At a Glance...

C3. Coding
Solve problems and create computational representations of mathematical situations using coding concepts and skills.

Learning Situation: In Pursuit of Sequels!

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Duration : approximately 100 minutes

Summary

In this learning situation, students use the power of nested control structures to create and extend repeated-pattern and increasing sequences.

Learning Goals

At the end of this learning situation, the student will be able to:

• use terminology such as code, sprite, sequential events, simultaneous events, repeating events, nested events, repeating pattern, pattern, growing pattern, table of values;
• to describe suites;
• create repeating and growing patterns by writing and executing code that includes sequential events, simultaneous events, repeating events, and nested events;
• read and modify codes that include sequential events, simultaneous events, repetitive events and nested events.

Criteria based on the Achievement Chart

Materials

• computer equipped with appropriate block coding software according to the level of the students
• objects representing patterns (two-coloured tokens, coloured tiles, etc.)

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

Course of Action

Duration: approximately 60 minutes, in addition to the time allotted for exploring the software, if needed

Assessment can be carried out through…

Present the students with a sequence of code that represents the bank situation. Do not show them the result of the code execution (do not click on the green flag).

In the examples provided, the notes in yellow are explanations of how the code works and should be omitted when the code is presented to students.

Have students study the code to predict what it will do when executed. Writing pseudocode could also help the student predict the outcome of the execution and better understand what the various blocks are for.

Example of Code Representing the Piggy Bank Problem Using Tokens

Example of a Pseudocode Representative of the Presented Code

After allowing sufficient time for the students to make their predictions, the code can be run, and they can compare their predictions with the result.

Ask students what stands out most in the code that has just been explored. There are several possible answers, but try to direct the questioning to the elements that are repeated. The code, as presented, is a repeating pattern. The pattern is as follows:

(Move token), (Pause for 1 second), (Stamp)

This pattern is repeated throughout the code. It can be reduced with a loop.

Note: If students are unfamiliar with the concept of a loop, it would be beneficial to have them explore the coding software using the loop so that they become familiar with this structure before continuing.

Example of Reduced Code with the Loop

Image Blocks of code: Events block stating “start on when green flag is clicked”. Looks block stating “show”. Pen extension stating “erase all” Motions block stating “go to x: ‘-200’ y: ‘-160'. Caption: “This block is not part of the main loop. It positions the sprite at the x and y coordinates indicated and is executed just once at the beginning of the code execution. Controls block stating “repeat 5”. Inside are 3 nested blocks. Controls block stating “wait ‘1’ seconds. “This block is inside the loop and will be executed 5 times”. Pen extension stating “stamp”. Motions block stating “change y by ‘20’.” Looks block stating “hide”. Caption: “This block hides sprite at the end of the code execution. Otherwise, the sprite would remain on the stage and would give the appearance that there was an extra stamp. In other words, if the sprite wasn’t hidden, there would appear to be 6 stamps instead of 5.

Note that the result of this code produces the same result as the longer code without the loop. Point out to students that the code also produces a representation identical to the shape in position 1 - January, created in the situation. Ask them to modify the code so that it reproduces the mathematical situation of the piggy bank. There are several ways to continue.

1. If students are beginning their exploration of coding, it would be beneficial to show them, through trial and error, how to modify the code to insert loops. By modeling their suggestions, students can work together to find a solution to the problem.
2. If students have a little more experience with the coding software, pairs or even individual work would be beneficial for students to discover code sequences in their own way that will represent the mathematical situation.
3. If students' experience and comfort levels vary widely in the class group, random or purposeful groupings could put them in a peer learning situation. Teachers could also use this opportunity to provide explicit instruction in small groups based on student needs.

Example of Pseudocode and Code that Represents the Piggy Bank Situation with Loops

This pseudocode represents 2 months (initial position 1 and initial position 2). By determining the trend, we can extend this sequence of code, which again looks like a sequence, to represent several months.

Connections with Other Strands

Number

B2.2 Recall and demonstrate multiplication facts for 1 × 1 to 10 × 10, and related division facts.

Nested loops create more complex representations of multiplications than simple loops. For example, you can get 24 repetitions of a code sequence by placing it in a 4-repeat loop, and place the 4-repeat loop in a 6-repeat loop.

Algebra

C1.1 Identify and describe repeating and growing patterns, including patterns found in real-life contexts.

C1.2 Create and translate repeating and growing patterns using various representations, including tables of values and graphs.

C2.1 Identify and use symbols as variables in expressions and equations.

The nested events create growing patterns. A first loop defines the pattern core, and we place it in a second loop that determines the number of repetitions. After that, it is a matter of adding blocks of code and variables to modify the pattern rule.

Spatial Sense

E2.5 Use the row and column structure of an array to measure the areas of rectangles and to show that the area of any rectangle can be found by multiplying its side lengths.

Nested loops can help represent the array. The inner loop represents the number of elements in a row, and the outer loop represents the number of rows.

Financial Literacy

F1.3 Explain the concepts of spending, saving, earning, investing, and donating, and identify key factors to consider when making basic decisions related to each.

Instructional Differentiation and Universal Design for Learning

Students comfortable with block coding could use variables to further automate the code. See below for example code that asks for the number of months to represent. The student uses the answer to represent the mathematical situation. The code could also be studied in order to predict the result or provided for the student to modify according to their personal objectives.

The student who has difficulty using the coding software could team up with more comfortable students to learn from their partners. A group of students with the same level of experience with the software would also facilitate direct instruction as needed by the group.

Several coding software allow the sharing of projects. Students could be given assembled code blocks in advance in order to put them in the right places to make the code work.

Example