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Example:Grade 4 patterns, functions and algebra. Conceptual understanding, procedural fluency, strategic competence, adaptive reasoning and productive disposition
The split the money in ratio. 5:9.10
1. How much less did Bobo make than Thabo?
2. Bobo complains about making so much less. The boys decides to divide their pay in a ratio of 3:4:5. Howuch more does Bobo make than (1)?
1. Explain how part to part ratio occur in:
i. Geometry
ii. Algebra
iii. Probability
2. The ratio of the sides of a pentagon is 5:3:2:4:1 . The perimeter of the pentagon is 75cm. How long is the shortest side?
5+3+2+4+1, so x is?
a. 5/15 × 75/1 = 25cm
b. 2/15 × 75/1 = 10cm
c. 3/10 × 75/1 = 5cm
d. 1/5 × 75/1 = 5cm
The population of a culture of bacteria is modeled by the logistic equation
P(t) = 14/1 +29e - 0.62tTo the nearest tenth, how many days will it take the culture to reach 75% of its carrying capacity? What is the carrying capacity? What is the initial population for the model? Why a model like P(t) = P0 ekt , where P0 is the initial population, would not be plausible?
Go to www.desmos.com/calculator and type
y = 14250 / (1 + 29 . e-0.62 x). {0 < x < 15} {0 < y < 15000}
y = 14300 {0 < x < 15}
(you will find the command “÷” in the desmos calculator after selecting “14250”, or you type “/” after selecting “14250”, and you will also find the function “exp” ). Adjust the x and y axes settings to 0 < x < 15 and 0 < y < 15000. Plot the graph you have obtained (you can use a screenshot, save as image, and copy it into word)
1. A retirement account is opened with an initial deposit of $8,500 and earns 8.12% interest compounded monthly. What will the account be worth in 20 years? What if the deposit was calculated using simple interest? Could you see the situation in a graph?
2. Graph the function and its reflection about the line y=x on the same axis, and give the x-intercept of the reflection. Prove that . [Suggestion: type {- 7 < x < 2} {0 < y < 7} in desmos, and then type its inverse function.]
3. How long will it take before twenty percent of our 1,000-gram sample of uranium-235 has decayed? [See Section 6.6 Example 13]
The decay equation is , where t is the time for the decay, and K is the characteristic of the material. Suppose T is the time it takes for half of the unstable material in a sample of a radioactive substance to decay, called its half-life. Prove that . What is K for the uranium-235?
Reflect on the concept of exponential and logarithm function. What concept (only the names) did you need to accommodate these new concept in your mind? What is the simplest exponential and logarithm function with base b ≠ 1 you can imagine? In your day to day, is there any occuring facts that can be interpreted as exponential or logarithmic function? What strategy are you using to get the graph of exponential and logarithmic function?
how many different computer passwords are possible if
(a) digits and letters can be repeated
(b) digits and letters cannot be repeated
Question: 3 digits followed by 2 letters
Find one-half of these fractions.
1. 1/4
2. 2/3
3. 3/4
2x^2
