Grade 6: "Mystery Integers"
(From: OAME)The lessons and activities within “Mystery Integers” will unfold over a number of math classes (60 minutes each).
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The Mystery Integers lesson plan has the following sections (each could be considered for a single 60-minute lesson)
Note to Teachers: Consider this lesson if your students require instruction or further development on the use of variables and lists.
“Mystery Integers!” lesson plan:
Part 1: Introduction
Part 2: Direct Instruction for Pseudocode
Part 3: Transitioning from Pseudocode to Coding
Part 4: Creating Variables in Coding
Part 5: Creating Lists in Coding
Part 6: Identifying the Correct Answer Coding
Sample Scratch Project, Starter Scratch Project, Opposite Integers Project to consolidate learning
Connecting Math Algorithms to Coding
Coding and Integers with Scratch
Number
B1. demonstrate an understanding of numbers and make connections to the way numbers are used in everyday life
B1.2 read and represent integers, using a variety of tools and strategies, including horizontal and vertical number lines
B1.3 compare and order integers, decimal numbers, and fractions, separately and in combination, in various contexts
Algebra
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 efficient 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 outcomes and the efficiency of the code
C4. apply the process of mathematical modelling to represent, analyse, make predictions, and provide insight into real-life situations
Spatial Sense
E1. describe and represent shape, location, and movement by applying geometric properties and spatial relationships in order to navigate the world around them
E1.3 plot and read coordinates in all four quadrants of a Cartesian plane, and describe the translations that move a point from one coordinate to another
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 recognize sources of stress and cope with challenges and build relationships and communicate effectively as they apply the mathematical process problem solving (develop, select, and apply problem-solving strategies) and reflecting (demonstrate that as they solve problems, they are pausing, looking back, and monitoring their thinking to help clarify their understanding), so they can work through challenging math problems, understanding that their resourcefulness in using various strategies to respond to stress is helping them build personal resilience, 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.
use pseudocode or create a flowchart to show our mathematical thinking.
align lines of code, through block-based programming (Scratch), within a mathematical algorithm.
understand my mathematical thinking and algorithms when I play an Input/Output/Mystery Integer game.
understand my mathematical thinking and algorithms when I break them apart into individual actions or steps.
match up Scratch blocks with actions listed in my pseudocode &/or flow chart.
make & name a variable to act as a container to hold one piece of information/data and make & name a list to act as a container to hold more than one piece of information/data.
make a stack of blocks to identify the mystery integer.
add additional blocks to give clues to the project user if their answer is <, >, or = to the mystery integer.
For the classroom:
Computer and Internet
Projector or screen sharing
For further reading:
Scratch Off-Line Version links:
Offline Editor Information from Scratch Wiki
Download Off-Line Version of Scratch
Articles from Scratch Wiki about Variables and Lists::
Information from Scratch site:
Information from Scratch Wiki on Student and Teacher Accounts
Number: integers, number lines
Math activity: input/output machine
Coding: Students may learn about conditional statements with these lessons or consolidate previous incidental learning regarding conditional statements.
Prior Learning about Scratch Coding:
Experience with coding in Scratch or other block coding will be helpful for this lesson. However, for each project, there are
links to files with screenshots and written instructions for various aspects of Scratch coding. For example, How to use the Paint Editor; How to make a Variable; How to make a List; and The MOD operator block. Teachers and students should use as much or as little as they need.
This lesson is a series of alternate coding activities that could be used:
in place of those in Lesson Plan Which Integer is Greater? or
if students need more time to develop key concepts, models, and strategies or to continue to practise and consolidate their learning
Lesson plan involving learning how to make pseudocode and examining a Scratch Project from pseudocode (Mystery Integer - Input/Output Machine)
Part 2 - Lesson Plan Mystery Integer - Direct Instruction for Pseudocode
Part 3 - Lesson Plan Mystery Integer - Transitioning from Pseudocode to Coding
Note: In the lesson plan, Coding with Integers, there is a chart sorting blocks to match pseudocode statements. This lesson plan uses questions to guide the student to answer with suitable block choices. Teachers should consider using the method that suits their students best.
Part 4 - Lesson Plan Mystery Integer - Creating Variables in Coding.pdf
Note: Although the blocks are tailored for the Mystery Integer Scratch project, the concepts are transferable to others and might be useful for background information on variables for teachers &/or their students.
Part 5 - Lesson Plan Mystery Integer - List Making Code
Note: Although the blocks are tailored for the Mystery Integer Scratch project, the concepts are transferable to others and might be useful for background information on lists for teachers &/or their students.
Part 6 - Lesson Plan Mystery Integer - Identifying the Correct Answer Coding.
Scratch Sample Project Mystery Integer
Lesson Plan Mystery Integer Starter Project
Teacher Moves
Teacher moves are contained in the lessons plans as scripts, charts and screenshots. Look for “Teacher says” and screenshots with instructions to move students’ thinking.
In Part 2, the teacher will act as a scribe for the students’ ideas to develop a pseudocode.
In Part 3, the teacher will guide the students to identify the Scratch blocks needed to carry out the actions in the pseudocode
In Part 4, the teacher will demonstrate the steps required to create variables in Scratch coding. Variables are often used in Scratch projects.
In Part 5, the teacher will demonstrate the steps required to create Lists in Scratch coding. Lists are often used in Scratch Projects.
In Part 6, the teacher will model the selection and assembly of additional blocks required to identify the correct answer for the Mystery Integer project. This shows students how to continue to enhance projects.
The teacher can refer to the Scratch Sample Project Mystery Integer as needed.
Scratch Starter Project Mystery Integer: Teacher reviews information in Scratch project with students and guides their coding of the project.
Classroom Opportunities for Social-Emotional Learning:
Paired Programming
Classroom Advice Space & Buddy Programming
Classroom Opportunities for Social Emotional Learning
Questions Social Emotional Learning
Opportunities for Differentiation (meeting the needs of all learners)
This project can consolidate learning in addition to those ideas found in the Grade 6 Coding lesson: Which Integer is Greater?. The lesson plans for Mystery Integers are complementary ones to “Which Integer is Greater?”. Based on the needs of the students, teachers are encouraged to make a hybrid from sections of both lessons or use one or both, depending on the background knowledge of their students for coding and integers. See Consolidation of Learning for Lesson Plan “Which Integer is Greater?”
Scratch Project: Opposite Integers
Up until now the coding lessons for Integers have involved starting with the creation of a pseudocode for the math concept and translating those actions to Scratch coding blocks. With this activity, as a consolidation activity, students watch the teacher play the Opposite Integers game, or they play it themselves and then discuss what the possible blocks might be. Then from the list of blocks connect back to the math concepts. In this program the “Cat” generates a random integer. The user is then asked to input (type) the opposite integer. The program coding declares it true (and if so, the User gets a point) or false (the Cat gets a point). Scores are kept and a winner is declared when either the User or the Cat gets to 10.
There are several additional ideas presented in this project such as Randomization and Scores. The idea of a “game” is one that is interesting to students and this will give them an entry level example to build upon for future projects.
Opportunities for Assessment
The checklist below can be used by students to track their use of Scratch coding elements or used by teachers to assess student projects.
Checklist for Evaluating a Project -Editable Version
Questions for Coding in General
In addition to those ideas found in the lesson, an extension for Opposite Integers is to add blocks to plot the Input and Output integers as x & y coordinates. This can be a lead into Algebraic patterns. See Scratch Project: Mystery Integer Graphing Extension.
See also “Further Consolidation/Next Steps for students and teachers” in Lesson Plan “Which Integer is Greater?”