# Math

Math

|Unit 2: Day 1: Linear and Quadratic Functions |MCT 4C | | |Learning Goals |Materials | |Minds On: 15 |Activate prior knowledge by reviewing features of linear and quadratic functions such as what the |PPT 2. 1. 1 | | |graphs look like, how could the graphs be described, and whether or not the graphs represent |BLM 2. . 1 | | |functions. |BLM 2. 1. 2 | | |Consolidate understanding of domain and range |BLM 2. 1. 3 | | |Learn end behaviour terminology and the definition of the leading coefficient |LCD projector | |Action: 20 | | | Consolidate:40 | | | |Total =75 min | | | | Assessment | |Opportunities | |Minds On… |Individuals or Pairs ( Activity | | | | | |Students complete BLM 2. 1. 1 using prior knowledge of linear and quadratic functions | | | | | | | | | | | |Curriculum Expectations/Observations/Checklist | | | | |Observe students as they complete BLM 2. 1. 1 and assess their prior knowledge, in particular what | | | | | |they recall about linear and quadratic functions. Use this information to determine the depth in

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| | | | | |which these functions need to be reviewed as a class. | | | | | | | | | |Action! |Whole Class( Discussion | | | | | |Students share the results of the activity with the class to verify the correct answers. | | | | | |Students will discuss any concerns that arise when the answers are presented. | | | | | | | | | | |Review necessary terminology and introduce the new terminology (end behaviour and leading | | | | | |coefficient) using the PowerPoint presentation PPT 2. 1. 1 | | | | | | | | | | | |Mathematical Process Focus: | | | | |Reflecting – Reflect on prior knowledge of linear and quadratic functions; Connecting † Students | | | | | |connect prior content to new terminology introduced | | | | | | | | | | |Consolidate |Small Group( Activity | | | |Debrief |Students will work in small groups (2 to 4) on the assigned function. | | | | | |Students fill in their information on the BLM 2. 1. 2 worksheet for the function that they are | | | | | |assigned by the teacher. Students may have to approximate the y-values for the range. | | | | | | | | | | |Whole Class ( Presentation | | | | | |Students present their results to the class, allowing all groups to fill in BLM 2. 1. 2 for all of | | | | | |the functions. | | | | | | | | | Concept Practice |Home Activity or Further Classroom Consolidation | | | | |Complete BLM 2. 1. 3. | |If necessary, review how| | | | |to graph a function | | | | |using a table of values. | | | | | 2. 1. 1: Match It! Match each given function with the graph on the right-hand side. 1. ______ [pic] 2. ______ [pic] 3. ______ [pic] 4. ______ [pic] 5. ______ [pic] 6. ______ [pic] 7. ______ [pic] 8. ______ [pic] 2. 1. 2: Linear and Quadratic Functions |Function |Domain and Range |Degree |Leading Coefficient |End Behaviour | | | | | | |1. [pic] | | | | | | | | | | | | | | | | | | | | | | |2. [pic] | | | | | | | | | | | | | | | | | | | | | | | 3. [pic] | | | | | | | | | | | | | | | | | | | | | | | |4. pic] | | | | | | | | | | | | | | | | | | | | | | | |5. pic] | | | | | | | | | | | | | | | | | | | | | | | |6. pic] | | | | | | | | | | | | | | | | | | | | | | | |7. pic] | | | | | | | | | | | | | | | | | | | | | | | |8. pic] | | | | | | | | | | | | | | | | | 2. 1. 3: Linear and Quadratic Functions † Practice For each of the given functions, sketch the graph of the relation, creating a table of values if necessary.

Use the graph and the equation to fill in the table relating to each graph. 1. [pic] |Domain | | |Range | | |Degree | | |Sign of Leading Coefficient | | |End Behaviour | | |Is the relation a function? | | . [pic] |Domain | | |Range | | |Degree | | |Sign of Leading Coefficient | | |End Behaviour | | |Is the relation a function? | | 2. 1. 3: Linear and Quadratic Functions † Practice (continued) 3. [pic] Domain | | |Range | | |Degree | | |Sign of Leading Coefficient | | |End Behaviour | | |Is the relation a function? | | 4. [pic] |Domain | | Range | | |Degree | | |Sign of Leading Coefficient | | |End Behaviour | | |Is the relation a function? | | 5. Is it possible to graph a line of the form [pic] that will not result in a function? Explain your reasoning. 6. Is it possible to graph a quadratic relation of the form [pic] that will not result in a function?

Explain your reasoning. |Unit 2: Day 2: A Higher Degree |MCT 4C | | |Learning Goals: |Materials | |Minds On: 10 |Investigate cubic and quartic functions and explain why they are functions. |BLM 2. 2. 1 | | |Graph the equations of cubic and quartic functions and investigate end behaviours, domain and range. |BLM 2. 2. 2 | |Describe end behaviours and the impact of the leading coefficient (positive and negative values). |BLM 2. 2. 3 | | | |Graphing calculators | |Action: 60 | | | |Consolidate: 5 | | | Total =75 min | | | | Assessment | |Opportunities | | |Minds On… |Pairs ( Activity | |Teacher should copy BLM | | | |Pairs are given a section of BLM 2. 2. 1 and take a few minutes to consider the relations. Each | |2. 2. and cut the page | | | |pair will have two functions from y = x, y = x2, y = x3, and y = x4 and must hypothesize about | |in half. There should | | | |how the relations will be the same and how they will be different, with reference to the following| |be one Venn diagram for | | | |items: | |each pair of students in| | | |effect of leading coefficient, end behaviour, degree, maximum number of x-intercepts, domain, | |the class. | | |range, whether or not the relations are functions | | | | | |Students will fill in the Venn Diagram in BLM 2. 2. 1 with their results. | | | | | | | | | | |Action! |Small Groups ( Jigsaw (Home Groups) | | | | |In groups of 4 , students should each select a different chart to complete on BLM 2. 2. 2. | | | | | | | | | | | |Small Groups ( Jigsaw (Expert Groups) | | | | | |Students form expert groups according to the chart that selected. Each group creates graphs for | | | | |each function in BLM 2. 2. 1 using a graphing calculator. Students make conclusions about the | | | | | |behaviour of cubic and quartic functions based on the investigations. | | | | | | | | | | | |Curriculum Expectations/Oral Questions/Rubric | | | | |Assess students as they complete BLM 2. 2. 1 in their expert groups on their understanding of the | | | | | |key components of functions. | | | | | | | | | | | |Small Groups ( Jigsaw (Home Groups) | | | | | |Students regroup too share their results.

Students use the information shared to complete all | | | | | |charts and questions. | | | | | | | | | | | |Mathematical Process Focus: | | | | | |Reasoning and Proving † Students use their reasoning skills to determine patterns related to | | | | | |properties of polynomials. | | | | | | | | | |Consolidate |Pairs( Activity | | | | |Debrief |Students work in the same pairs from the Minds On activity and compare their hypotheses with the | | | | | |actual results. They should make any necessary changes to their Venn Diagram. | | | | | | | | |Reflection |Home Activity | | | | |Complete a Frayer Model (BLM 2. 2. 3) for cubic and quartic functions. | | | 2. 2. 1: Comparing Functions by Degree ( 2. 2. 1: Comparing Functions by Degree 2. 2. 1: Comparing Functions by Degree 2. 2. 1: Comparing Functions by Degree 2. 2. 1: Comparing Functions by Degree ( 2. 2. 1: Comparing Functions by Degree 2. 2. 2: Investigation – Cubic and Quartic Functions Part 1 1. Look at each equation and state the value of the leading coefficient. Fill in the information in the column specified below. The first one is done for you. 2. Graph each of the following functions on a graphing calculator and sketch a copy of what you see on the given grids. Use the sketch to fill in the other columns in the table. Again, the first one is done for you. Equation |Leading coefficient |Graph |Number of |End behaviour | | | | |x-intercepts | | | | | | | | |y = x3 |1 | |1 |As x((, y(( and as | | | | |x(-(, y(-( | | | | | | | | | | | | | | | | | | | | | | | | |y = x3 † 2×2 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |y = 2×3 † 3 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |y = x3 + 3×2 † x † 3 | | | | | | | | | | |y = 3×3 † 9x | | | | | | | | | | | |y = 3×3 + x | | | | | | | | | | 2. 2. 2: Investigation – Cubic and Quartic Functions Part 1 (continued) Refer to the chart that you just completed on the previous page to answer questions 3 † 7. 3. What is true about the leading coefficient of all of the polynomials? 4. What is true about the degree of all of the polynomials? 5. What is true about the end behaviour of all of the polynomials? 6. What is the maximum number of x-intercepts for all of the polynomials? 7. Do the graphs of the relations represent functions?