Grade 7. Strand: Number Specific Learning Outcomes It is expected that students will:

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1 Strad: Number Specific Learig Outcomes It is expected that studets will: 7.N.1. Determie ad explai why a umber is divisible by 2, 3, 4, 5, 6, 8, 9, or 10, ad why a umber caot be divided by 0. [C, R] [C] Commuicatio [PS] Problem Solvig [CN] Coectios [R] Reasoig [ME] Metal Mathematics [T] Techology ad Estimatio [V] Visualizatio Geeral Learig Outcome: Develop umber sese. Achievemet Idicators The followig set of idicators may be used to determie whether studets have met the correspodig specific outcome. Determie if a umber is divisible by 2, 3, 4, 5, 6, 8, 9, or 10, ad explai why. Sort a set of umbers based upo their divisibility usig orgaizers, such as Ve or Carroll diagrams. Determie the factors of a umber usig the divisibility rules. Explai, usig a example, why umbers caot be divided by 0. 7.N.2. Demostrate a uderstadig of the additio, subtractio, multiplicatio, ad divisio of decimals to solve problems (for more tha 1-digit divisors or 2-digit multipliers, techology could be used). [ME, PS, T] Solve a problem ivolvig the additio of two or more decimal umbers. Solve a problem ivolvig the subtractio of decimal umbers. Solve a problem ivolvig the multiplicatio or divisio of decimal umbers (for more tha 1-digit divisors or 2-digit multipliers, techology could be used). Place the decimal i a sum or differece usig frot-ed estimatio (e.g., for , thik , so the sum is greater tha 260). Place the decimal i a product usig frot-ed estimatio (e.g., for $ , thik $12 2, so the product is greater tha $24). Place the decimal i a quotiet usig frot-ed estimatio (e.g., for m 2.1, thik 50 m 2, so the quotiet is approximately 25 m). Check the reasoableess of aswers usig estimatio. Solve a problem that ivolves operatios o decimals (limited to thousadths), takig ito cosideratio the order of operatios. Explai, usig a example, how to use metal math for products or quotiets whe the multiplier or the divisor is 0.1 or 0.5 or Kidergarte to Grade 8 Mathematics: Maitoba Curriculum Framework of Outcomes (2013)

2 Strad: Number (cotiued) Specific Learig Outcomes It is expected that studets will: 7.N.3. Solve problems ivolvig percets from 1% to 100%. [C, CN, ME, PS, R, T] 7.N.4. Demostrate a uderstadig of the relatioship betwee repeatig decimals ad fractios, ad termiatig decimals ad fractios. [C, CN, R, T] Geeral Learig Outcome: Develop umber sese. Achievemet Idicators The followig set of idicators may be used to determie whether studets have met the correspodig specific outcome. Express a percet as a decimal or fractio. Solve a problem that ivolves fidig a percet. Determie the aswer to a percet problem where the aswer requires roudig, ad explai why a approximate aswer is eeded (e.g., total cost icludig taxes). Predict the decimal represetatio of a fractio usig patters (e.g., 1 = 0.09, 2 = 0.18, [C] Commuicatio [PS] Problem Solvig [CN] Coectios [R] Reasoig [ME] Metal Mathematics [T] Techology ad Estimatio [V] Visualizatio =? ). Match a set of fractios to their decimal represetatios. Sort a set of fractios as repeatig or termiatig decimals. Express a fractio as a termiatig or repeatig decimal. Express a repeatig decimal as a fractio. Express a termiatig decimal as a fractio. Provide a example where the decimal represetatio of a fractio is a approximatio of its exact value Geeral ad Specific Learig Outcomes 127

3 [C] Commuicatio [PS] Problem Solvig [CN] Coectios [R] Reasoig [ME] Metal Mathematics [T] Techology ad Estimatio [V] Visualizatio 7.N.5. 7.N.6. Strad: Number (cotiued) Specific Learig Outcomes It is expected that studets will: Demostrate a uderstadig of addig ad subtractig positive fractios ad mixed umbers, with like ad ulike deomiators, cocretely, pictorially, ad symbolically (limited to positive sums ad differeces). [C, CN, ME, PS, R, V] Demostrate a uderstadig of additio ad subtractio of itegers, cocretely, pictorially, ad symbolically. [C, CN, PS, R, V] Geeral Learig Outcome: Develop umber sese. Achievemet Idicators The followig set of idicators may be used to determie whether studets have met the correspodig specific outcome. Model additio ad subtractio of positive fractios or mixed umbers usig cocrete represetatios, ad record symbolically. Determie the sum of two positive fractios or mixed umbers with like deomiators. Determie the differece of two positive fractios or mixed umbers with like deomiators. Determie a commo deomiator for a set of positive fractios or mixed umbers. Determie the sum of two positive fractios or mixed umbers with ulike deomiators. Determie the differece of two positive fractios or mixed umbers with ulike deomiators. Simplify a positive fractio or mixed umber by idetifyig the commo factor betwee the umerator ad deomiator. Simplify the solutio to a problem ivolvig the sum or differece of two positive fractios or mixed umbers. Solve a problem ivolvig the additio or subtractio of positive fractios or mixed umbers, ad determie if the solutio is reasoable. Explai, usig cocrete materials such as iteger tiles ad diagrams, that the sum of opposite itegers is equal to zero. Illustrate, usig a horizotal or vertical umber lie, the results of addig or subtractig egative ad positive itegers (e.g., a move i oe directio followed by a equivalet move i the opposite directio results i o et chage i positio). Add two itegers usig cocrete materials or pictorial represetatios, ad record the process symbolically. Subtract two itegers usig cocrete materials or pictorial represetatios, ad record the process symbolically. Solve a problem ivolvig the additio ad subtractio of itegers. 128 Kidergarte to Grade 8 Mathematics: Maitoba Curriculum Framework of Outcomes (2013)

4 [C] Commuicatio [PS] Problem Solvig [CN] Coectios [R] Reasoig [ME] Metal Mathematics [T] Techology ad Estimatio [V] Visualizatio 7.N.7. Strad: Number (cotiued) Specific Learig Outcomes It is expected that studets will: Compare ad order fractios, decimals (to thousadths), ad itegers by usig bechmarks place value equivalet fractios ad/or decimals [CN, R, V] Geeral Learig Outcome: Develop umber sese. Achievemet Idicators The followig set of idicators may be used to determie whether studets have met the correspodig specific outcome. Order the umbers of a set that icludes fractios, decimals, or itegers i ascedig or descedig order, ad verify the result usig a variety of strategies. Idetify a umber that would be betwee two umbers i a ordered sequece or o a horizotal or vertical umber lie. Idetify icorrectly placed umbers i a ordered sequece or o a horizotal or vertical umber lie. Positio fractios with like ad ulike deomiators from a set o a horizotal or vertical umber lie, ad explai strategies used to determie order. Order the umbers of a set by placig them o a horizotal or vertical umber lie that cotais bechmarks, such as 0 ad 1 or 0 ad 5. Positio a set of fractios, icludig mixed umbers ad improper fractios, o a horizotal or vertical umber lie, ad explai strategies used to determie positio. Geeral ad Specific Learig Outcomes 129

5 [C] Commuicatio [PS] Problem Solvig [CN] Coectios [R] Reasoig [ME] Metal Mathematics [T] Techology ad Estimatio [V] Visualizatio 7.PR.1. 7.PR.2. Strad: Patters ad Relatios (Patters) Specific Learig Outcomes It is expected that studets will: Demostrate a uderstadig of oral ad writte patters ad their correspodig relatios. [C, CN, R] Costruct a table of values from a relatio, graph the table of values, ad aalyze the graph to draw coclusios ad solve problems. [C, CN, R, V] Geeral Learig Outcome: Use patters to describe the world ad solve problems. Achievemet Idicators The followig set of idicators may be used to determie whether studets have met the correspodig specific outcome. Formulate a relatio to represet the relatioship i a oral or writte patter. Provide a cotext for a relatio that represets a patter. Represet a patter i the eviromet usig a relatio. Create a table of values for a relatio by substitutig values for the variable. Create a table of values usig a relatio, ad graph the table of values (limited to discrete elemets). Sketch the graph from a table of values created for a relatio, ad describe the patters foud i the graph to draw coclusios (e.g., graph the relatioship betwee ad 2 + 3). Describe the relatioship show o a graph usig everyday laguage i spoke or writte form to solve problems. Match a set of relatios to a set of graphs. Match a set of graphs to a set of relatios. 130 Kidergarte to Grade 8 Mathematics: Maitoba Curriculum Framework of Outcomes (2013)

6 7.PR.3. 7.PR.4. 7.PR.5. Grade 7 Strad: Patters ad Relatios (Variables ad Equatios) Specific Learig Outcomes It is expected that studets will: Demostrate a uderstadig of preservatio of equality by modellig preservatio of equality, cocretely, pictorially, ad symbolically applyig preservatio of equality to solve equatios [C, CN, PS, R, V] Explai the differece betwee a expressio ad a equatio. [C, CN] Evaluate a expressio give the value of the variable(s). [CN, R] [C] Commuicatio [PS] Problem Solvig [CN] Coectios [R] Reasoig [ME] Metal Mathematics [T] Techology ad Estimatio [V] Visualizatio Geeral Learig Outcome: Represet algebraic expressios i multiple ways. Achievemet Idicators The followig set of idicators may be used to determie whether studets have met the correspodig specific outcome. Model the preservatio of equality for additio, subtractio, multiplicatio, or divisio usig cocrete materials or usig pictorial represetatios, explai the process orally, ad record it symbolically. Solve a problem by applyig preservatio of equality. Idetify ad provide a example of a costat term, a umerical coefficiet, ad a variable i a expressio ad a equatio. Explai what a variable is ad how it is used i a expressio. Provide a example of a expressio ad a equatio, ad explai how they are similar ad differet. Substitute a value for each ukow i a expressio ad evaluate the expressio. 7.PR.6. Model ad solve problems that ca be represeted by oe-step liear equatios of the form x + a = b, cocretely, pictorially, ad symbolically, where a ad b are itegers. [CN, PS, R, V] Represet a problem with a liear equatio ad solve the equatio usig cocrete models. Draw a visual represetatio of the steps required to solve a liear equatio. Solve a problem usig a liear equatio. Verify the solutio to a liear equatio usig cocrete materials or diagrams. Substitute a possible solutio for the variable i a liear equatio to verify the equality. Geeral ad Specific Learig Outcomes 131

7 7.PR.7. Grade 7 Strad: Patters ad Relatios (Variables ad Equatios) (cotiued) Specific Learig Outcomes It is expected that studets will: Model ad solve problems that ca be represeted by liear equatios of the form: ax + b = c ax = b x a = b, a 0 cocretely, pictorially, ad symbolically, where a, b, ad c, are whole umbers. [CN, PS, R, V] [C] Commuicatio [PS] Problem Solvig [CN] Coectios [R] Reasoig [ME] Metal Mathematics [T] Techology ad Estimatio [V] Visualizatio Geeral Learig Outcome: Represet algebraic expressios i multiple ways. Achievemet Idicators The followig set of idicators may be used to determie whether studets have met the correspodig specific outcome. Model a problem with a liear equatio ad solve the equatio usig cocrete models. Draw a visual represetatio of the steps used to solve a liear equatio. Solve a problem usig a liear equatio ad record the process. Verify the solutio to a liear equatio usig cocrete materials or diagrams. Substitute a possible solutio for the variable i a liear equatio to verify the equality. 132 Kidergarte to Grade 8 Mathematics: Maitoba Curriculum Framework of Outcomes (2013)

8 [C] Commuicatio [PS] Problem Solvig [CN] Coectios [R] Reasoig [ME] Metal Mathematics [T] Techology ad Estimatio [V] Visualizatio 7.SS.1. 7.SS.2. Strad: Shape ad Space (Measuremet) Specific Learig Outcomes It is expected that studets will: Demostrate a uderstadig of circles by describig the relatioships amog radius, diameter, ad circumferece of circles relatig circumferece to pi ( ) determiig the sum of the cetral agles costructig circles with a give radius or diameter solvig problems ivolvig the radii, diameters, ad circumfereces of circles [C, CN, R, V] Develop ad apply a formula for determiig the area of triagles parallelograms circles [CN, PS, R, V] Geeral Learig Outcome: Use direct or idirect measuremet to solve problems. Achievemet Idicators The followig set of idicators may be used to determie whether studets have met the correspodig specific outcome. Illustrate ad explai that the diameter is twice the radius i a circle. Illustrate ad explai that the circumferece is approximately three times the diameter i a circle. c Explai that, for all circles, pi ( ) is the ratio of the circumferece to the diameter ( d ), ad its value is approximately Explai, usig a illustratio, that the sum of the cetral agles of a circle is 360. Draw a circle with a give radius or diameter with or without a compass. Solve a cotextual problem ivolvig circles. Illustrate ad explai how the area of a rectagle ca be used to determie the area of a triagle. Geeralize a rule to create a formula for determiig the area of triagles. Illustrate ad explai how the area of a rectagle ca be used to determie the area of a parallelogram. Geeralize a rule to create a formula for determiig the area of parallelograms. Illustrate ad explai how to estimate the area of a circle without the use of a formula. Apply a formula for determiig the area of a circle. Solve a problem ivolvig the area of triagles, parallelograms, or circles. Geeral ad Specific Learig Outcomes 133

9 [C] Commuicatio [PS] Problem Solvig [CN] Coectios [R] Reasoig [ME] Metal Mathematics [T] Techology ad Estimatio [V] Visualizatio 7.SS.3. Strad: Shape ad Space (3-D objects ad 2-D shapes) Specific Learig Outcomes It is expected that studets will: Perform geometric costructios, icludig perpedicular lie segmets parallel lie segmets perpedicular bisectors agle bisectors [CN, R, V] Geeral Learig Outcome: Describe the characteristics of 3-D objects ad 2-D shapes, ad aalyze the relatioships amog them. Achievemet Idicators The followig set of idicators may be used to determie whether studets have met the correspodig specific outcome. Describe examples of parallel lie segmets, perpedicular lie segmets, perpedicular bisectors, ad agle bisectors i the eviromet. Idetify lie segmets o a diagram that are parallel or perpedicular. Draw a lie segmet perpedicular to aother lie segmet, ad explai why they are perpedicular. Draw a lie segmet parallel to aother lie segmet, ad explai why they are parallel. Draw the bisector of a agle usig more tha oe method, ad verify that the resultig agles are equal. Draw the perpedicular bisector of a lie segmet usig more tha oe method, ad verify the costructio. 134 Kidergarte to Grade 8 Mathematics: Maitoba Curriculum Framework of Outcomes (2013)

10 [C] Commuicatio [PS] Problem Solvig [CN] Coectios [R] Reasoig [ME] Metal Mathematics [T] Techology ad Estimatio [V] Visualizatio 7.SS.4. 7.SS.5. Strad: Shape ad Space (Trasformatios) Specific Learig Outcomes It is expected that studets will: Idetify ad plot poits i the four quadrats of a Cartesia plae usig ordered pairs. [C, CN, V] Perform ad describe trasformatios of a 2-D shape i all four quadrats of a Cartesia plae (limited to itegral vertices). [C, CN, PS, T, V] Geeral Learig Outcome: Describe ad aalyze positio ad motio of objects ad shapes. Achievemet Idicators The followig set of idicators may be used to determie whether studets have met the correspodig specific outcome. Label the axes of a Cartesia plae ad idetify the origi. Idetify the locatio of a poit i ay quadrat of a Cartesia plae usig a ordered pair. Plot the poit correspodig to a ordered pair o a Cartesia plae with uits of 1, 2, 5, or 10 o its axes. Draw shapes ad desigs, usig ordered pairs, i a Cartesia plae. Create shapes ad desigs i a Cartesia plae ad idetify the poits used. (It is iteded that the origial shape ad its image have vertices with itegral coordiates.) Idetify the coordiates of the vertices of a 2-D shape o a Cartesia plae. Describe the horizotal ad vertical movemet required to move from a give poit to aother poit o a Cartesia plae. Describe the positioal chage of the vertices of a 2-D shape to the correspodig vertices of its image as a result of a trasformatio or successive trasformatios o a Cartesia plae. Perform a trasformatio or cosecutive trasformatios o a 2-D shape, ad idetify coordiates of the vertices of the image. Describe the image resultig from the trasformatio of a 2-D shape o a Cartesia plae by comparig the coordiates of the vertices of the image. Geeral ad Specific Learig Outcomes 135

11 [C] Commuicatio [PS] Problem Solvig [CN] Coectios [R] Reasoig [ME] Metal Mathematics [T] Techology ad Estimatio [V] Visualizatio 7.SP.1. 7.SP.2. 7.SP.3. Strad: Statistics ad Probability (Data Aalysis) Specific Learig Outcomes It is expected that studets will: Demostrate a uderstadig of cetral tedecy ad rage by determiig the measures of cetral tedecy (mea, media, mode) ad rage determiig the most appropriate measures of cetral tedecy to report fidigs [C, PS, R, T] Determie the effect o the mea, media, ad mode whe a outlier is icluded i a data set. [C, CN, PS, R] Costruct, label, ad iterpret circle graphs to solve problems. [C, CN, PS, R, T, V] Geeral Learig Outcome: Describe ad aalyze positio ad motio of objects ad shapes. Achievemet Idicators The followig set of idicators may be used to determie whether studets have met the correspodig specific outcome. Determie mea, media, ad mode for a set of data, ad explai why these values may be the same or differet. Determie the rage of a set of data. Provide a cotext i which the mea, media, or mode is the most appropriate measure of cetral tedecy to use whe reportig fidigs. Solve a problem ivolvig the measures of cetral tedecy. Aalyze a set of data to idetify ay outliers. Explai the effect of outliers o the measures of cetral tedecy for a data set. Idetify outliers i a set of data ad justify whether or ot they are to be icluded i the reportig of the measures of cetral tedecy. Provide examples of situatios i which outliers would or would ot be used i determiig the measures of cetral tedecy. Idetify commo attributes of circle graphs, such as Q title, label, or leged Q the sum of the cetral agles is 360 Q the data is reported as a percet of the total ad the sum of the percets is equal to 100% Create ad label a circle graph, with or without techology, to display a set of data. Fid ad compare circle graphs i a variety of prit ad electroic media, such as ewspapers, magazies, ad the Iteret. Traslate percetages displayed i a circle graph ito quatities to solve a problem. Iterpret a circle graph to aswer questios. 136 Kidergarte to Grade 8 Mathematics: Maitoba Curriculum Framework of Outcomes (2013)

12 [C] Commuicatio [PS] Problem Solvig [CN] Coectios [R] Reasoig [ME] Metal Mathematics [T] Techology ad Estimatio [V] Visualizatio 7.SP.4. 7.SP.5. 7.SP.6. Strad: Statistics ad Probability (Chace ad Ucertaity) Specific Learig Outcomes It is expected that studets will: Express probabilities as ratios, fractios, ad percets. [C, CN, R, T, V] Idetify the sample space (where the combied sample space has 36 or fewer elemets) for a probability experimet ivolvig two idepedet evets. [C, ME, PS] Coduct a probability experimet to compare the theoretical probability (determied usig a tree diagram, table, or aother graphic orgaizer) ad experimetal probability of two idepedet evets. [C, PS, R, T] Geeral Learig Outcome: Use experimetal or theoretical probabilities to represet ad solve problems ivolvig ucertaity. Achievemet Idicators The followig set of idicators may be used to determie whether studets have met the correspodig specific outcome. Determie the probability of a outcome occurrig for a probability experimet, ad express it as a ratio, fractio, or percet. Provide a example of a evet with a probability of 0 or 0% (impossible) ad a evet with a probability of 1 or 100% (certai). Provide a example of two idepedet evets, such as Q spiig a four-sectio spier ad a eight-sided die Q tossig a coi ad rollig a twelve-sided die Q tossig two cois Q rollig two dice ad explai why they are idepedet. Idetify the sample space (all possible outcomes) for a experimet ivolvig two idepedet evets usig a tree diagram, table, or aother graphic orgaizer. Determie the theoretical probability of a outcome for a experimet ivolvig two idepedet evets. Coduct a probability experimet for a outcome ivolvig two idepedet evets, with or without techology, to compare the experimetal probability to the theoretical probability. Solve a probability problem ivolvig two idepedet evets. Geeral ad Specific Learig Outcomes 137

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