Big Idea: Using code (Scratch) to investigate algebraic patterns with fractions and decimals

Expectations:

Algebra

• C1. identify, describe, extend, create, and make predictions about a variety of patterns, including those found in real-life contexts

  • C1.2 create and translate growing and shrinking patterns using various representations, including tables of values and graphs

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

  • C2.1 translate among words, algebraic expressions, and visual representations that describe equivalent relationships

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

  • 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

  • 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

• B1. demonstrate an understanding of numbers and make connections to the way numbers are used in everyday life

  • B1.7 describe relationships and show equivalences among fractions, decimal numbers up to hundredths, and whole number percents, using appropriate tools and drawings, in various contexts

  • B1.3 represent equivalent fractions from halves to twelfths, including improper fractions and mixed numbers, using appropriate tools, in various contexts

  • B1.5 read, represent, compare, and order decimal numbers up to hundredths, in various contexts

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

  • B2.5 add and subtract fractions with like denominators, in various contexts

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 think critically and creatively as they apply the mathematical process connecting (make connections among mathematical concepts, procedures, and representations, and relate mathematical ideas to other contexts

• (e.g., other curriculum areas, daily life, sports)) and communicating (express and understand mathematical thinking, and engage in mathematical arguments using everyday language, language resources as necessary, appropriate mathematical terminology, a variety of representations, and mathematical conventions), 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 make connections between math and everyday contexts to help them make informed judgements and decisions.

teacher background

• Some experience with decimal and fraction equivalents.

Take students outside. Use trundle wheels or measuring tapes to measure a distance (for example from school to fence - a distance of at least 30 m is good)

Put students at one side of this area, and tell them they are going to walk half way to the other side. (Some students can help measure this out). Then tell them to walk half the remaining distance (this will be 12 of the 12 , which will be 14 of the original distance - students should now be 34 of the way to the other side. Keep measuring and telling them to move 12 the distance that remains.

Eventually, they will come to a small distance

“T: Ok, there is 1 cm left, so you can only move 12 cm. Now you can move 12 of that remaining that distance” ( 14 cm.)

Ask students - “T: Will you ever actually reach the other side?”

Ss: “No- there is always a small gap, as the “half” keeps getting smaller.”

Opportunities for Differentiation

• When outside, different students can be chosen to measure, divide the numbers (with a calculator) or walk the given distances.

Math Congress: Choose some pairs/groups who created models of different fraction patterns and share them with the class.

Ask: “How does this model represent the problem? How is it the same as or different from the model your group created? What can we generalize about fraction patterns in which we add on of the amount left of the whole? How can you connect the fractions, decimals and the paper model?”

Consolidate important lesson ideas with the class: (Students can discuss questions with an elbow partner, then share answers back with the class.)

T: “What is better about the different representations, the code or the paper?”

Ss: “Paper helps you visualize what is happening. Code is more precise and does the calculating for you.”

T: “When does 1/2 plus 1/2 NOT equal 1 whole?”

Ss: “When the size of the whole has changed. Half of what is left, is not the same as 1/2 of the original whole.”

Opportunities for Assessment

Observe students to see if they can make a paper model that matches the problem.

Ask students to make connections

• Between the paper model, the experiment outside and the Scratch program math

• Between the fractions

• 1/2,1/3,1/4 and their decimal equivalents

Once students have tried 2 different fractions in the code, have them make a prediction about what will happen with a third, new fraction.

Give a Math journal question:

A student has worked on the following problem:

“Ali ate 1/4 a chocolate bar at lunch, then 1/4 of the rest of the chocolate bar after school. How much of the chocolate bar has he eaten?”

If they said that “Ali has eaten the 1/2 chocolate bar, since 1/4+1/4 = 2/4 or 1/2 ”

Are they correct? Why or why not? How could you represent your ideas to prove that you are correct?

• Students can continue work with adding fractions with like denominators.

• Students should have more opportunity to think about fractions when the size of the whole changes.

T: “If this is 1 whole, what would 1/2 look like?”

T: “If this is 1 whole, what would 1/2 look like?”

• Students can continue to work on fraction/ decimal equivalence.