At a Glance...

C3. Coding:

Solve problems and create computational representations of mathematical situations using coding concepts and skills.

Learning Situation: Shoe Sizes

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Total Duration: approximately 180 minutes

Overview 

In this learning situation, the student collects the shoe sizes of the students in their class in order to suggest an inventory of shoes for preteens at the community shoe store. From the data, the student creates code using a block coding program in order to find the mean and the median of the shoe sizes of the students in the class. The student observes that adding or subtracting data can affect measures of central tendency

Achievement Chart Criteria

* Custom Blocks:  This screenshot shows the menu for creating a new block in the Scratch coding program. By creating a new block, one can make the code more efficient by summarizing a sequence of code to be repeated at various places in the code into a single block. Creating blocks in other block coding program might have an interface that differs from this one.

Materials

• block-based program
• paper
• pencil

Note: The examples in this learning situation were created using Scratch.

Active Learning (Exploration)

Duration: approximately 150 minutes

Assessment can be carried out through…

Getting Ready for Coding 

Explain to the students that the data concerning the shoe sizes of the students in the class needs to be collected. Using this data, students are to write code to determine the mean and median of shoe sizes using a block-based program.

Discussion Questions and Sample Responses

• What data about the shoes do we need to collect?
  We need the shoe sizes of the students in the class.
• How can the data collection be automated?
  Using a code (in blocks or in a spreadsheet), visiting a website where you can create surveys, filling out a form, etc.
• Is it possible to write a code for the data collection? What will the code need to do?
  The code should ask for a student's shoe size, store that shoe size in a list, then ask another student until all the data is 
  collected (a pseudocode could help with this step).
• Is it easier to write code to determine the mean, median or mode?
• Some student may say that the median or the mode are easier to code because it is simply a matter of finding a number in a list, while the mean requires a mathematical operation. In reality, the code to sort the list of data in ascending order is much more demanding than the code to do mathematical operations. It would be interesting and relevant to ask this question again at the time of consolidation.
• What does the code need to do to calculate or recognize each of the measures of central tendency?
  
  • For the mean, the code has to calculate the sum of all the data, then divide this sum by the number of data values in the 
    list.
  • For the median, the code has to sort the data in ascending order and recognize the central value, either by finding 
    the value in the center of the list (odd number of data) or by calculating the mean of the two values in the center of 
    the list (even number of data).
  • For the mode, the code needs to total the number of shoes sizes and determine which has the greatest total.

As a class, present the pseudocode below to help students understand what a pseudocode is.

• What are the variables? What do they represent?
  The variables are:
  • nb1: the value of the first datum collected;
  • nb2: the value of the second datum collected;
  • sum: the sum of all data.
• What is the purpose of the three "set to 0" blocks at the beginning of the code?
  Without the "set to 0" blocks, all the variables that were set during the last execution of the code will remain active. This could have undesirable outcomes from the code. It is like pressing the "CE" key on a calculator.
• What would be the code, in a block-based program, for this pseudocode? 
  Invite students to transfer the pseudocode into code for a block-based program.

Sample code

Note: In this part of the learning situation, the students individualize their blocks of code by the questions they ask and the variables they use. If the students have prior experience in using the coding program, it is possible for them to go directly to the next part o fthe activity, which is data collection. This activity can also be used as a diagnostic assessment to determine if students have everything they need to move on to data collection.

Take the time to circulate among the students and listen to their conversations. Based on their observations and your active listening, question them, if necessary, to guide them or better understand their reasoning.

Coding to collect data

Ask the students to create a pseudocode to collect data from all the students in the class. Students can start from the code prepared in the previous step or start a new code.

Example of pseudocode:

Variables:

_ number of data to enter

_ shoe size

_ shoe size data list

Once the pseudocode is complete, invite students to create their code to collect data related to the size of students' shoes and then compile it into a list.

Sample code

Note: Several block-based coding programs make block customization options. If so, students can create a block (custom block) and define it with their code. This way, the main code becomes less cluttered.

Example of a custom block

Once this block is created, the main code would look like this:

Coding to Analyze Data 

Ask students what the computer will need to do to find the average shoe size from the data collected. If necessary, the starting image with the formula for the mean could be redisplayed to activate students' prior knowledge. The mean formula can also be transformed into pseudocode. Invite them to write the instructions for the computer to calculate the mean of the data collected.

Here is an example of pseudocode:

Variables:

_ list number (or list element)

_ sum

_ list of shoe sizes

Sample code

Ask students the following questions:

• What happens if I add more shoe sizes to my list?
• Will the mean stay the same? Why?
• Can this code be made more efficient?

This code is structured in this way in order to separate the steps and to encourage student questioning and exploration. A simpler version of this code would see the list items appended to the value of the "sum" variable at data collection time, eliminating that whole step. This code would look like this:

Invite students to write pseudocode and code to find the median shoe size of the students in the class.

Possible questions

• What steps are needed to determine the median?
• Is there a block that can cause the data to be ordered in ascending order? Can we create one? (Students may mention that the elements of the list of shoe sizes must be sorted in ascending order in order to find the median.)

Example of pseudocode:

Variables:

_ central value 1

_ central value 2

\* list of shoe sizes

Note: If the list contains an even number of data values, highlight to students that the median is the average of the two middle numbers.

Here is a sample of code that places the list of data into an ascending order. Again, the code has been turned into a custom block. This step is helpful, but not necessary.

Short explanation of the logic of the code

This code works by comparing a value in the list with the surrounding value. If the value is smaller, the positions of the elements in the list are reversed. The code is repeated the same number of times as there are elements in the list to ensure that each value is smaller than the next.

Ordering numbers in ascending order is a complex problem for the computer, which must compare the data values and then order them. This kind of problem lends itself very well to an Internet search. There are several communities and a range of existing projects that can answer questions from students and staff. By modelling this kind of resourcefulness, students become more comfortable doing the same, and learn more about what is possible with block-based coding programs.

Sample code to find the median

Ask students the following questions: What happens if I add shoe sizes to my list? Will the median stay the same? Why?

Links to Other Curriculum Expectations

Number

B2.1  Use the properties and order of operations, and the relationships between operations, to solve problems involving whole numbers, decimal numbers, fractions, ratios, rates, and percents, including those requiring multiple steps or multiple operations.

By using conditional statements (if, then, else), it would be possible to write code that can analyze a mathematical problem and determine the processes to be followed to solve it by using subprograms (for example, subprograms for the priorities of operations, for the addition of fractions).

Algebra

C4. Apply the process of mathematical modelling to represent, analyse, make predictions, and provide insight into real-life situations.

Using subprograms and custom blocks allows you to generalize a situation by creating models and calling on those models at various points in the code.

Data

D1.5 Determine the impact of adding or removing data from a data set on a measure of central tendency, and describe how these changes alter the shape and distribution of the data.

By creating a subprogram for each measure of central tendency, it would be possible to write code that calls each subprogram at different times, creating more efficient and easy to read/alter code.

Instructional Differentiation and Universal Design for Learning

• Suggest to the student who is looking to take up a challenge that they write a code to find the mode of the students' shoe 
  sizes. This code will use the list of data sorted in ascending order, but the conditions to be determined will be very different.
• By using a coding program where project sharing is possible, some of the code could already be in place so that students do 
  not always start from a blank canvas.
• Work at the pace of the students. Transferring mathematical knowledge and concepts to coding can take time. Allocate the 
  necessary time to each part of the learning situation.
• Provide students with pseudocodes so they can turn them into codes. The pseudocode can also have a color code that 
  guides the student to the correct category of blocks in the chosen coding program.
• Provide a cheat sheet on the function of some more complex blocks, such as operators and conditions.