5.5.2 Find Missing Angles

① Simplify to the simplest form the expression: 2x (2 x + 1) + 3𝑥 (𝑥 + 2), then find the numerical value of the expression when 𝑥 = 1 ② Find by inspection: (2𝑥 + 1)(𝑥 + 4) ③ Find the expansion of: (𝑥 − 5)2 ④ If (𝑥 − 5)(𝑥 + 5) = 𝑥2 − 𝑐 , then what is the value of c ? Assessment ④ (B) Time: 15 min ① Simplify to the simplest form the expression: 2𝑥 (2𝑥 + 1) + 3𝑥 (𝑥 + 2), then find the numerical value of the expression when 𝑥 = −1 ② Find by inspection: (𝑥 + 3)(𝑥 + 4) ③ Find the expansion of: (𝑥 + 1) 2 ④ If (𝑥 − 5)(𝑥 + 5) = 𝑥2+ 𝑏𝑥 + 𝑐 , then what is the value of 𝑏 ? Assessment ⑤(C) Time: 15 min ① If: (𝑥 + 𝑦 ) = 3, (𝑥 – 𝑦 ) = 9 , then what is the value of: (𝑥2 − 𝑦2 )? ② If: (3𝑥 − 4) 2 = 𝑎𝑥2 + 𝑏𝑥 + 𝑐 , then what is the value of b ? ③ A square its side’s length is (𝑥 + 3) length unit, calculate its area in terms of 𝑥 . ④ (𝑥 + 3)(𝑥 + 2) = 𝑥2 + 𝑏𝑥 + 6 , then what is the value of b ? ⑤ Find the solution set of the following inequality in Z: 5 − 3𝑥 ≥ 14

GRADE 4 Module 6 Lesson 3. Interpret Remainders This PowerPoint file contains instructional aids for teachers who have purchased Into Math. It is intended to be projected to students and used in conjunction with the Student Edition and manipulatives as needed. These slides can be used to move the conversation forward in the classroom, but they should not serve as a replacement for student-centered, collaborative conversations in which students have the space they need to find an entry point, construct meaning, and build understanding. About the Slide Presentation Presenter View: Use the Presenter view to see notes while presenting. Customization: Add or delete content or notes to get the best learning experience for your classroom. 1 Problem of the Day. Which equations can be used to solve the following problem? Rita makes 40 bracelets and gives an equal number to 8 friends, including Veronica. Veronica gives 2 of the bracelets that she received to her sister. How many bracelets does Veronica have left? A. 40 – 8 = 32 32 ÷ 2 = 16 B. 40 ÷ 8 = 5 5 + 2 = 7 C. 8 + 2 = 10 40 ÷ 10 = 4 D. 40 ÷ 8 = 5 5 – 2 = 3 2 I Can. I Can solve a division problem and interpret the remainder in the context of the problem. 3 Spark Your Learning. Aiden is building solar toy cars in his science club. The cars collect and use energy from the sun for power. Aiden buys 18 wheels. Each car needs 4 wheels. How many cars can Aiden build? Show your thinking. 4 Turn and Talk. What is the remainder in this problem? What does the remainder mean? Professional Development note: Use the Professional Learning Cards to provide language routines that may help students access the meaning of the problem. 5 Build Understanding • Task 1 ACTIVITY. There are 57 students going to the science museum. Each van can take 5 students. How many vans are needed to take all the students? Use a visual model to show how the students are divided into groups of 5. 6 Turn and Talk. How can you use the whole-number quotient and remainder to answer these questions? How many vans will be full? How many students will ride in the van that is not full? Professional Development note: Use the Professional Learning Cards to provide language routines that may help students access the meaning of the problem. 7 Step It Out • Task 2 ACTIVITY.. Amanda has 73 inches of wire for a science experiment. She needs to cut all the wire into 8 identical pieces. How many inches long will each piece be? 8 Turn and Talk. Why is this problem a good situation to write the remainder as a fraction? Professional Development note: Use the Professional Learning Cards to provide language routines that may help students access the meaning of the problem. 9 Check Understanding. 1. Maya needs 44 batteries for smoke alarms. The batteries come in packs of 6. How many packs does Maya need to buy? For 44 ÷ 6, the whole-number quotient is ____ and the remainder is ____. Maya needs to buy ____ packs. Circle how you interpreted the remainder to solve the problem. 10 I Can Scale. 4 I can explain how to solve a division problem and interpret the remainder in the context of the problem. 3 I can solve a division problem and interpret the remainder in the context of the problem. 2 I can solve a division problem and identify the whole-number quotient and the remainder. 1 I can solve a division problem with a remainder. 11 Exit Ticket. Mr. Jenkins’ class is giving speeches during a 46-minute class. Each student will be able to talk for 4 minutes. How many students can give speeches? Justify your answer.

How is personal data collected? There are several ways that an unauthorised person can try and collect your data. These include: •phishing •smishing •vishing •pharming. Phishing Phishing is when a person sends a legitimate looking email to a user. The email contains a link to a website that also looks legitimate. The user is encouraged to click the link and to input personal data into a form on the website. The email could also simply ask the user to reply to the email with their personal data. The user is tricked into giving their personal data to a source that they believe is legitimate. However, both the email and the linked website are from a fake unauthorised source. The personal data that is input is then collected by an unauthorised person. This person can then use this data for criminal acts, for example, to commit fraud or steal the person's identity. Intimidation has become a common feature of phishing emails, threatening the user that they must click the link and rectify a situation immediately, or there will be a further issue. The aim of a phishing attack is to steal the user's personal data. Figure 5.1: Phishing. A real-life example of phishing PayPal have been the subject of several different phishing emails. Users receive an email that looks as though it has been sent from PayPal, as it has the PayPal branding. The email normally warns of an issue such as unexpected activity on their account, or that some kind of verification of their account is required. The user is then asked to click a link to log into their account and resolve the issue. The link takes them to a webpage that looks like the PayPal login page. If the user inputs their login details into this page, they will not be taken to their account. It is often at this stage that the user may realise that the email and webpage are fake. However, they have already given the unauthorised person their PayPal login details. Figure 5.2: An example of a phishing email claiming to be from PayPal. How to recognise phishing There are several guidelines to be aware of regarding emails to avoid being subjected to phishing. These include: •Don't even open an email that is not from a sender that you recognise or a trusted source. •Legitimate companies will never ask you for your personal data using email. Be immediately suspicious of any email that requests your personal data. •Legitimate companies will normally address you by your name. Be suspicious of any email that addresses you as ‘Dear Member' or ‘Dear Customer'. •Legitimate companies will send an email that uses their domain name. If you hover your mouse over the sender's name, it will show the email address that the email is sent from. If this does not look legitimate, for example, does not contain the correct domain name, then it is probably fake. For example, if the sender's email is user@paypal1.com rather than user@paypal.com, this is from an incorrect domain name. •Legitimate companies are protective of their professional reputation and thoroughly check any communications. They will make sure that all information given is grammatically and correctly spelt. Be suspicious of any email that contains bad grammar or spelling mistakes. •A link in an email from a legitimate company will also normally contain the domain name of the company. You can sometimes hover over the link, or right click and inspect the link, to see the address of the URL that is attached. If the URL does not contain the domain name, or also contains typical errors such as spelling mistakes, then be suspicious of this. PRACTICAL ACTIVITY 5.02 Ask a friend or a member of your family if they have ever received an email that they believed was a phishing email. Ask them how they identified it was phishing. Ask them if they know all of the given guidelines for identifying phishing emails. Smishing Smishing (or SMS phishing) is a variant of phishing that uses SMS text messages to lure the user into providing their personal details. The user is sent an SMS text message that either contains a link to a website, in the same way that phishing does, or it will ask the user to call a telephone number to resolve an urgent issue. The same advice can be followed for smishing as given for phishing. The user must question at all times any links that are sent from an unknown or suspicious user. It is advisable that if a user believes the message may be legitimate, to type in the domain name for the legitimate company website into their web browser, rather than following the link in the message. Users should block any numbers that they believe are suspicious to prevent any further risk of smishing from that number. Figure 5.3: Smishing. Vishing Vishing (or voice phishing) has the same aim as phishing, to obtain a user's personal details. The user receives a telephone call that could either be an automated system or could be a real person. An automated voice could speak to the user and advise them that an issue has occurred, such as there has been suspicious activity regarding their bank account. The user may then be asked to call another number, or just to simply press a digit and be directed to another automated system. This system will ask them to provide their bank account details to resolve the issue. The bank account details have then been obtained by the unauthorised user and can be used to commit a crime against the user. The automated system could be replaced by a real person who will try to do the same thing. They will try to convince the user that there has been an issue with an account they have and to provide the log-in details or PIN for the account to verify who they are so the issue can be resolved. The precaution to take for vishing is that no company will ever call you and ask you to provide any log-in details or PIN details over the telephone. They may ask you to provide other personal information, and if you are in doubt that the person on the other end of the phone is legitimate, it is always advisable to put the phone down and call the company back on a legitimate number that you may already know or can obtain. Figure 5.4: Vishing. Pharming Pharming is when an unauthorised user installs malicious code on a person's hard drive or server. The malicious code is designed to redirect a user to a fake website when they type in the address of a legitimate one. The fake website is designed to look like the legitimate one, to trick the user and make sure they are not aware that their request has been redirected. The user will then enter their personal details into the fake website, believing it is the legitimate one, and the unauthorised person will now have their personal data. A common technique used in pharming is called domain name server (DNS) cache poisoning. This technique exploits vulnerabilities in the DNS and diverts the internet traffic intended for a legitimate server toward a fake one instead. The unauthorised user needs to find a way to install the malicious code on the computer. They often hide the malicious code in an email attachment or link. When the user opens the email attachment or clicks the link, the malicious code is downloaded also. Figure 5.5: Pharming. The aim of a pharming attack is also to steal a user's personal data. A real-life example of pharming In 2007 50 different companies all over the world were subject to a pharming attack, these included PayPal, eBay, Barclays bank and American Express. Over a three-day period, hackers managed to infect over 1000 PCs a day with a malicious pharming code. When users who had been infected visited the websites of the different companies, they were redirected to a legitimate-looking version of the site that was designed to steal their personal data. The original email, containing the malicious code, was set up to look like a shocking news story. Users were encouraged to click a link in the email to find out more information. The code was downloaded when the user clicked the link. This was quite a sophisticated attack that required legitimate looking websites to be set up for a large number of companies. It is not known how much money the hackers were able to retrieve as a result. How to prevent pharming All of the guidelines to avoid being subjected to phishing are also relevant for recognising pharming. There are also several other precautions that can be taken to check for pharming attacks. These include: •Have a firewall installed and operational. A firewall monitors incoming and outgoing traffic from your computer. It checks this traffic against set criteria and will flag and stop any traffic that does not meet the criteria. A firewall could detect and block suspicious traffic, such as a malicious code trying to enter your system. •Have an anti-virus program installed that is designed to detect malicious pharming code. You need to scan your computer on a regular basis to check for any malicious code. It is advisable to set up an automatic scan on a daily basis at a time when your computer will normally be switched on. •Be aware when using public Wi-Fi connections. A hacker could look to directly access your computer and install the malicious code if you are connected to a public Wi-Fi connection. It is often advisable to use a VPN when using public Wi-Fi. This will help shield your internet activity and personal details from a hacker, making it more difficult for them to access your computer. Smishing can also be used as a form of pharming. A user is sent a link, that when they click is designed to download malware onto their mobile device. Therefore, it is advisable to have security software installed on your mobile and also scan it regularly to detect any presence of malware.

5.2 Readiness - I find out the meaning of Latin, Greek, or other roots and affixes.

Select all the numbers that can be used as a common denominator to rewrite the fractions __ 2 6 and __ 1 2 . A 3 D 12 B 6 E 16 C 8 2 Aaron ran __ 5 8 mile to his friend’s house. Then he ran another __ 1 4 mile to the park. 1 1 8 1 8 1 8 1 8 1 8 1 8 1 8 1 8 1 8 1 8 1 8 1 8 1 4 Which equation shows how many miles Aaron ran? A __ 5 8 – __ 1 4 = __ 2 8 C __ 5 8 + __ 1 4 = __ 7 8 B __ 5 8 – __ 1 4 = __ 3 8 D __ 5 8 + __ 1 4 = __ 8 8 3 Select all the expressions that can be used to find the sum of __ 6 8 and ___9 12. A ___ 36 48 + ___ 36 48 D ___ 18 20 + ___ 17 20 B ___ 24 36 + ___ 27 36 E ___ 18 24 + ___ 18 24 C ___ 14 16 + ___ 13 16 4 Write a pair of equivalent fractions for __ 3 4 and __ 2 5 using a common denominator of 20. __ 3 4 = __ 2 5 = 5 Katie spent __ 4 5 hour painting and __ 1 2 hour drawing. ? 1 1 2 1 5 1 5 1 5 1 5 How much more time in hours did she spend painting than drawing? 6 Dave is planting a garden. He plants cucumbers in ___2 12 of his garden and tomatoes in __ 2 3 of his garden. What fraction of his garden does Dave plant with cucumbers and tomatoes? 7 Of the students in Maria’s class, __ 2 5 have dogs and __ 1 3 have cats. No students have both a dog and a cat. What fraction represents how many more students in Maria’s class have dogs? 52 © Houghton Mifflin Harcourt Publishing Company Module 6 • Form A Name Module Test DO NOT EDIT--Changes must be made through "File info" CorrectionKey=NL-C 9 Mr. Gonzales used __ 3 4 quart of broth and __ 1 2 quart of milk to make soup. How many quarts of liquid did he use? Part A Complete the fraction model to represent the problem. 1 1 2 1 4 1 4 1 4 Part B Write an equation to show how many quarts of liquid Mr. Gonzales used to make soup. 10 A bowl of cereal contains __ 2 3 cup of oats and __ 2 8 cup of raisins. Write a numerical expression using equivalent fractions with a common denominator of 24 to model how many more cups of oats than raisins there are in the bowl. 11 Jessica read __ 1 6 of her book on Thursday, __ 2 9 of her book on Friday, and __ 1 2 of her book on Saturday. Part A Write a numerical expression using equivalent fractions to model how much of her book she has read so far. Part B What fraction of her book has Jessica read?

READINESS 5.2 (B) I use the sentences in a text to find out or clear up the meaning of the word I need to understand.

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