CAHSEE Math Problem of the Day -- Week 12

CAHSEE Math Problem of the Day -- Week 12Teacher Notes & AnswersWeek Week 12 – Day 2Concept/Skill Writing equations.Standard 7 AF:1.1 Use variables and appropriate operations to write anexpression, an equation, an inequality, or a system of equations orinequalities that represents a verbal description (e.g., three less than anumber, half as large as area A).Materials CAHSEE Math Released Item # 61• Review that Equalities are statements that have an equal sign. Students can tell if astatement is an equality if it says something is and gives a specific answer as opposedto something is greater than or less than..Have students review how to to change a statement into an equality:1. Write the symbol for each part of the statement. If the statement says “number”substitute n Where the statement says “is” put an =2. Determine if each answer is correct or wrong.• Have students do the guided practice on Day 2 of the student CAHSEE MathProblem of the Day -- Week 12 worksheet.Example:Multiply a number by 6 and add 2 to the result.________ 6n __________ + 2The answer is 20.________ = 20Which of the following equations matches these statementsA 20=2n+6 __ correct __ x wrong (should be 6n not 2n)B (6+2)n=20 __ correct __ x wrong [should be 6n not (6+2)n]C 6n=2 __ correct __ x wrong (should equal 20 not 2)D 6n+ 2=20 __ x correct __ wrongThe correct ANSWER is ______. DDay 2 is continued on next page.Laura Westermeier, Ed.D. Fall 2007SAUSD, Educational Services Week 12 – Teacher - Page 3 of 9

CAHSEE Math Problem of the Day -- Week 12Teacher Notes & AnswersWeek Week 12 – Day 3Concept/Skill Writing expressions with variables.Standard 7 AF:1.1 Use variables and appropriate operations to write anexpression, an equation, an inequality, or a system of equations orinequalities that represents a verbal description (e.g., three less than anumber, half as large as area A).Materials CAHSEE Math Released Item # 60• Have students review how to write an expression given a written statement:1. Circle each part of the statement that needs to be used in the expression.2. Subtract if the item is used or sold3. Add if more of the item is received or bought• Have students do the guided practice on Day 3 of the student CAHSEE MathProblem of the Day -- Week 12 worksheet.Example:The chef has x liters of cream. She uses 4 liters to make ice cream. The next day sheused 3y liters to make a mousse. Which expression represents the amount of cream shenow has?A x+4+3yB x+4-3yC x-4+3yD x-4-3yHow many liters does she start with? ______ xHow many liters does she use first? ______ 4Will you add or subtract? __________ subtractCross off the ANSWERS can you eliminate. (Cross off A and B)How many liters does she use next? ______ 3yWill you add or subtract? __________ subtractCross off the ANSWER can you eliminate. (Cross off C )The correct ANSWER is ______. DDay 3 is continued on next page.Laura Westermeier, Ed.D. Fall 2007SAUSD, Educational Services Week 12 – Teacher - Page 5 of 9

CAHSEE Math Problem of the Day -- Week 12Teacher Notes & Answers• You may choose to have students do an additional practice problem for Day 3.Have students practice eliminating the incorrect answers.Additional Practice:The donut maker has x dozen donuts. He makes 10 dozen more and then sells 6ydozen. Which expression represents the number of dozens of donuts he now has?A x + 10 + 6y (Wrong, you should add ten but since he sells 6y you need to substract)B x + 10 – 6y (Correct)C x – 10 + 6y (Wrong, since he makes 10 dozen more you should add 10, not subtract)D x – 10 – 6y (Wrong, since he makes 10 dozen more you should add 10, not subtract)The correct ANSWER is ______. B•• Have students do the CAHSEE released test item on Day 3 of the student CAHSEEMath Problem of the Day -- Week 12 worksheet.60. A shopkeeper has x kilograms of tea in stock. He sells 15 kilograms and thenreceives a new shipment weighing 2y kilograms. Which expression represents theweight of the tea he now has?A (Wrong, since he receives 2y kilograms you should add 2y)B (Wrong, since he sells 15 kilograms you should subtract 15)C (Wrong, since he sells 15 kilograms you should subtract 15)D(Correct)Laura Westermeier, Ed.D. Fall 2007SAUSD, Educational Services Week 12 – Teacher - Page 6 of 9

CAHSEE Math Problem of the Day -- Week 12Teacher Notes & AnswersWeek Week 12 – Day 4Concept/Skill Writing expressions using the distributive property.Standard 7 AF:1.1 Use variables and appropriate operations to write anexpression, an equation, an inequality, or a system of equations orinequalities that represents a verbal description (e.g., three less than anumber, half as large as area A).Materials CAHSEE Math Released Item #63• Review with students that many of the questions on the CAHSEE only require that theyknow how to write the mathematical expression. They do not need to find the answeror solve for x or y.• Review the steps to write an expression using the distributive property: .1.Write the cost of one of the itemsa. Subtract if the amount is used or is lessb.Add if more of the amount is received or is more2. If more than one of the items is bought put the expression from steps 1 inparentheses and multiply by that number.• Have students do the guided practice test item on Day 4 of the student CAHSEEMath Problem of the Day -- Week 12 worksheet.EXAMPLE:At a fast food restaurant the combo meal that cost x dollars can be super-sized for 1dollar more. How many dollars does it cost to buy 5 super-sized combo meals?A 5x-1B 5x+1C 5(x-1)D 5(x+1)How much does 1 super-size combo meal cost?______________x + 1How do you write 5 time the cost of one combo meal?____ 5 (_____ x + _____) 1Is 5x+1 the same as 5(x+1)? _______ No Using the distributive property, 5(x+1)=5x+5The correct ANSWER is ______. DDay 4 continued on next page.Laura Westermeier, Ed.D. Fall 2007SAUSD, Educational Services Week 12 – Teacher - Page 7 of 9

CAHSEE Math Problem of the Day -- Week 12Teacher Notes & Answers• Have students do the CAHSEE released test item on Day 4 of the student CAHSEEMath Problem of the Day -- Week 12 worksheet.63. At a local bookstore, books that normally cost b dollars are on sale for 10 dollarsoff the normal price. How many dollars does it cost to buy 3 books on sale?The price of one book is b – 10 . To buy 3 you need to multiple (b – 10) by 3 or 3(b – 10)A (Wrong, the10 also needs to be multiplied by 3)BCD(Wrong, the 10 needs to be subtracted)(Correct)(Wrong, the 10 needs to be subtracted since the books are 10 dollarsoff the normal price)Laura Westermeier, Ed.D. Fall 2007SAUSD, Educational Services Week 12 – Teacher - Page 8 of 9

CAHSEE Math Problem of the Day -- Week 12Teacher Notes & AnswersWeek Week 12 – Day 5Concept/Skill Writing equations with variables.Standard 7 AF:1.1 Use variables and appropriate operations to write anexpression, an equation, an inequality, or a system of equations orinequalities that represents a verbal description (e.g., three less than anumber, half as large as area A).Materials CAHSEE Math Released Item # 62Day 5• Students will need to use the strategies for writing mathematical expressions from thisweek to find the correct answer.Example:In a classroom, the number of boys, b, is equal to 2 times the number of girls, g._________ b _____ = _________________2 • gWhich equation matches the information?A2 • g = b (Correct since b=2g is the same as 2g=b using the Communicative Property)B 2 • b = g (Wrong, the g needs to be multiplied by 2, not the b)C 2 • b = 2 • g (Wrong, only the b should be multiplied by 2)D b • g = 2 (Wrong, b should not be multiplied by g)The correct ANSWER is ______. A• Have students do the CAHSEE released test item on Day 5 of the student CAHSEEMath Problem of the Day -- Week 12 worksheet.62. In a certain room, the number of chairs, c, is equal to 3 times the number oftables, t. Which equation matches the information?A 3 • c = tB 3 • t = cC 3 • c = 3 • tD c • t =3The expression should be written asc = 3 • t. Using the Communicative Propertythe expression can be rewritten as 3 • t = cThe correct answer is B• At the end of the week remind students to keep the student CAHSEE MathProblem of the Day -- Week 12 worksheet to use as a study guide as they continueto prepare for the CAHSEE.Laura Westermeier, Ed.D. Fall 2007SAUSD, Educational Services Week 12 – Teacher - Page 9 of 9