Summative Criterion B and D

Last updated over 2 years ago

8 questions

Criterion B Rubrics

Achievement level
Level descriptor
0
The student does not reach a standard described by any of the descriptors below.
1-2
The student is able to:
[   ] apply, with teacher support, mathematical problem-solving techniques  to discover simple patterns
[   ] state predictions consistent with patterns.
3-4
The student is able to:
[   ] apply mathematical problem-solving techniques to discover simple  patterns
[   ] suggest general rules consistent with findings.
5-6
The student is able to:
[   ] select and apply mathematical problem-solving techniques to discover  complex patterns
[   ] describe patterns as general rules consistent with findings
[   ] verify the validity of these general rules.
7-8
The student is able to:
[   ] select and apply mathematical problem-solving techniques to discover  complex patterns
[   ] describe patterns as general rules consistent with correct findings
[   ] prove, or verify and justify, these general rules.

Consider the following Sequence,
-6, -2, 2, 6, 10...
1. What would the next two terms of the sequence be?
2. What is the general rule of the sequence?

Consider the sequence 1(8-7), 2(10-8), 3(12-9), 4(14-10), …
1. What are the next 2 terms of the sequence?
2. What would the general rule of this sequence be? Write it in the form a(b-c).
3. What would the 10th term of the sequence be?

During the group stages of a football tournament, teams play each other without getting knocked out.

Depending on the number of teams in the group stages, the number of matches required so that every team can play against each other will change, as shown in the table below.

Here is a diagram showing the combinations the players will take.

1. Fill in the rest of the table and use diagrams to find the pattern and support your answer.

2. Find a general rule for the pattern given above.

3. Verify your general rule is valid by applying it to the 4th pattern.

4. At what point do you think you have too many teams in a group for it to be practical?

5. Justify why your rule works. Support your answer with mathematical reasoning.

Criterion D Rubrics

Achievement level
Level descriptor
0
The student does not reach a standard described by any of the descriptors below.
1-2
The student is able to:
[   ] identify some of the elements of the authentic real-life situation
[   ] apply mathematical strategies to find a solution to the authentic real-life situation, with limited success.
3-4
The student is able to:
[   ] identify the relevant elements of the authentic real-life situation
[   ] select, with some success, adequate mathematical strategies to model the authentic real-life situation
[   ] apply mathematical strategies to reach a solution to the authentic real-life situation
[   ] discuss whether the solution makes sense in the context of the authentic real-life situation.
5-6
The student is able to:
[   ] identify the relevant elements of the authentic real-life situation
[   ] select adequate mathematical strategies to model the authentic real- life situation
[   ] apply the selected mathematical strategies to reach a valid solution to the authentic real-life situation
[   ] explain the degree of accuracy of the solution
[   ] explain whether the solution makes sense in the context of the authentic real-life situation.
7-8
The student is able to:
[   ] identify the relevant elements of the authentic real-life situation
[   ] select appropriate mathematical strategies to model the authentic real-life situation
[   ] apply the selected mathematical strategies to reach a correct solution to the authentic real-life situation
[   ] justify the degree of accuracy of the solution
[   ] justify whether the solution makes sense in the context of the authentic real-life situation.

An overhead tank is in urgent need of cleaning.

The tank holds 150 gallons of water. 

A contractor is asked to first empty the tank and then clean it. The contractor uses a suction pump to empty the tank as shown in the table below. 

In the table below, T is the time in hours after the pump begins removing the water.

Complete the table below:

You need to make a math model (equation) for the flow of water from the table given above. What are some factors that affect the time taken, T, and the amount of water that remains in the tank, W?

Since the relationship between t and W is linear, the model could be represented as:
W = a + bT
What quantities do you think a and b represent in this equation? As in, W represents the water that remains and T the time taken. So what could a and b be? What units will you use to measure a and b?

Summative Criterion B and D

Consider the following Sequence,
-6, -2, 2, 6, 10...
1. What would the next two terms of the sequence be?
2. What is the general rule of the sequence?

Consider the sequence 1(8-7), 2(10-8), 3(12-9), 4(14-10), …
1. What are the next 2 terms of the sequence?
2. What would the general rule of this sequence be? Write it in the form a(b-c).
3. What would the 10th term of the sequence be?

You need to make a math model (equation) for the flow of water from the table given above. What are some factors that affect the time taken, T, and the amount of water that remains in the tank, W?

Since the relationship between t and W is linear, the model could be represented as:
W = a + bT
What quantities do you think a and b represent in this equation? As in, W represents the water that remains and T the time taken. So what could a and b be? What units will you use to measure a and b?

Calculate the average values of time taken,T and Water level,W. Using this, find the values of a and b.

Rewrite the model from earlier for the flow of water using the values of a and b that you had calculated.

Justify whether your solution (the model) makes sense in the given context of pumping water out. What other problems could you apply this model to?

Summative Criterion B and D

Consider the following Sequence,-6, -2, 2, 6, 10...1. What would the next two terms of the sequence be?2. What is the general rule of the sequence?

Consider the sequence 1(8-7), 2(10-8), 3(12-9), 4(14-10), …1. What are the next 2 terms of the sequence?2. What would the general rule of this sequence be? Write it in the form a(b-c). 3. What would the 10th term of the sequence be?

You need to make a math model (equation) for the flow of water from the table given above. What are some factors that affect the time taken, T, and the amount of water that remains in the tank, W?

Since the relationship between t and W is linear, the model could be represented as:W = a + bTWhat quantities do you think a and b represent in this equation? As in, W represents the water that remains and T the time taken. So what could a and b be? What units will you use to measure a and b?

Calculate the average values of time taken,T and Water level,W. Using this, find the values of a and b.

Rewrite the model from earlier for the flow of water using the values of a and b that you had calculated.

Justify whether your solution (the model) makes sense in the given context of pumping water out. What other problems could you apply this model to?

Consider the following Sequence,
-6, -2, 2, 6, 10...
1. What would the next two terms of the sequence be?
2. What is the general rule of the sequence?

Consider the sequence 1(8-7), 2(10-8), 3(12-9), 4(14-10), …
1. What are the next 2 terms of the sequence?
2. What would the general rule of this sequence be? Write it in the form a(b-c).
3. What would the 10th term of the sequence be?

Since the relationship between t and W is linear, the model could be represented as:
W = a + bT
What quantities do you think a and b represent in this equation? As in, W represents the water that remains and T the time taken. So what could a and b be? What units will you use to measure a and b?