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US$300

for 20 classes
班級

快速學習者代數 1:二次函數簡介

由 6 位學習者完成
年齡 11-14
現場團體小班課程
在這門嚴格的數學課程中,學習者將透過觀察模式、將二次函數與線性函數和指數函數進行對比、識別不同形式的二次函數並使用它們來解決問題來系統地學習二次函數。
平均評分:
5.0
評論數量:
(346 評論)
熱門課程

即時視訊會議
每週5次,共 4 週
3-6 名學習者(每班)
50 分鐘

包含什麼

20 現場會議
16 小時 40 分鐘 上課時間
作業
Students will complete one mathematical modeling projects.
評估
Students will receive regular written feedback.
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課堂經歷

英語程度 - 未知
美國 7 - 9 年級
This is the sixth course in a year-long sequence which covers standards and ideas in Algebra 1 intended for learners in middle school ready to begin Algebra 1 or high school learners who need additional support. These courses are taught in small-groups to provide individual instruction and social-learning opportunities aligned with a social constructionist or situated cognition view of learning. The curriculum is problem-based this means instead of lectures or videos students work together as a small group to solve problems to discover principles and strategies with teacher guidance, as necessary. Therefore, we will spend approximately 90% of each class period working on problems and discussing them as a group. The use of discussion and problem-solving leads to generalized mathematics or proofs and students will construct their own models or proofs of real-world scenarios in project based assignments. This process prepares students well who may seek advanced mathematics in high-school or beyond. 
In this unit, students build on their prior knowledge of functions, function notation, linear, and exponential functions. They explore quadratic patterns, contrasting them with linear and exponential growth, and recognize the impact of quadratic functions in modeling free-falling objects' height over time. They delve into the interpretation of the coefficients in quadratic functions, specifically addressing the initial height, upward path, and the effect of gravity. Additionally, students examine various scenarios represented by quadratic functions, including projectile motion, area, and revenue. They then explore standard and factored forms of quadratic expressions, discussing their usefulness in understanding graphs, intercepts, and the impact of coefficients. Finally, students investigate the vertex form of quadratic functions, gaining insights into how its parameters influence the graph and preparing them for future exploration of translation and stretch concepts in later courses.
Week 1: 
- Readiness Check which allows instructor to identify areas of potential acceleration or needs for extra support for individual learners and the whole group. 
- Encountering Quadratic Change in Geometric Contexts
- Quadratic Expressions
-Contrasting Quadratic, Linear, and Exponential Change
- Building Quadratic Functions from Geometric Patterns
- Comparing Quadratic and Exponential Growth over Time

Week 2:
- Using Quadratic Functions to Represent and Describe Situations
- Graphing Quadratic Functions
- Using Table to Represent Quadratic Functions
-Using Area Models to generate equivalent quadratic functions
-standard form and factored from

Week 3: 
- Graphing Functions in Standard and Factored Forms
-X Intercepts in Quadratic Equations
- Vertex and Y-Intercept
- Zero's and Domains
-Parameters of Standard Forma nd Facotred Form
- Contextualized Quadraitc Equations

Week 4:
- Vertex Form
-Graphing the Vertex Form
-Translating Quadratic Functions
-Real World Modeling Project
-End of Unit Assessment

學習目標

HSF-BF.A.1.a
Determine an explicit expression, a recursive process, or steps for calculation from a context.

HSF-BF.A.1.b
Combine standard function types using arithmetic operations. For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model.

HSF-BF.A.1.c
Compose functions. For example, if is the temperature in the atmosphere as a function of height, and is the height of a weather balloon as a function of time, then is the temperature at the location of the weather balloon as a function of time.

HSF-BF.A.2
Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.

HSF-BF.B
Build new functions from existing functions.

HSF-LE.A
Construct and compare linear, quadratic, and exponential models and solve problems.

HSF-LE.A.1
Distinguish between situations that can be modeled with linear functions and with exponential functions.

HSF-LE.A.1.a
Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals.

HSF-LE.A.1.b
Recognize situations in which one quantity changes at a constant rate per unit interval relative to another.

HSF-LE.A.1.c
Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another.

HSF-LE.A.2
Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).

HSF-LE.A.3
Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function.

HSF-LE.A.4
For exponential models, express as a logarithm the solution and  evaluate the logarithm using technology.

HSF-LE.B
Interpret expressions for functions in terms of the situation they model.


HSF-LE.B.5
Interpret the parameters in a linear or exponential function in terms of a context.
HSA-SSE.A.1
Interpret expressions that represent a quantity in terms of its context.

HSA-SSE.A.1.a
Interpret parts of an expression, such as terms, factors, and coefficients.

HSA-SSE.A.1.b
Interpret complicated expressions by viewing one or more of their parts as a single entity.
HSA-SSE.B
Write expressions in equivalent forms to solve problems.

HSA-SSE.B.3
Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.
HSA-SSE.B.3.c
Use the properties of exponents to transform expressions for exponential functions.

HSA-SSE.B.3.a
Factor a quadratic expression to reveal the zeros of the function it defines.

HSA-SSE.B.3.b
Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines. 


HSA-SSE.A.2
Use the structure of an expression to identify ways to rewrite it.

其他詳情

父母的引導和規範
Students will need to use Nearpod. They will need to click a link and enter their first name or initial. No other identifying information will be collected.
供應清單
Learners will need standard notetaking supplies. A teacher provided printable guided note-taking workbook will be provided.
外部資源
除了 Outschool 教室外,本課程也使用:
來源
The scope and sequence of this course is based on the open source Illustrative Mathematics curriculum and has been adapted for 2e, neurodiverse, and home-based learners. Illustrated Mathematics is licensed under a creative commons attribution license: https://creativecommons.org/licenses/by/4.0/ Pedagological Resources: Gravemeijer, K. (2020). A socio-constructivist elaboration of realistic mathematics education. In National reflections on the Netherlands didactics of mathematics (pp. 217-233). Springer, Cham. Vintere, A. (2018). A constructivist approach to the teaching of mathematics to boost competences needed for sustainable development. Rural Sustainability Research, 39(334), 1-7. Briscoe, L., & Van Kesteren, J. (2018). THE ART OF MATH. Gazette-Ontario Association for Mathematics, 57(2), 21-24.

認識老師

已加入 April, 2021
5.0
346評論
熱門課程
教師檔案
教師專業知識和證書
Professional Experience:
I have been a math tutor for over 12 years and have worked with students from ages 5-25 in small group and academic settings including serving as a primary teacher for home educated learners. I have received training and tutoring certification/awards from nationally recognized organizations. I was a group supplemental instruction leader for math at the collegiate level for four years at ETSU including working with dual enrolled and accelerated learners. I have taught and tutored math up to a graduate level in algebra, geometry, probability, and quantitative reasoning. 
Academic Experience: 
Constructivism and Mathematics, Science, and Technology Education
	This graduate level online course for educators used practical examples and empirical research to connect the educational philosophy of constructivism to best practices in STEM education and demonstrated online teaching strategies for this endeavor. It highlighted the power of solving problems through building and applying understandings rather than rote processes which influences the problem-centered curriculum This class also addressed common misconceptions or alternative schemas students develop for math and science prior to instruction and provided ideas for experiments and explorations to adjust these conceptions. 
Math 1410 Numbers, Concepts, and Algebra for Math Teachers
      This in-person semester long coursed prepared students to teach common core mathematics to students in grades kindergarten through eight including early access to algebra. It included practical teaching experience, ensuring the personal math conceptual fluency of each educator, and demonstrating expertise on the Praxis math exam for educators. 
Math 1420: Logic, Problems, and Geometry for Math Teachers
      This in-person semester long course prepared teacher candidates to teach common core mathematics to students in grades kindergarten through eighth including advanced ideas of logic, problem solving, and geometry using a constructivist lens. 


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