We can add integers without using a calculator or a number line. When the data points in a scatter plot seem to roughly follow the path of a line, we can use our knowledge of linear patterns to study the data and make predictions. In this lesson, we explore how to represent a sequence graphically. Measures of central tendency, like the mean, median, and mode, attempt to summarize data by measuring the middle (or centre) of a data set. Register for contests through our website by the deadline. In this lesson, we discuss the features of a histogram and practise creating histograms from numerical data sets. We recommend that students spend some time preparing for our contests by trying to solve problems. We define corresponding, alternate, and co-interior angles, and use angle relationships to solve for unknown angles in a diagram. In this lesson, we practise interpreting the underlying data displayed in different graphs. In this lesson, we practise using measures of central tendency to compare two data sets, draw conclusions, and discuss factors that might influence which measure of central tendency is most appropriate for a particular comparison. See the most recently available results booklet. Our active work toward reconciliation takes place across our campuses through research, learning, teaching, and community building, and is centralized within our, Outside North and South America PDF poster, Visit our Coronavirus Information webpage, New Individual/Home School Application form. In this lesson, we review how to generate a list of multiples of an integer. In this lesson, we learn how to organize data into frequency tables, calculate relative frequencies, and create and compare frequency and relative frequency graphs. Basic algebra is introduced with the addition of variables into topics including patterning, and proportional reasoning. In this lesson, we investigate various properties of the diagonals in quadrilaterals. Our main campus is situated on the Haldimand Tract, the land promised to the Six Nations that includes six miles on each side of the Grand River. Since 2003, the CEMC has developed another contest for grade 9—11 students. We begin our discussion on equivalent ratios using diagrams and exploring how two ratios can represent the same relationship between two quantities. We then expand our understanding to include the multiplication of any two fractions. We relate volume and capacity, and explore how to convert between units of volume. In this lesson, we practise identifying and interpreting information provided in a histogram, and drawing conclusions supported by the histogram. Visit our Coronavirus Information webpage We use number lines as motivation for finding a common denominator, then we move to adding fractions without the use of visual aids. Letters are included beside the unit names to help group the units into similar themes. In this lesson, we review the “greater than” and “less than” symbols. In this lesson, we begin our discussion on transformations by exploring the translations of polygons. In this lesson, we plot negative fractions on the number line to help us understand and compare the values of these numbers. Topics include representing negative fractions and negative decimals, comparing the values of any two rational numbers, exponential notation, and using factor trees and prime factorizations to find the LCM or the GCF of a pair of positive integers. In this lesson, we explore how data can be influenced by the wording of survey questions, the types of answers accepted in a survey, and the sample group that is being used in the survey to represent the population. This lesson concludes with an extension that explores how prisms can be sliced to produce various polygonal faces. We also practise solving simple equations by inspection. We conclude by solving problems that require a ratio to be applied to large quantities. We discuss how reliable, or unreliable, our predictions might be and explore how we might design experiments in a way that makes our predictions as reliable as possible. We also explore how to use polygons to help us estimate the circumference and the area enclosed by a circle. Written in May. We discuss the advantages and disadvantages of these organization tools and practise choosing appropriate intervals for given data sets. This can be done by performing a particular type of transformation: a dilatation. Dates and Location The conference was held virtually through the Centre for Education in Mathematics and Computing and the University of Waterloo from August 18 - August 20. We also explore how the interval size of a histogram can affect the conclusions drawn by someone who is analyzing the data in a histogram. We conclude by solving some word problems involving percents. We conclude by solving word problems that require us to apply factors to different contexts. Our hope is that these resources make it to as many parents, teachers, and students as possible. We discuss the roles that the two variables play in a scatter plot and explore what information might be revealed when we consider the shape formed by the data points as a whole. Topics include calculating the circumference and area of circles; calculating the volume and surface area of cylinders; and properties of angles formed by intersecting lines including parallel lines and transversals. Scatter plots are used to display a relationship between the two variables in question. We solve examples and highlight rules for performing calculations without using a calculator. Probability theory is the study of random experiments including different ways to measure the likelihood that a particular outcome or event will occur. Our goal is to show two triangles are congruent by matching only three corresponding parts. In this lesson, we explore how this unit rate manifests in an equation, a table, or a graph representing the relationship between the two quantities. Part A (Lessons 1–7) Specifically, we look at how the sign of each integer in a product impacts the sign of the product. 200 University Avenue West We begin our discussion of patterning by examining number and image sequences. In this lesson, we discuss strategies for drawing accurate circles. We then develop and apply the formulas for finding the areas of parallelograms, triangles, and trapezoids. In this lesson, we visualize equations using weights and a balanced scale. We focus on how this might affect the mean, median, and mode in different ways. Part A (Lessons 1–5) For most students, test prep books and practice questions are not enough, and classes and tutors are too expensive. Its mission is to increase … Part A (5 credits each) 1. In this lesson, we will learn how to choose appropriate models for simulations and practise running simulations to obtain probability estimates. We solve equations with one operation using algebraic techniques and learn how to verify a solution of an equation. Part A (Lessons 1–4) These skills can be helpful for experiments with too many outcomes to list efficiently. Specifically, we look at drawing circles when given a centre and a radius, a centre and a point that must lie on the circle, and also given two or more points that must all lie on the circle. In this lesson, we define a percent and explore the relationships among fractions, decimals and percents. Following toggle tip provides clarification. Susan wants to place 35.5 kg of sugar in small bags. The order of operations is reviewed and used to perform calculations involving integers, fractions, and decimals. In this lesson, we focus on working with continuous data sets. In this lesson, we learn how to solve calculations that involve the division of whole numbers by fractions and decimals. Factors, like multiples, have to do with multiplication. Topics include different types of data; population, sample and census; bias in data collection arising from question wording, accepted answers and choice of sample group; frequency and relative frequency tables and graphs; reading and creating circle graphs; choosing an appropriate graph type for a data set; bias in data representation arising from the chosen graph type, graph structure and shape, and axis labels and scales. You will continue to practise finding the general term of a sequence, concluding the lesson with some application problems. We also explore how to compare data presented in histograms. We learn how to identify a linear relationship represented in a graph, in a table of values, or in an equation. Our main campus is situated on the Haldimand Tract, the land promised to the Six Nations that includes six miles on each side of the Grand River. We define supplementary, complementary, and opposite angles, and use angle relationships to find unknown angles in a diagram. In this lesson, we discuss fractional percents and percents greater than 100 percent. We start by organizing data using stem-and-leaf plots and then exploring how frequency tables can be used if we divide the data into intervals. In this lesson, we learn about rates which are comparisons of two measurements with different units. Part A (Lessons 1–6) Topics include representing and comparing positive rational numbers (integers, fractions, and decimals), finding multiples and factors of positive integers, and determining the least common multiple (LCM) and the greatest common factor (GCF) of a pair of positive integers. Then, we develop strategies for finding equivalent ratios numerically. Our goal is to use equivalent fractions to solve subtraction problems without the use of a calculator or the number line. The relationship between proportional quantities is often given in the form of a unit rate. In this lesson, we revisit the order of operations for arithmetic. Math Circles is a weekly enrichment activity for grade 6 to 12 students organized by the Faculty of Mathematics of the University of Waterloo.. Information about the audience, dates and location. In this lesson, we define and explore decreasing sequences. In this lesson, we look beyond the typical sequences discussed in this unit and explore more naturally occurring sequences. We conclude by using the distributive property to simplify calculations. In this lesson, we take the application of circles beyond the wheel and discuss the role of circles in roundabout design, the use of circles in the design of structures, and how circles of different diameters interact in machines that use gears. We review how to classify triangles according to side lengths and angle measurements. In this lesson, we learn how to multiply integers mentally. A histogram is a similar type of graph in which numerical data are first grouped into ranges and then the frequency of each range is plotted using a bar. If you are a grade 7 to 10 student, check out Homework Help! If you can determine the chances that a particular event will occur in an experiment, then you can use this information to make predictions involving this experiment. Multiplication is the operation that is used to scale or resize a quantity. Topics include solving equations using algebraic techniques, comparing the differences between evaluating an expression and solving an equation, exploring equations with multiple variables, and the Pythagorean Theorem. 69 likes. Grades 7 and 8 and interested students from lower grades. Mathematics Grades 7 & 8 Mathematics Enter. This lesson explores the art of tessellations. In this lesson, we explore the minimum conditions needed to verify that two triangles are similar. In this lesson, we learn how to graph the image of a polygon under a rotation. Often random experiments include more than one object, for example, an experiment might include tossing a fair coin and rolling a standard die. We discuss what information might be gained or lost by presenting data in a histogram, and explore the effects of interval choice on the shape of the graph. In this lesson, we discuss the effect of outliers on the mean, median, and mode of data sets, and explore different contexts in which one particular measure might be the most appropriate for summarizing the given data. In this lesson, we use expressions and equations to model and solve real-world problems. In this lesson, we discuss the effects of adding data to (or removing data from) a data set. In this lesson, we discuss the features of a scatter plot and practise creating scatter plots from paired data sets. In these situations, mathematicians often run simulations that resemble the real situation in terms of probabilities. In this lesson, we extend our previous discussion on integer addition and examine strategies for performing integer addition mentally. In this lesson, we explore the notion of proportionality using examples like image enlargement and paint mixing. Part B (Lessons 5–8) Share this information in person or electronically and let's get In this lesson, we discuss the connections between fractional representations and decimal representations, specifically, when it comes to plotting numbers on the number line. In this lesson, we learn the precise definition of similar polygons, explore the scale factor between two similar polygons, and learn how to use the scale factor to solve problems. Emphasis is put on determining which of these three representations is most appropriate in a particular problem-solving situation. Additionally, we explore the importance of brackets; when they are needed and when they can be removed from an expression. In this lesson, we develop strategies to evaluate division expressions that involve whole numbers and decimal numbers. Rob Gleeson from the Faculty of Mathematics and CEMC from the University of Waterloo. Part A (Lessons 1–11) Topics include quadrilateral diagonals, circle terminology and construction, and applications of circles in the real-world. In this lesson, we analyze different patterns that generate the same sequence of numbers. In this lesson, we practise comparing proportional relationships that are presented in different ways. Division is the opposite operation of multiplication, and so the strategies we learn for dividing integers will be similar to those we used when multiplying integers. The examples focus on popular puzzles and real-life growth and depreciation scenarios. Students writing online will not receive their results immediately. Some focus is given to where percentages appear in everyday life and how estimation can be helpful when working with percentages. We conclude by discussing, through an example, how apparent patterns can sometimes be deceiving. The University of Waterloo acknowledges that much of our work takes place on the traditional territory of the Neutral, Anishinaabeg and Haudenosaunee peoples. Private Math tutor in Waterloo, Canada. In this lesson, we compare theoretical probabilities to probability estimates found through experimentation, and explore how the number of trials performed in an experiment might impact probability estimates. In this lesson, we practise solving equations by trial and error. This lesson concludes with a discussion on substitution, where we evaluate expressions by substituting a number for a variable in the general term. Topics include congruence of polygons, triangle congruence rules, plotting points on the Cartesian plane, the image of a polygon on the Cartesian plane under translations, reflections and/or rotations on the Cartesian plane, and tessellations. We generate various expressions to represent the different interpretations of a pattern, and learn how to determine whether two expressions are equivalent. Part B (Lessons 6–9) Finally, we learn how to compare any two rational numbers. We learn how to draw the image of a polygon under a translation and relate the definition of congruence to translations. This lesson explores equivalent fractions in preparation for when we must add and subtract fractions. Connections between different number systems are highlighted to set the groundwork for comparisons and operations. Academic and student services booths – 6 to 7 p.m. This lesson focuses on the relationship between squaring a number and taking the square root of a number. Schools and Individuals/Home Schools that have not registered for previous contests are encouraged to participate, and can start by filling out either a New School Application form or a New Individual/Home School Application form. In this lesson, we investigate the relationship between the side lengths of a right triangle. We then compare negative fractions with negative decimals. In particular, different polygons are classified based on their side lengths and angle measurements. We then apply these strategies to convert between units of time and units of area. The University of Waterloo has put up an online course for Grade 7 and 8 math with some extensions. We focus on how to write unit rates and how unit rates can be used to solve word problems. Problem of the Week Subscribe to the In this lesson, we connect the different sequences that we have studied so far. The goal of the online tool is to provide a wide variety of fun and educational ways to do math and computer science with kids while they’re at home practicing physical distancing. We then calculate the surface area of cylinders and solve word problems involving surface area. Mathematicians often use the number line to solve problems. Topics include using variables in expressions and equations, identifying and exploring linear relationships, and solving equations by inspection, trial and error, and using visual models. In this lesson, we learn how to visualize the surface of a 3D solid using a net. In this lesson, we review how to represent a sequence using a table, a general term, or a graph. In this lesson, we review how to determine probabilities of independent events using lists, tables, and tree diagrams to display all possible outcomes. We also examine how some sequences of numbers that arise from physical situations cannot continue forever due to real-world boundaries. In math, symbols are important for communication. Exponential notation is then used to represent whole numbers in expanded form using powers of ten. homeworkhelp.ilc.org Students can get FREE help with their homework from Sunday to Thursday, 5:30pm - 9:30pm. This lesson concludes with an application of triangle properties to construct a 60-degree angle using a compass. This lesson introduces the terminology and notation of basic geometric objects, with a focus on written and oral communication. In geometry, the word “similar” is used to indicate when two objects have the same shape, but not necessarily the same size. All students will receive their results from their Contest Supervisor in the weeks after they write the contest. Standard bar graphs are not always an appropriate way to display a given numerical data set. In this lesson, we focus on the addition of integers, specifically how positive and negative numbers can be added using a number line. We begin this lesson by reviewing how to multiply a fraction by a whole number. CEMC is housed within the faculty of mathematics at the University of Waterloo and organizes various contests for students in grade … For the math contest, I received a distinction award as I scored in the top 25th percent among all Canada. Since circles are very different from polygons, we introduce new terminology to use when studying circles. For more information about the structure and general use of this courseware, see the, Equations and the Pythagorean Theorem (A), Lesson 2: Representing Rational Numbers on the Number Line, Lesson 4: Describing Fractions as Decimals, Lesson 2: Adding Integers: Mental Arithmetic, Lesson 4: Adding Rational Numbers on the Number Line, Lesson 8: Multiplying Whole Numbers by Rational Numbers, Lesson 10: Dividing Whole Numbers by Rational Numbers, Lesson 18: Square Roots of Positive Integers, Lesson 19: Order of Operations with Exponents, Lesson 7: Proportionality in Tables and Graphs, Lesson 10: Rates and Proportional Relationships, Lesson 1: Areas of Parallelograms, Triangles, and Trapezoids, Lesson 6: Circumference and Area of a Circle, Lesson 7: Volume and Capacity of a Cylinder, Lesson 10: Parallel Lines and Transversals, Lesson 3: The Cartesian Coordinate System, Lesson 4: Graphing Images Under Translations, Lesson 5: Graphing Images Under Reflections, Lesson 6: Graphing Images Under Rotations, Lesson 8: Equivalent Expressions for the General Term, Lesson 9: Representing Sequences Using Equations, Lesson 4: Solving Equations Using Visual Models and by Inspection, Lesson 5: Solving Equations by Trial and Error, Lesson 6: Solving One-Step Equations Using Algebra, Lesson 7: Solving Two-Step Equations Using Algebra, Lesson 8: Evaluating Expressions and Solving Equations, Lesson 9: Equations with Multiple Variables, Lesson 3: Organizing Data in Tables and Graphs, Lesson 7: Organizing Numerical Data Into Intervals, Lesson 2: Changes in Measures of Central Tendency, Lesson 3: Choosing a Measure of Central Tendency, Lesson 7: Rate of Change on Scatter Plots, Lesson 8: Using Measures of Central Tendency to Make Comparisons, Lesson 4: Using Probabilities to Make Predictions, Lesson 5: Experimental Versus Theoretical Probability, Lesson 7: Simulations Using Probability Models. However, users can access the 2020 Gauss solutions on our. We also combine all three transformations and graph the image of a polygon under a translation, reflection, and rotation on the Cartesian plane. Letters are included beside the unit names to help group the units into similar themes. Rational numbers can be written as fractions or decimals. Continuing our discussion on intersecting lines, in this lesson we explore the angles formed by parallel lines and transversals. In this lesson, we define and explore the notion of complementary events. For more information about the structure and general use of this courseware, see the Course Information unit. Additionally, some focus is given to estimating the values of products. In particular, we use expressions for the general term of a sequence to form equations to represent relationships in sequences. In this lesson, we practise identifying and interpreting information provided in a scatter plot, and drawing conclusions supported by the scatter plot. In this lesson, we explore how to calculate the probability that two independent events occur, for example, the probability that a head is tossed and an even number is rolled. We explore proportional relationships between two quantities and learn how to recognize when a situation is and is not proportional. More information for the organizing teachers is available. A scatter plot is a graph consisting of points which are formed using the values of two variable quantities. We then investigate the side-angle relationship in triangles. What integer is closest in value to 7 3 4 × ? Through their supervisor, each student writing online will be provided a link and a password to access a secure online platform assembled specifically for our 2021 multiple choice contests. Usually, the grade 9—11 contests take place in February, the grade 12 contest takes place in April, and the grade 7—8 contests typically take place in May.