1ST 9-WKS 2016-17
Clarity of the Standard / Resources / Ready Lessons and Questar Emphasis
Topic 1 – Addition and Subtraction of Rationals
7.NS.1
STARTING IN 2017-18, 7TH GRADE WILL NO LONGER TEACH 7.NS.1
1. A. Describesituationsinwhichoppositequantitiescombinetomake 0.
B. Understandp+qasthenumberlocatedadistanceIqIfromp,inthepositiveornegativedirection dependingonwhetherqispositiveornegative.Showthatanumberanditsoppositehaveasumof 0(areadditiveinverses).Interpretsumsofrationalnumbersbydescribingreal-worldcontexts.
C.Understand subtractionofrationalnumbersasaddingtheadditiveinverse,p-q=p+(-q).Show thatthedistancebetweentworationalnumbersonthenumberlineis theabsolutevalueoftheir difference,andapplythisprincipleinreal-worldcontexts.
D.Applypropertiesofoperationsasstrategiestoaddandsubtractrationalnumbers. / I Can:
7.NS. 1.A Describe situations in which opposite quantities equal zero
7.NS.1.A Explain and compute absolute value.
7.NS.1.B Add and subtract rational numbers.
7.NS.1.B Apply the additive inverse property
7.NS.1.B Describe situations in which opposite quantities equal zero.
7.NS.1.C Describe real-life contexts of rational sums.
7.NS.1.CRecognize the sum of positive and negative integers as application of the additive inverse.
7.NS. 1.D Apply properties to simplify combining rational numbers. / Example 1:
Use a number line to subtract: -6 – (-4)
Solution:
This problem is asking for the distance between -6 and -4. The distance between -6 and -4 is 2 and the direction from -4 to -6 is left or negative. The answer would be -2 (Note that this answer is the same as adding the opposite of -4)
-6 + 4 = -2
Example 2:A hydrogen atom has 0 charge when its two constituents are oppositely charged. Explain.
Example 3:
Use a number line to illustrate:
- p – q ie. 7 – 4
- p + (-q) ie. 7 + (– 4)
- Is this equation true p – q = p + (-q)?
Example: Ella says that when you combine two numbers and one is negative, you always get a negative answer. Is her statement always true, never true, or sometimes true? Explain your answer. / Integers
Integer activity
Word problems
Worksheet with thoughtful questions Integer Add.Sub Variations 7.NS.1.docx
Formative Assessment Lesson Plan
Ga Unit
/ Ready Lessons 1-3
Questar Emphasis
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10/75 questions are from 7.NS
Topic 2 – Multiplication and Division of Rationals
7.NS.2
.Apply and extend previous understandings of multiplication and division and of fractions to multiply
and divide rational numbers.
Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats. / I Can:
Convert rational numbers to decimal numbers.
Recognize a terminating or repeating decimal / Multiplication and division of integers is an extension of multiplication and division of whole numbers.
Examples:
- Examine the family of equations. What patterns do you see? Create a model and context for each of the products.
2 x 3 = 6 / / Selling two posters at $3.00 per poster
2 x -3 = -6 / / Spending 3 dollars each on 2 posters
-2 x 3 = -6 / / Owing 2 dollars to each of your three friends
-2 x -3 = 6 / / Forgiving 3 debts of $2.00 each
/ Granite Schools lesson plan / Ready Lessons 4 - 6
Questar Emphasis
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10/75 questions are from 7.NS
.
Topic 3 – Solving Problems with Rational Numbers
7.NS.3
Solve real world and mathematical problems involving the four operations with rational numbers.
NOTE: Computations with rational numbers extend the rules for manipulating fractions to complex fractions. / I Can:
Set up word problems involving unit rate.
Solve word problems involving unit rate. / Example 1:
Calculate: [-10(-0.9)] – [(-10) • 0.11]
Solution: 10.1
Example 2:
Jim’s cell phone bill is automatically deducting $32 from his bank account every month. How much will the deductions total for the year?
Solution:
-32 + (-32) + (-32) + (-32)+ (-32) + (-32) + (-32) + (-32) + (-32) + (-32) + (-32) + (-32) = 12 (-32)
Example 3:
It took a submarine 20 seconds to drop to 100 feet below sea level from the surface. What was the rate of the descent?
Solution:
-100 feet or - 5 feet
20 seconds 1 second
Example 4:
A newspaper reports these changes in the price of a stock over four days: , , , . What is the average daily change?
Solution:
The sum is ; dividing by 4 will give a daily average of /
LESSON PLAN / Ready Lessons 7-8
Questar Emphasis
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10/75 questions are from 7.NS
7.EE.3
Solve multi-step real-life and
mathematical problems posed with positive and negative
rational numbers in any form (whole numbers, fractions,
and decimals), using tools strategically. Apply properties of operations to calculate with
numbers in any form; convert
between forms as appropriate;
and assess thereasonableness of answers using mental computation and
estimation strategies.
4. A Solve word
problems leading to
equationsof the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. / I Can:
Solve multi-step real-life problems involving positive and negative fractions.
Apply properties to solve equations.
Assess the reasonableness of answers to questions. / Example: Alex spends 2 hours mowing the lawn and then of an hour weeding each flower bed. If he spends a total of 3 hours mowing and weeding, write an equation to show this information.
Example: Solve: (6x – 9) = 5 / Worksheet with integer word problems to set up and solve
/ Questar Emphasis
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12/75 questions are from 7.EE
Topic 4 – Algebraic Expressions
7.EE
A.Usepropertiesofoperationstogenerateequivalentexpressions.
1.Applypropertiesofoperationsasstrategiestoadd,subtract,factor,andexpandlinearexpressionswith rationalcoefficients.
2.Understandthatrewriting an expressionindifferentformsinaproblemcontextcanshedlightonthe problemandhowthequantitiesinitarerelated.
4a.Solvewordproblemsleadingtoequationsoftheformpx+q=randp(x+q)=r,wherep,q,andrarespecificrationalnumbers.Solveequationsoftheseformsfluently.Compareanalgebraicsolutionto anarithmeticsolution,identifyingthesequenceoftheoperationsusedineachapproach. / I Can:
Apply properties of real numbers to combine like terms.
Simplify expressions by combining like terms
Justify how different forms of an expression are equivalent.
Explain how rewriting an expression can help solve a problem. / Omani wants to place a computer 24½ inches long in the center of a table that 28 ¾ inches wide, about how far from the edge will you place the table?
Which of these have a solution of .5?
- 5(x-3) = -12.5 b. 6x + 3-8x – 11= -7
- Which of these expressions are equivalent to:
- 6x – 5 b. 8x - c. 6x - e. 6x – 3.75
- Which of the equivalent expressions in the above problem would you use if it was part of an equation?
khan academy
Formative Assessment Lesson Plan
Learn Zillion
7.EE.2
Engage NY
7.EE.4a
performance task
/ Ready Lessons
14-15
Questar Emphasis
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12/75 questions are from 7.EE
Topic
5 – Solving Equations
7.EE.4a
Solvewordproblemsleadingtoequationsoftheformpx+q=randp(x+q)=r,wherep,q,andrarespecificrationalnumbers.Solveequationsoftheseformsfluently.Compareanalgebraicsolutionto anarithmeticsolution,identifyingthesequenceoftheoperationsusedineachapproach. / I Can:
Solve a one-variable equation with a single solution and check the answer.
Accurately solve linear equations.
Compare the algebraic solution to a problem with an arithmetic solution.
/ Inthisunit,theyareexpectedtocontinueto buildfluencywithwritingandsolvingmulti-step equations(7.EE.B.4a)andtheyextendthose understandingstoinvestigatesolvingword problemsleadingtoinequalities(7.EE.B.4b)
Solve and graph: .2(3x – 5) -8 = -11
Is 6 a solution for 3(5-2x) < -3
Write an inequality to illustrate the following situations:
You buy soup cans weighing ¾ of a pound. You also buy one ½ pound can of tuna. How many soup cans can you buy if your bag only holds 2 ¾ pounds?
You have saved $50. You earn $ 20 per week doing extra chores. How long will you have to work to have the $185 you need to buy a new phone? / 7.EE.4a
performance task
7.EE.4b
lesson plan for inequalities / Ready Lesson
16
Questar Emphasis
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12/75 questions are from 7.EE
7.NS.3
Solvereal-worldandmathematicalproblemsinvolvingthefouroperationswithrationalnumbers.1
NOTE:Computationswithrationalnumbersextendtherulesformanipulatingfractionstocomplex fractions. / I Can:
Solve real world problems involving rational numbers. / Example: Tom had pieces of rope. Rope 1 was 5 ½ fee long. Rope was 74 inches long. Rope 3 was 1 ½ yards long. What is the total length of rope? /
LESSON PLAN / Questar Emphasis
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10/75 questions are from 7.EE
7.EE.3
3.Solvemulti-stepreal-lifeandmathematicalproblemsposedwithpositiveandnegativerationalnumbersinanyform(wholenumbers,fractions,anddecimals),usingtoolsstrategically.Applypropertiesofoperationstocalculatewithnumbersinanyform;convertbetweenformsasappropriate;andassessthereasonablenessofanswersusingmentalcomputationandestimationstrategies. / I Can:
Calculate/and/or convert between the various forms of rational numbers.
Solve multi-step equations.
Solve problems using algebraic expressions.
Assess reasonableness of answers. / Forexample:Ifawomanmaking$25anhourgetsa10%raise,shewillmakeanadditional1/10ofhersalaryanhour,or$2.50,foranewsalaryof$27.50.
Ifyouwanttoplaceatowelbar93/4incheslonginthecenterofadoorthatis271/2incheswide,youwillneedtoplacethebarabout9inchesfromeachedge;thisestimatecanbeusedasacheckontheexactcomputation. / Worksheet with integer word problems to set up and solve
/ Questar Emphasis
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12/75 questions are from 7.EE