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 block-based programming software 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.

Criteria According to the Achievement Chart

Materials

• block-based programming software
• paper
• pencil
• appendix 1 (Warm-Up)
• appendix 2 (Pseudocode)

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 data concerning the shoe sizes of the students in the class are to be collected. Using this data, students will create codes to help find the mean and median of shoe sizes in block-based programming software.

For Thought 

• What data are we looking for?
  We are looking for the shoe sizes of the students in the class.
• How can 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.
• Would it be possible to create a code for data collection? What will the code need to do?
  The code should ask for a person's shoe size, add that shoe size to a list, then ask someone else until all the data is 
  collected (a pseudocode could help with this step).
• Is it easier to code for mean, median or mode?
  Some students might 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 the Review.
• 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 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 has to sort the data in ascending order, then compare the values to determine which one is found most often in the list.

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 block-based programming software, for this pseudocode?
  Invite students to create the code for the situation that the pseudocode represents. Codes may vary. There are several ways to represent this pseudocode using block-based coding.

Sample code:

Blocks of code:Events block stating ‘’when green flag is clicked’’.Variable block stating, “set “n”” b” one to zero”.Variable block stating, “set 2 “n” ” b” zero”.Variable block stating, “set sum to zero”.Sensing block stating, “ask what your first number is, question mark, and wait.”Variable block stating, “set my variable to motion block stating, “answer’’.”Sensing block stating, “ask what your second number is, question mark, and wait.”Variable block stating, to “n”” b” 2 motion block stating, “answer.”Variable blocks stating, “set sum to operators block 1 “n”” b” plus, “n”, ”b”, “2 “

Note: In this part of the learning situation, the students make the blocks their own by means of which the questions are asked and the value of the variables is modified. If the students have already used the coding software in question, it would be possible to go directly to the next part of the activity, which is the data collection. This activity can also be used as a diagnostic assessment to determine if students have what 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

Once the pseudocode is complete, have students create their code to collect data related to students' shoe sizes, then compile it into a list.

Sample code:

Blocks of code:Events block stating ‘’when green flag is clicked’’. Control block stating, “repeat until operator block “answer no”. Inside 5 nested blocks.A sensing block stating, “ask what is the students shoe size and wait.”Variables block stating, “set shoe size to motion block stating, “answer”.”List block stating, “add, variable block stating, “shoe size” to show size list”.”Variables block stating, “change sum by shoe size.”A sensing block stating, “ask do you have another data value to add, question mark, open parenthesis, answer yes or no, closed parenthesis. And wait. “

Note: Several block-based coding software make block customization possible. 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:

Blocks of code:My blocks stating, “define data entry.”Control block stating, “repeat until operators block “answer, equal, no”.”Inside 5 nested blocks. Sensing block stating, “ask what is the student’s shoe size and wait.”Variables block stating, “set shoe size to motions block stating, “answer”.”List blocks stating, “add variable block stating, “shoe size” to shoe size list”.”Variables block stating, “change sum by shoe size. “A sensing block stating, “Do you have another data value to add, question mark. Open parenthesis, answer yes and no, closed parenthesis, and wait.

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

Coding to Analyze Data 

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

Here is an example of pseudocode:

Variables:   *list number (or list element)

Sample code:

Blocks of codeEvent block stating, “when this sprit clicked.”Variables set stating, “set list number to one.”Variables block stating, “set sum to zero.”Control block stating, “repeat” list block stating, “length of shoe size list.”Inside 2 nested blocks.Variables block stating, “change sum by” list block “item of list number of shoe size list.”Variable block stating, “change list number by one.”Looks block stating, “say join the average shoe size is sum divide length of shoe size list.”

Ask students the following questions:

• What happens if I add shoe sizes to my list?
• Will the mean be the same? Why?
• Could this code be made even more effective?

Note: 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:

Blocks of codeEvents block stating, “when green flag is clicked.”Inside 5 nested blocks. Sensing block stating, “ask what is the students show size and wait.”Variable block stating, “set shoe size to’’ sensing block “answer”.List block stating, ‘’add’’ variable block stating, shoe size list.”Variable block stating, “change sum by shoe size.Caption: This code block allows the shoe size to be added to a running sum during each iteration of the loop.A sensing block stating, “ask do you have another data value to add, question mark. Open parenthesis, answer yes or no, closed parenthesis, and wait’’.

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

Possible questions:

• What are the steps to follow 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.)

Pseudocode example::

Variables:   * central value 1

Note: If the list contains an even number of data, point out to students that calculating the median takes the same form as calculating the mean. Essentially, the mean of the two central values is found.

Here is a sample code to place the data list in ascending order. Again, the code has been turned into a custom block. This step is helpful, but not necessary.

Blocks of codes:My block stating, “define sort the list ascending.”Control block stating, “repeat” variable block “stating, length of shoe size list.”Inside 2 nested blocks.Control block stating, “repeat” variable block stating, “length of show size list minus One.”Inside 2 nested blocks.Control block stating, “if item list number of shoe size list less then item list number minus one of shoe size list then.”inside 2 nested blocks.List block stating, “insert item list name of shoe size list at list number minus one of shoe size list.”List block stating, “delete list number plus one of show size list.”Variables block stating, “change list number by one.”Variables block stating, list “set list number to 2.”

Short explanation of the logic of the code:

This code works by comparing a value in the list with the neighbouring value. If the value is smaller, the positions of the list elements 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 value.

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 software.

Sample code to find the median:

Blocks of codeControl block stating, “if length of shoe size list mod 2 equals zero then.”Caption: This modules operation block, open parenthesis, mod, closed parenthesis, returns the remainder of a division. An even number divided by 2 will return a value of zero, open parenthesis, ex 6 mod 2, equals, zero, closed parenthesis.”Inside 2 nested blocks. Variables block stating, “set central value to length of show size list divided by 2. Variables block stating, “set median to item central value of shoe size list, plus, item central value of shoe list divided 2.”Control block stating, “else”.Variables block stating, “set median to item length of shoe size list plus 1 divided 2 of shoe size list.”

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 create 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 create 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 coding software 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 software.
• Provide a cheat sheet on the function of some more complex blocks, such as operators and conditions.