Mrs. Leo's Math Blog - Blog



Week 1: Hello all! I hope that everyone is doing well.For our math lessons moving forward, I am going to include two main things: Something Old and Something New.The Something Old lesson will be reviewing one of the big concepts from the school year. This will be something major that may follow you for a while outside of my class! I feel like it’s worth reviewing, and since we’ve already done it in class once, you may already have some resources to help you. The Something New lesson is exactly what it sounds like: something we haven’t learned in class yet! This will be what I supply the most resources for on my blog, as well, but I will provide written instructions on the handout to help.If you are able to, I will be posting additional resources on my blog every Monday for the week (bmsmath7.). I will also be online every day from 9am-12pm in some way shape or form! During my office hours, I am directly by my computer to answer any questions you may have via email—or if you need to jump on zoom or a phone call, just let me know! On Tuesdays, I will also be hosting an hour long Zoom meeting where I’ll provide additional instruction to help with the packet for the week. Our schedule will look something like this:ScheduleMondayTuesdayWednesdayThursday FridayAll resources for the week (beside Zoom links) posted on the class blog9am-12pm Office Hours9am-11amOffice Hours11am-12pmZoom Meeting and Instruction! I will send out the link on Tuesday mornings and post the link on my blog.9am-12pm Office Hours9am-12pm Office Hours9am-12pm Office HoursPhotos of Week 1 Work due by the end of the day.-289560303530Keep an eye out for the camera icon! If you see this, this means that the problem next to it is one that I need to see to give you credit for the work that you’ve done. There are a few ways to show me this work:1) Take a picture of your work and email it to me2) Email me a description of how you solved the problem and what the final answer is3) Attend a zoom meeting and show me your work through your camera(If these don’t work for you, please call the school, myself, or Mr. Baron and let us know so that we can work out another option!) Pictures of work due to Mrs. Leo by the end of the day on Friday.These are wild times, but we’ll make this work! Thank you all so much!bmsmath7. (Math blog, with weekly resources posted)moreaua@bas- (Mrs. Leo’s email. Keep in contact as much as you can!)Something Old (Week 1): The Distributive PropertyThe Distributive Property is a tool that you first learned in sixth grade math. We went a little more in depth with it during our time together, as well! This seems like a perfect place to start some review ?What is the Distributive Property?In math talk, the Distributive Property tells us how to solve expressions in the form of a(b+c). Basically, we need to work with both the Order of Operations and with Multiplication! We’ll show two examples: one working with a distribution problem using Order of Operations, and one using the Distributive Property.Order of Operations4(11 + 5) 4(11+5) = 4(16)First, we solve what’s in the Parenthesis.4(16) = 64Remember: that “smush” happening between the 4 and the parenthesis is always showing multiplication!So our final answer is 64! The Distributive Property4(11 + 5)Since the “smush” happening between the 4 and parenthesis is showing multiplication, we are really saying that we want the (11 + 5) to happen 4 times:(11 + 5) + (11 + 5) + (11 + 5) + (11 + 5)Well that looks annoying! But notice that we have 11 four times, and 5 four times. That means we can rewrite this:(4?·?11) + (4?·?5)Now, we simplify:(4?·?11) + (4?·? 5) = (44) + (20)First, we solve what’s in the Parenthesis.(44) + (20) = 64Then, we add.So our final answer is 64QuestionsBut Mrs. Leo! The Distributive Property looks like a lot of extra work compared to using the Order of Operations by itself!Hey, that’s a fair thing to notice! But what’s cool about the distributive property is that it shows us a pattern that we can work with. Notice that we can make that problem a lot shorter if we go directly to our multiplication!4(11 + 5) = (4?·?11) + (4?·?5)Then we can solve from there!Why do we use the Distributive Property?Sometimes, there are values in the parenthesis that we can’t simplify any further, like a variable. When that happens, the Distributive Property is our only approach that we can use. We’ll see some examples of that on the next page.More Examples Using the Distributive Property:10 (5 + 10)10 (5 + 10) = (10?·?5) + (10?·?10)(10?·?5) + (10?·?10) = 50 + 10050 + 100 = 150So our final answer is 1505 (11 – 4)5 (11 – 4) = (5?·?11) – (5?·?4)(5 ?·?11) – (5?·?4) = 55 – 2055 – 20 = 35So our final answer is 354 (y + 2)4(y + 2) = (4?·?y) + (4?·?2)(4?·?y) + (4?·?2) = 4y + 8So our final answer is 4y + 8! We can’t combine any further using addition. Now you try a few. The final answer is already given. Using the Distributive Property, show all the steps to get to the final answer:7(13 – 2)So our final answer is 77.5(x + 7)So our final answer is 5x + 35Some final notes:Since area = l x w, we also can show distribution as an area model. Using the area model, 3(2 + 6) could be written as:If someone else is helping you, they may also be familiar with something called the “rainbow method” to help solve distribution problems, as well! 4610100269875------------------------------------------------------------------------------------------------------------------------------------------Practice: For each of the problems, use the Distributive Property to simplify.5(6 + 12)11(12 – 7)7(x + 4)10(11 – x)7(2x + 3)Something New (Week 1): Examining DataOur “Something New” for the rest of the year will be about data and probability. In class, we usually do a lot of activities in this unit. Unfortunately, that’s not entirely possible all the time, but I’ll do my best to incorporate as many activities as I can!To start our Probability off, I’d like for you to do some coin flipping! Find any coin (a penny, a quarter, whatever, so long as there’s a clear “head” and “tail” side). I’d like for you to flip that coin 20 times and record your data below:Trial1234567891011121314151617181920Outcome(H or T)As a fraction, what is the total amount of time you flipped “tails”? Hint: Our denominator should be our total number of trials, and our numerator should be how many times we have “T” as an outcome.4937760254635What is the total percentage of tails you flipped? As a fraction, what is the total amount of time you flipped “heads”?What is the total percentage of heads you flipped? What should happen if you add your fraction of total tails to your fraction of total heads? Why?What should happen if you add your percentage of total tails to your percentage of total heads? Why?Notable Vocabulary:Outcome: The different results that we can get. For our example here, our outcomes are heads and tails.Equally Likely: In this experiment, it is equally likely for us to get heads as a result, and tails as a result.Looking Ahead: How can we prove that heads and tails are equally likely in this case? If we had an unfair or weighted coin, would heads and tails have equally likely outcomes? How would you be able to tell if your coin was unfair or weighted? ................
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