Mr. Duggan - 7th Grade Mathematics
Seventh grade mathematics builds upon and extends previous concepts including ratios and proportional relationships, the number system, expressions and equations, geometry, and statistics and probability. A solid mathematical foundation of these topics will be achieved through rigorous activities and projects where students will learn through problem solving. Students will be engaged in real-world investigations designed to enhance their thinking skills with a focus on logical reasoning and critical analysis.
45% Classwork & Homework Assignments
(Also includes active Participation, Student Engagement, Accountable Talk, Peer Interaction)
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Current Unit of Study
Numbers and Operations
1. Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.
Using integer chips to model adding integers
Add Integers using the number line.
Subtract Integers using the number line
Subtract integers using the additive inverse.
2. Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.
Multiply and divide integers using the number line
3. Solve real-world and mathematical problems involving the four operations with rational numbers.
Ratios, Proportions and Percents
1. Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units.
Video Link: Unit Rates
Video Link: Fractions and Unit Rates
2. Recognize and represent proportional relationships between quantities.
Video Link: Proportional Graphs.
Video Link: Solve proportions using algebra
3. Use proportional relationships to solve multistep ratio and percent problems.
Expressions, Equations and Inequalities
Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.
Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically.
Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies.
Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.
Additional Video links
Understand Theoretical Probability
Probability of compound events
Independent and Dependent Events
Use random sampling to draw inferences about a population.
1. Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences.
2. Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions.
Draw informal comparative inferences about two populations.
3. Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around 1/2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event.
4. Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability. For example, when rolling a number cube 600 times, predict that a 3 or 6 would be rolled roughly 200 times, but probably not exactly 200 times.
5. Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy. 43
Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events. For example, if a student is selected at random from a class, find the probability that Jane will be selected and the probability that a girl will be selected.
Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process. For example, find the approximate probability that a spinning penny will land heads up or that a tossed paper cup will land open-end down. Do the outcomes for the spinning penny appear to be equally likely based on the observed frequencies?
8. Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.
Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs.
Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. For an event described in everyday language (e.g., “rolling double sixes”), identify the outcomes in the sample space which compose the event.
Design and use a simulation to generate frequencies for compound events. For example, use random digits as a simulation tool to approximate the answer to the question: If 40% of donors have type A blood, what is the probability that it will take at least 4 donors to find one with type A blood? 44
Additional Video links
Equations, Inequalities and Expressions.
Translating verbal expressions to algebraic expressions.
Evaluating algebraic expressions using the order of operations.
Writing and solving equations
Graphing Inequalities on the number line