were sent home and should be sent back signed with $20 for anyone participating. These are due by Friday, October 25th, 2019.
Inquiry into Math – Today, we completed another review for the test on Monday and I’ve sent one more for the weekend. This is an optional review and the answers will be posted to the blog on Sunday. Please feel free to ask any questions. Here is what we covered this unit:
Lesson 2.1 – What is a Ratio?
A ratio is mathematically used to compare two things. For example, if I have 3 blue counters, 4 green counters, and 5 red counters, I have a total of 12 counters.
I can write a ratio comparing a part of my total to the whole number. This is called a part-to-whole ratio. For example, I have a ratio of 5:12 (this is the ratio of red counters to the total number of counters).
I can write a ratio comparting a part of my total to another part. This is called a part-to-part ratio. For example, I have ratio of 3:5 (this is the ratio of blue counters to red counters).
We use ratios all the time when we do recipes for example. They are very practical in the real world!
Lesson 2.2 – Equivalent Ratios
An equivalent ratio is when you multiply or divide the terms of a ratio by the same number. For example, let’s say we have 4 squares and 3 triangles. The ratio of squares to triangles is 4:3. But what if the ratio is 4:3 but I have 6 triangles? Since 3 x 2 = 6, I must multiply 4 by 2 as well to ensure my ratio is equal. Since 4 x 2 is 8, the new ratio is 8:6.
A ratio is mathematically used to compare two things. For example, if I have 3 blue counters, 4 green counters, and 5 red counters, I have a total of 12 counters.
An equivalent ratio is when you multiply or divide the terms of a ratio by the same number. For example, let’s say we have 4 squares and 3 triangles. The ratio of squares to triangles is 4:3. But what if the ratio is 4:3 but I have 6 triangles? Since 3 x 2 = 6, I must multiply 4 by 2 as well to ensure my ratio is equal. Since 4 x 2 is 8, the new ratio is 8:6.
Lesson 2.3 – Comparing Ratios
To compare ratios (just like comparing measurements), we must ensure that either both first numbers or both second numbers are the same. To do this, we write an equivalent ratio to the ones we are given.
Let’s say we have two pizzas. The first has 6 slices and 20 pieces of pepperoni. The second has 8 slices and 22 pieces of pepperoni. Which one has more pepperoni per slice?
We find the LCM of 6 & 8, which is 24.
Pizza #1 – 6:20 à x 4 à 24:80
Pizza #2 – 8:22 à x 3 à 24:66
We wrote two equivalent ratios with 24 slices of pizza. Since pizza 1 has 80 pieces of pepperoni for every 24 slices and pizza 2 has only 66, we know that pizza 1 has more pepperoni per slice.
To review, when converting a smaller unit to a larger unit, you divide. When converting a larger unit to a smaller unit, you multiply. Here are our conversions:
· mm à cm – move one decimal place left (divide by 10)
· cm à m – move two decimal places left (divide by 100)
· m à km – move three decimal places left (divide by 1000)
· km à m – move three decimal places right (multiply by 1000)
· m à cm – move two decimal places right (multiply by 100)
· cm à mm – move one decimal place right (multiply by 10)
Just like comparing ratios, we cannot properly apply ratios unless our units are the same. For example, if you are looking at a map scale, you can’t write that the scale is 1:5 when 1 is measures in centimetres and 5 is measured in metres. First, you would convert 5 m into centimetres. 5m = 500 cm. Then, you could write the ratio of 1:500.
We looked at Gulliver’s Travels, a book where Gulliver (1.8 m tall) meets little people who are 15 cm tall and giants who are 18 m tall.
First, we write everything in the same units.
· Little people: 15 cm
· Gulliver: 1.8 m x 100 = 180 cm
· Giants 18 m x 100 = 1800 cm
Now, we can write these as equivalent ratios, and simplify them to determine the ratios of how tall each of these people are in comparison! For example, Gulliver:giants = 180:1800. When you divide by 180, you get a ratio of 1:10. Therefore, the giants are 10 times as tall as Gulliver!
You also use this for scales when drawing diagrams (such as a map or a house).
Lesson 2.5 – Rates
A rate is a comparison of two quantities that use different units (it is a special type of ratio). For example, when a car is travelling, we measure the speed of the car in kilometres per hour. This is a rate. Let’s say that a person travels a distance of 140 kilometres in 2 hours. We would write that they travelled 140 km/2h. The ‘/’ symbol means ‘per’.
A unit rate is a special type of rate where the comparison is made with a denominator of 1. The word unit indicates that we are interested in a “quantity per one of” comparison.
For example, let’s say that a person’s heart is beating 20 beats every 15 seconds, and we need to express this as a unit rate. The rate is 20 beats/15s.
15 seconds x 4 = 60 seconds, which is 1 minute.
20 x 4 = 80
Therefore, the unit rate would be 80 beats/minute. The most common unit rate we hear on a daily basis is kilometres per hour, since this is the average speed at which cars travel!
French – Right after this, we had French with Mme. Stella, which you can read about on her blog (https://stjudesfrench-stella.blogspot.com).
Inquiry into Language – After lunch, we sat in our literature circle groups and had a discussion about chapter fifteen. Every day I will be sitting down with a different group to hear these discussions. A reminder of the roles:
1. The discussion director comes up with insightful questions that will fuel discussion in the group.
2. The literary luminary chooses important passages for the group to read and discuss.
3. The connector makes connections between their own lives and the book (i.e. movies, other books they’ve read, real events, the current UOI, etc.)
4. The illustrator/mapper creates an illustration (i.e. comic, picture, mind map, etc.) based on what they felt during the chapter for the group to discuss.
5. The word wizard chooses 3 words that were interesting or new for everyone to discuss as a group.
French – Right after this, we had French with Mme. Stella, which you can read about on her blog (https://stjudesfrench-stella.blogspot.com).
Inquiry into Energy – Today, we continues working on and finished our zentangle designs. I am so excited to see the pinwheels and will be posting them to the blog once they are finished.
Science Fair – At the end of the day, students who were done their zentangle designs were able to work on their cars. Congratulations to Adn for being the first in our class to get her car moving!
Homework:
- The math review is optional and the answers will be posted to the blog on Sunday.
We do our best to complete work in class. In the event this is not possible, it will go home for homework.
As always, please feel free to email me with any questions.
Mr. Conte
