Recalling Math Facts Through Coding

(Source: Ontario Association of Math Educators: Ontario Math Support)

Expectations:

Algebra

• C3. solve problems and create computational representations of mathematical situations using coding

• C3.1 solve problems and create computational representations of mathematical situations by writing and executing code, including code that involves conditional statements and other control structures concepts and skills

• C3.2 read and alter existing code, including code that involves conditional statements and other control structures, and describe how changes to the code affect the outcomes

Number

• B2. use knowledge of numbers and operations to solve mathematical problems encountered in everyday life

• B2.2 recall and demonstrate multiplication facts from 0 × 0 to 12 × 12, and related division facts

Social-Emotional Learning (SEL) Skills in Mathematics and the Mathematical Processes

• A1. Throughout this grade, in order to promote a positive identity as a math learner, to foster well-being and the ability to learn, build resilience, and thrive, students will apply, to the best of their ability, a variety of social-emotional learning skills to support their use of the mathematical processes and their learning in connection with the expectations in the other five strands of the mathematics curriculum.

Visual Arts

• D1. Creating and Presenting: apply the creative process to produce a variety of two- and three-dimensional art works, using elements, principles, and techniques of visual arts to communicate feelings, ideas, and understandings

Big Idea:

• In this lesson, to the best of their ability, students will learn to identify and manage emotions and think critically and creatively as they apply the mathematical process selecting tools and strategies (select and use a variety of concrete, visual, and electronic learning tools and appropriate strategies to investigate mathematical ideas and to solve problems), so they can express and manage their feelings, and show understanding of the feelings of others, as they engage positively in mathematics activities, and so they can make connections between math and everyday contexts to help them make informed judgements and decisions.

Write on screen or board this equation:

6 x 4 = 24

Ask students, “What kind of equation is this? Are there words that we can use to describe the parts in this equation?” (i.e., 6 and 4 are the factors and 24 is the product).

Then ask, “is there a way to use these same numbers, but write them in a different equation?” Students may suggest, 4 x 6 = 24 (note that the order of factors doesn’t matter).

If they don’t suggest it independently, encourage students to write these same three numbers as a division equation.

Ex. 24 4 = 6

Explain the difference between the dividend (24), the divisor (4) and the quotient (6).

Ask students to write out a different division equation using the same three numbers, identifying the three parts in a division equation.

Ex. 24 6 = 4

To begin, have students follow along Google Slides Conditional coding in Sheets opened as a class. If possible, project the slides while students work individually on computers to follow instructions and program their own Google Sheet.

Possible modification: Teachers could also share the premade Google Slides for exploration purposes prior to having students code their own Google Slides. In this case, be sure to assign each student their own copy.

In the first tab, students will see that the digits 0 through 9 have all been colour coded. Ask students, “How could you make blue using a multiplication or division equation?” Students will respond that the answer would have to be 5, so they can list some equations that might work (like =35/7 or =60/12 or = 1 x 5).

Teacher Moves:

If students come across an issue, such as the cell does not change colour, try to lead them to debugging through questioning. Have other students help with the problem solving so students get familiar with the vocabulary. Here are some examples of questions:

• When you applied the conditional coding, did you have all the cells selected that you want to include in the pixel art grid?

• Was the correct condition applied? (i.e., The text is exactly…)

• Was there a mistyped number?

While students are exploring equations being written in a specific cell, you can have some students explore repetitive additions that lead to the same result : i.e. =2+2+2 is the same as =3 x 2. (Strand A: problem solving: develop, select, and apply problem-solving strategies)

The teacher should enquire with students:

• Are there other multiplication facts you could find that result in the same product?

• What other strategy could be used if you get stuck on a question? (example: A student is stuck on 7x6, one could go back to 7x5 and then add another group of 7 to the product to find the answer)

Things to keep in mind: Sheets recognizes an equation when the typed information begins with “ = “ and multiplications are represented with “ * “

Example: = 2*2

This can be modelled in the already prepared Google Sheets. (Second tab)

Opportunities for Differentiation Allow students to consult the multiplication chart as needed. Students can work together in pairs. Limit the number of colours so that some students only need to use a few. (i.e. up to 9x9, meaning 9 colours instead of 12). Students can use graph paper to plan out their design and then transfer it into the spreadsheet.

Diagnostic Assessment: Note students’ understanding of the relationship between products and quotients.

Formative Assessment: Note how students express their observations and to what degree they incorporate the vocabulary (factor, product, divisor, dividend, quotient).

Summative Assessment: Refer to the Success Criteria and the way students create pixel art. Take note of the various levels of complexity, the way they use different equations, and detail.