Mrs. Leo's Math Blog - Blog



Week 4: Hello all! I hope that everyone is doing well.So first off, as a reminder, 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 is listed below!ScheduleMondayTuesdayWednesdayThursday FridayAll resources for the week posted on the class blogZoom email sent9am-12pm Office Hours9am-11amOffice HoursZoom meeting reminder sent11am-12pmZoom Meeting and Instruction! I will send out the link with my weekly emails.9am-12pm Office Hours9am-12pm Office Hours9am-12pm Office HoursPhotos of Week 4 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 with your phone/webcam 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 camera4) Schedule a time to call me, and we can talk through some of the work that you did.5) Write answers directly into this word document, then email me your finished work6) Copy your work onto a separate piece of paper, then send me a picture of that!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! I know that these are weird times, so I am really flexible for how you show me what you do. 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!)3444240000Something Old (Week 4): Linear PatternsSince we spent last week writing at linear equations, let’s spend this week examining linear patterns. We’ll be looking at tables and graphs to predict how our linear pattern changes! Remember, that’s the main point of a linear pattern… to be able to predict future values!Here are a few recapping vocabulary words before we practice this again!Linear Equation: A linear equation is in the form of y=mx+b. This means that the pattern will always change by the same amount. The breakdown of this from last week is shown here, too!Linear Pattern: A series of numbers that show a constant rate of change. In other words, as long as there is a constant change in our numbers, the pattern is linear.Let’s take a look at some examples of this:In a table:x012Y61116X is changing by a constant of 1Y is changing by a constant of 5Since there is a constant change, this is a linear pattern.14414522860000In a graph:As X changes by 1, Y is always changing by -2. Therefore, this is a constant of -2!Since there is a constant change, this is a linear pattern.In a word problem:I put $100 in a bank account, then put $15 into the account every week to help save money.Since I am making a change into this bank account every week, I have a constant of 15. This is a linear pattern!Prediction:So, in this pattern, if x is 5, what should y be?I can either keep following this table, or I can write this as an equation from last week!y = 5x + 6y = 5(5) + 6y = 25 + 6y = 31Prediction:So, in this pattern, if x is -2, what should y be?I can either work backwards on the graph, or I can write this as an equation from last week!y = -2x + 5y = -2(-2) + 5y = 4 + 5y = 9Prediction:So, in this pattern, how much money would I have saved after 7 weeks?I can either keep counting forward on this problem, or I can write this as an equation!y = 15x + 100y = 15(7) + 100y = 105 + 100y = 205QuestionsDo I need to write out the equation if I can follow the pattern?Again, that’s some awesome mental math if you can mentally work out the problem instead of writing it out! As we move towards graphing this equations next week, please get into the habit of writing the equation so that you feel comfortable with doing so!What exactly is the y-intercept again?The y-intercept is where our pattern crosses the y-axis. In other words, it’s whenever our independent variable (x) is equal to zero! We used to call this our starting point, because in a lot of word problems, it’s the first value (like, how much money you put in your bank account right away). Otherwise, we can look at a graph (where the line crosses the y-axis) or a table (when x = 0) to see this value!-533400Practice: For each problem:1) Write down the constant change in the problem.2) Write down the y-intercept (when x = 0!) in the problem.2) Write the equation for the pattern. 3) Then, solve for the given value.ProblemConstant ChangeY-InterceptEquationSolve if…The constant in this graph is…The graph crosses the y-axis at…The y=mx+b form of this pattern is…If x = 5, what will y be?Days012Bank Account$15$25$35The constant in this table is…The y-intercept of this table is…The y=mx+b form of this pattern is…After 14 days, how much money is in this bank account?I am able to walk at 2.5 meters per second, and I am given a head start of 10 meters. The constant in this statement is…The y-intercept of this statement is…The y=mx+b form of this pattern is…After 7 seconds, how far ahead will I be?190500556260Challenge Problems: Give these a try if you feel up to the challenge!(These are not part of the “camera” problem, but are an extra challenge for you!)For the graph and table below, try to write the linear equation for each!3581400255270Equation:Equation:Something New (Week 4): AND vs. ORThis week, we’re going to look at two weirdly important words in probability: the word AND, and the word OR. When we’re working with probability, these two words mean very different things for us!(Review) Theoretical Probability: The probability based on what SHOULD happen with an experiment.(Review) Experimental Probability: The probability found from conducting trials and collecting data.(Review) Sample Space: A list of all of the possible outcomes from an event.So now let’s break down this week’s works!ANDIf we are looking at multiple outcomes and comparing them using the word AND, that means BOTH outcomes must happen!ORIf we are looking at multiple outcomes and comparing them using the word OR, that means that one OR the other outcome must happen.4335780127000So, let’s compare this using a spinner. AND: If I use the word AND, that means all of the outcomes I ask formust happen! So, let’s look at the theoretical probability of spinning a blue AND an even number.Since both outcomes need to happen, there are only two outcomes that satisfy this: (Blue, 6) and (Blue, 4)The probability of spinning a blue AND an even number are 2/8, or 25%OR: If I use the word OR, that means that either of the outcomes I ask forcan happen. So, let’s look at the theoretical probability of spinning a yellow OR and 8.Since both outcomes can happen, we have 2 yellow options, and 1 option thathas an 8. So the probability of spinning a yellow OR an 8 is 3/8, or 37.5%Let’s use an example a little more fun than a spinner: playing cards! Below is a picture of every outcome with a standard deck of playing cards (not including jokers). There are 4 different suits, and 13 cards per suit. We call these suits CLUBS, SPADES, HEARTS, and DIAMONDS.Overall, there are 52 total outcomes in this sample space: {Ace of Clubs, 2 of Clubs, 3 of Clubs… Queen of Diamonds, King of Diamonds}23480408322752296560935235-26670073723500Let’s look at an AND probability first!What is the theoretical probability of pulling a Club AND a Face Card? (jack, queen, king)So we need BOTH outcomes to happen. There are only three cards that are BOTH a club and a face card: {Jack of Clubs, Queen of Clubs, King of Clubs}Therefore, there are 3 total outcomes that work, out of 52 total outcomes in our sample space.3 cards52 total cards =6%So we have a 6% chance of pulling a card that is both a club AND a face card.2781480152196028135201434840-1705201776480-26670063436500Let’s look at an OR probability next.What is the theoretical probability of drawing a Diamond OR the King of Hearts from a deck of cards?Since either outcome works, we can just combine the two of them together!There are 13 total diamonds + 1 King of Hearts. Therefore, there are 14 total outcomes out of our sample space of 5214 cards52 total cards =27%So we have a 27% chance of pulling a diamond card OR the King of HeartsA VERY IMPORTANT NOTE ABOUT “OR”OVERLAP.50115657294755019485973555496728598795548693659080355018765958795730805868075697685944395745565740275Sometimes, it’s possible to have a card in BOTH categories. We can only count the outcome as happening ONCE in these situations!For example, let’s work with the theoretical probability of drawing a club OR a king.In this case, there are 13 total clubs, and 4 total kings. Notice, though, that since there we already counted the King of Clubs once, we don’t need to count it again! There are technically 16 cards that satisfy our conditions!16 cards52 total cards =31%51206400PracticeFor each problem, write the probability as both a fraction and a percentage! Please use the blank version of the cards on the previous page if you need it ? What is the theoretical probability of…1) Drawing a Diamond OR a Heart?2) Drawing a Spade OR a 10 of Diamonds?3) Drawing a Heart OR an Ace? (Watch the overlap!)4) Drawing a Club AND a 7?5) Drawing a Diamond AND a card smaller than 5?Extra!Is it possible to draw a card that is a Diamond AND a Club? Explain your answer ................
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