Variables and Patterns: - 7th Grade Math - Home



7th Grade Math ReviewName: _______________________________1st Semester ExamExam Date: ___________________________Topics to Study:Variables and PatternsRecognize situations in which variables are related in predictable waysDescribe patterns of change in words, data tables and graphsUse data tables and graphs to solve problemsAccentuate the NegativeCompare and order rational numbers and locate them on a number lineUnderstand the relationship between a number and its opposite (additive inverse)Relate direction and distance to the number lineDevelop and use different models (number line, chip model) for representing addition, subtraction, multiplication, and divisionDevelop algorithms for adding, subtracting, multiplying, and dividing integersInterpret and write mathematical sentences to show relationships and solve problemsWrite and use related fact families for addition/subtraction and multiplication/division to solve simple equationsUse parentheses and the Order of Operations in computationsStretching and ShrinkingIdentify similar figures by comparing corresponding sides and anglesUse scale factors and ratios to describe relationships among the side lengths, perimeters, and areas of similar figuresConstruct similar figures (scale drawings) using informal methods, scale factors, and geometric toolsUse algebraic rules to produce similar figures and recognize when a rule shrinks or enlarges a figureUse scale factors or ratios to find missing side lengths in a pair of similar figuresComparing and ScalingAnalyze comparison statements for correctness and qualityUse ratios, rates, and percents to write comparison statementsDistinguish between and use part-to-part and part-to-whole ratios to make comparisonsScale a ratio, rate, or percent to solve a problemSet up and solve proportionsOther Review Tools:Your past quizzes and testsNotes and Assignments in your binder7th grade math websiteVariables and Patterns:1)The table shows some data Anita collected while walking.Anita’s WalkTime (minutes)051015202530Distance (miles)00.511.251.51.751.8a.What are the two variables? ______________________ , ______________________b.Graph the data on the axes below.c.What does the point (15, 1.25) tell about Anita’s progress?d.In what time periods did Anita travel the farthest? ______________________How does this show up in the table?How does this show up in the graph?e.In what time periods did Anita travel the least? ______________________How does this show up in the table?How does this show up in the graph?f.Is this problem easier to answer using the table or the graph? _______________ Why? Accentuate the Negative:Draw a picture (number line, chip board, or something else) that would explain how to solve this problem:2)3)4)Write a story to represent the following problem: –50 – ( –125 )51092101016000Use the chip board to help answer problems 5 – 7. 5)What is the current value of the chip board? ___________6)What are TWO ways to change the value of the board to –2?Write a number sentence describing each change.7)What move could you make that would change the number of chips on the board, but wouldn’t change the value?8)Mady is using a chip board to do the following problem. Describe the steps she would use.3 – (–4) Simplify. Show your work.9)10)11)12)13)14)Explain how to add ANY two integers together.15)Explain why subtracting a negative number is equivalent to adding a positive number.Stretching and Shrinking:39751008597900BA10.5 in3 in7 in2 in00BA10.5 in3 in7 in2 in16)Are these two figures similar? Explain.504825184150017)The triangles are similar. Find the value of the missing side lengths.457200175895486918019621511.7cm6.3 cm0011.7cm6.3 cm18)The rectangles below are similar. Find the perimeter and the area of the shaded rectangle.32575501714503.5 cmx cm003.5 cmx cm19)Make two sketches of the triangle shown. First, draw a new triangle using a scale factor of 3. Then, make a second drawing of the original triangle using a ? scale.114300173355Shown here is an incorrect sketch a student made to reduce the size of the triangle. What is wrong with the drawing?00Shown here is an incorrect sketch a student made to reduce the size of the triangle. What is wrong with the drawing?10922017970500-45720012192000Use your scale drawings from number 19 to answer problems 20 – 23.20.)What is the area and perimeter of the original figure?21.)How does the perimeter of each of your drawings compare to the perimeter of the original shape?22.)How does the area of each of your drawings compare to the area of the original shape?23.)How do the angles of the similar triangles compare?Comparing and Scaling:24.)Four different recipes for chocolate chip cookies are shown below. 49720505080Mix T21 cups dough6 cups chocolate chips0Mix T21 cups dough6 cups chocolate chips32480255080Mix S10 cups dough3 cups chocolate chips0Mix S10 cups dough3 cups chocolate chips16287755080Mix R15 cups dough4 cups chocolate chips0Mix R15 cups dough4 cups chocolate chips95255080Mix Q18 cups dough5 cups chocolate chips0Mix Q18 cups dough5 cups chocolate chipsWhich recipe makes cookies that are the most chocolatey?Show all your work below.25.)Find each unit price and the best buy. Explain.a)3 lbs. of beef for $4.29 b)20 yards of fabric for $65.005 lbs. of beef for $7.1950 feet of fabric for $55.0026.)Solve the following proportions.a)b) c) 27.)For every 8 minutes of commercials on TV, Caleb gets to see 22 minutes of the show he is watching. How long does Caleb watch TV if he sees 20 minutes of commercials?About how many minutes of commercials will he see if he watches 1 hour of TV?Mr. Hanton’s & Mrs. Pyne’s Test Studying StrategiesEveryone has different test studying strategies. Here are some for you to try!Anticipate what material will be covered on the test. Is it an entire chapter? Is it just the notes from the last few weeks? If your teacher doesn’t write it down for you, write it down yourself. Or, ask your teacher what the test will cover.Highlighting the most important parts of your notes and reviewing just the highlighted parts will help you study what you really need to know in less time.If your test is based on a textbook chapter, look at the textbook to see what was important from each chapter. Often, textbooks will list learning objectives or goals at the beginning of each section. They also will bold or highlight important vocabulary. These are great places to start!Gather all materials that you think the test will cover. If your teacher didn’t make a study guide, these will be helpful!Making flashcards to memorize vocabulary or even important concepts is very helpful! Online sites also let you make flashcards and play games to learn the information. My favorite flashcard website is . Flashcards can even be used to do math! Put an example problem from your notes on one side and the full solution on the back. Try to answer the problem on a separate sheet of paper. Then, flip the card over to see if you are correct. If you were incorrect, follow the example solution to see where you are having trouble.Avoid cramming for tests. If you know you didn’t understand something in class or had trouble with one of the homework questions, get help right away! Teachers love to answer questions and help you, but you might have to ask. It will save you time and frustration in the future.If you choose to study in a group, only study with others who are serious about the test.Find a comfortable and quiet place to study with good lighting and little distractions (try avoiding your bed & TV; it is very tempting to just lie down and take a nap).Your brain gets tired. Study for a set amount of time (an hour or less) and take a break. For example, set a timer for 30 minutes. When it rings, take a break! Make sure to get enough sleep the night before a test. Studies show that you cement information in your brain when you sleep!Be confident that you have studied the best you can and that you WILL do well on the test. Researchers have found that people who think they can do something are more likely to succeed than those who didn’t think they could. Thinking positively pays off. ................
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