for students who have just explored exponential function. This is a practice without graphing calculator. Correction: the 2nd x input is -1, not 1 sorry for typo
This activity is mainly an introduction of Constant Rate of Change with y intercept in y = mx + b form. Students observe two different equations of two lines to learn the concept of slope. The second activity (revised from my previous Two-Robot cases) concentrate on concept of y intercept - Align on CCSS 8.EE.5 and 8.F.5 but can be used on higher grade levels. The first page of plotting points and questions can serve as informal assessment in order to know your entire students the first day to make adjustment on teaching. On mini quiz of "Real Life..." file covers (f+g)(x) in #4 & 5
Many of my students are in trouble understanding what and why using right Triangle ratio.... The traditional word problems seem to be abstract with light house, boat, or cliff. I therefore made the simple index card and "post it note" project with ruler and ask them to measure and calculate the missing length or missing angle with graphical calculator. On the back of this activity, teacher may change assessment into continuous activity and distribute "Post It Note". The picture on the back of the sheet is actually depicted from actual 3 x 3 (7.6 x 7.6) post it note.
This activity serves the beginning of Congruence Shortcut of Triangles with the touch of Transformation (for reviewing and connecting purpose). The students should have to get used to write three-line statement with a conclusion after investigation and observation.
I googled the image for testing my students knowledge understanding the concept of vertex point, zeros, y intercept, quadratic equation in vertex form, in standard form and in factored form. However, I am afraid that the straightforward questions might not be a challenges for them. To improve them analyzing and reasoning skills, I have decided to write the case for the image I found from the google site. I hope this written case with image and questions can improve students analytical ability. Correction and comment are greatly appreciated
This is stpe by step guided quiz for students. On the front side, studnet use SohCahToa to develop the trig ratios of Sine, Cosine and Tangent with specific angle (angle of interest) teacher assign then identify (label) Opposite, Adjacent and Hypotenuse on the picture. Work trig ratio with formula SohCahToa. On the back, it is the application of trig ratios for making equation to solve missing leg of Triangle
Students are introduced the scenario with two robots then we can start from there. This can be done and extnded to more specific linear modeling or to serve a preview of system of equation. This also can be a guided assessment if you have taught and delivered your students Linear equation concept. If students are patience enough, you may add questions by asking them to organize the data set with table and creating equations during the same class period.
Use the graph to make equation in following: 1. Factored Form 2. Standard Form 3. Vertex Form Also embedded assessment /practice can be given for reviewing: zeros, y intercept, axis of symmetry, corresponding point. The second file is analyzed case with some application scenario. The whole scenario is made up. The pictures source are found with Google. I believe the key is to learn to analyze and to make inference with graph and equations.
The traditonal textbook generally presents the quadratic model in standard form for students to work on. Students only need to be familar with certain formulas for answers. However, students may not have ideas where the model come from and how the real life scenarios can contribute to quadratic model. Therefore, I google out the example on the web* and rewrote this example for my students. They are expected to build up knowledge about how quadratic model is created through this activity. *Source: http://www.purplemath.com/modules/quadprob3.htm
into (yx-y1) over (x2-x1)
Composition of Transformation to Congruent triangle images
Exploring parabolas through input table value, graphing axis of symmetry, y intercept, x intercept(s), corresponding point and vertex point
Beginning on Dilation
This servers the introduction of Reflection in Geometry. Patty paper is used here in this activity
This investigation is used for Geometry class to teach slope. First, students investigate definition of Parallelogram with two pairs of parallel lines in Quadrilateral. Teacher can link Rise over Run concept to Slope formula. Second, students define perpendicular with two diagonal lines inside the Kite. Students have to plot points and draw their own diagram on coordinate plane with practicing of Coordinate Geometry. In my class, they have to use (y2-y1)/ (x2-x1) for this activity with linking knowledge of Rise over Run
Students learning the above topics through investigation through their own investigation. They could also have preview (or review) or ideas of polygons. It is the first start up for Algebra students walking into the Geometry Class. They should eventually find out those definition on their own with teacher's facilitating... The PDF document is download from math-aids.com
I read CCSS 6.R.1 example wings to beak as 2:1 extend to arms to body\ies of the whole class. With more time, teacher also can ask fingers to arms (5:1) or fingers to bodies (10:1) If taught at elem level, remind them to find out fast way to sum the total. If there are four 4-people groups and two 6-people groups, how they sum the number of total arms or total bodies? Remind students they do not need to always add for total number. They can also use multiplication for the total
Warm up practice for Geometry students after winter break. Can be assessment too. The figures of images are googled from the web sites
model both linear and quadratic functions then evaluate with the specific value of x. Students connect (review) Geometry concept along with learning modeling function. Throughout those questions, the have better idea on P(10) is not just plugging 10 into x. They actually use the function they just created to evaluate the object - Perimeter (or area) of rectangel in this case. Page 1 can be guided assessment and the page 2 can be individual quiz
Here is the opening activity I made for opening activity in teacing slope at my Geometry classes. #9, #10 is rivised and edited. Rather than Constant Rate of Change in Algebra class, I use Rise over Run in similar or non-similar trialges to open up sloope topic. This lesson is made with ideas of CCSS 8.EE.6 - There could be same slope in several Similalr Triangles. Students should be familar with the concept of Rise over Run then can be brought to Slope Formula (y2-y1) as Rise and (x2-x1) as Run... Comment and Suggestion is appreciagted
Use patty paper for this activity. It is better to trace everything then ask student to place x+, y+ and x-, y- next to x-axis and y- axis on patty paper. This is an alternative way to ask students to make rule. For example, when they rotate over origin on patty paper ccw 90 degree, they can see +x axis rotate to y+ axis and y+ axis rotate to x- axis. The rule is made (x, y) -> (y, -x)