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, sequential events, simultaneous events, repeating events, nested events, repeating pattern, pattern, growing pattern, table of values;
• describe patterns;
• create repeating and growing patterns by writing and executing code that includes sequential events, simultaneous events, repeating events, and nested events;
• read and alter codes that include sequential events, simultaneous events, repetitive events and nested events.

Criteria based on the Achievement Chart

Materials

• technology equipped with a block coding program familiar to 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 code that represents the piggy 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 read the code and ask them to predict the outcome when it is executed. Students may wish to rewrite their code as pseudocode to help them with their prediction.

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. The number of lines in the code can be reduced by using a loop command.

Note: If students are unfamiliar with the concept of a loop, have them explore using the coding program with which they are familiar.

Example of Code Using a 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.

Have students read the code and predict its outcome. Execute the code to verify their predictions. Highlight to the students that the outcome represents the amount of money in the piggy bank for January. Ask students to alter the code so that it reproduces the mathematical situation of the piggy bank to include other months as well. There are several ways to have students work on this. Below are some suggestions.

1. If students are beginning their exploration of coding, it would be beneficial to show them, through trial and error, how to alter 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 program, have students work as pairs or as individuals to discover how they can sequence their code sequences to represent the mathematical situation.
3. If students' experience and comfort levels vary widely in the class, use random or purposeful groupings. Teachers can 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 who are comfortable with block coding can begin to use variables for the code. See below for an example of code.

The student who finds coding challenging can team up with students who are more experienced to learn from them. Students with the same level of understanding can be grouped together for direct instruction as needed.

Several coding programs allow the sharing of projects. Consider when appropriate to assemble blocks of code in advance, then give to students to arrange in the right order for the code to work.

Example