"making change"

Big Ideas:

There are a variety of appropriate ways to estimate sums and differences depending on the numbers involved and the context. Estimates are useful for both checking calculations and because sometimes an estimate is all that’s needed.

Expectations:

Number

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

  • B2.5 represent and solve problems involving the addition and subtraction of whole numbers that add up to no more than 1000, using various tools and algorithms

Algebra

• C2. demonstrate an understanding of variables, expressions, equalities, and inequalities, and apply this understanding in various contexts

  • C2.1 describe how variables are used, and use them in various contexts as appropriate

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

  • C3.2 read and alter existing code, including code that involves sequential, concurrent, and repeating events, and describe how changes to the code affect the outcomes

Financial Literacy

• F1. demonstrate an understanding of the value and use of Canadian currency.

  • F1.1 estimate and calculate the change required for various simple cash transactions involving whole dollar amounts and amounts of less than one dollar

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.

In this lesson, to the best of their ability, students will learn to maintain positive motivation and perseverance and to build relationships and communicate effectively as they apply the mathematical processes reasoning and proving (develop and apply reasoning skills (e.g., classification, recognition of relationships, use of counter-examples) to justify thinking, make and investigate conjectures, and construct and defend arguments)) and problem solving (develop, select, and apply problem-solving strategies), so they can recognize that testing out different approaches to problems and learning from mistakes is an important part of the learning process, and is aided by a sense of optimism and hope, and so they can work collaboratively on math problems – expressing their thinking, listening to the thinking of others, and practising inclusivity – and in that way fostering healthy relationships.

• • Day 1 Mini lesson: Practice skip counting money using a video like Skip counting Canadian money (you may wish to start at 2:18 min).

  • Play a quick skip counting game with the students such as Skip Around the Circle to review counting efficiently with 5s, 10s, and 25s.

  • Challenge students with queries such as: If the circle kept going what would student X say? How do you know? \

• Day 2 Mini Lesson:

Have students estimate the change required for a few simple cash transactions. Share strategies used to estimate. This situation allows students to defend their thinking and to prove their reasoning.

• Review what was discussed from the first lesson.

Day 1:

• Explain to the students that they will be working with code that lets a shopkeeper make change.

• Display the project page of a change making code like Making Change. Have students assist you by deciding what to buy and estimating the change they will need. Then have them decide what combinations of coins would add up to the total amount of change you would be given. Complete the task more than once so students can see what happens when the coin choice is correct and when it is incorrect.

• Have the students work in small groups to explore the program and determine the various sections of the code.

• Bring the class together, or work with the small groups, to discuss and confirm the various sections of the code.

• Explain that the code makes change to the penny. Discuss how rounding is used in real stores and how even though pennies may not be given as change in Canada, they are still legal tender and cents are included in prices

• Short consolidation of Day 1

• Ask students to take a few minutes to pause and think or reflect about what they have learned in this lesson. Provide time to share orally with a partner.

Day 2:

Have students observe how variables are used in the code. Ask the students to identify the variables in the existing code. What do they notice about the variable names? What are the variables doing? (Variables are used in coding so that the code can be run more than once with different numbers).

How can we use variables to keep track of the coins used to make change? How would we name the variable to make the code meaningful?

Students then work with a partner or in small groups to remix their code to add a variable or variables to count their code. Students can either create one variable to count the coins or can create a variable for each type of coin.

Math Congress

Explore the strategies the students used to read and understand code. How did they test their ideas?

Ask: This code uses variables. Where are they?

What do you notice about the variable names? What are the variables doing?

(Note: In mathematics notation, variables are only expressed as letters or symbols. When coding, variables may be represented as words, abbreviated words, symbols, or letters)

What strategies did you use to decide which coins to give when you were making change?

Make anecdotal notes to record observations, check if student can:

• Read the code and identify the purpose of each section

• Follow an organized problem solving process

• Make reasonable predictions

• Explain reasoning

• Note difficulties

Student self assessment:

What are my successes?

What areas still need work?

What is my next step or goal? What can I do to improve my ability to read and analyze code?

Make anecdotal notes to record observations, check if student can:

• Identify variables and other features of the code

• Remix code to add or change variable(s)

• Realize that multiple solutions are possible

• See the advantages and disadvantages of each solution

SEL Student Self-Assessment FRENCH / ENGLISH SEL Teacher Rubric