Math Program
Math Program
Desmos
Desmos
Embedded Files
Math Overview - Grade 6
The Newton Public Schools mathematics program is designed so that every child develops a comprehensive mathematical identity, and learns challenging and relevant mathematics through the development of conceptual understanding, procedural fluency and application. Student success in school mathematics depends on a combination of teacher skill, a strong core program, sufficient time for instruction, teacher-guided exploration of mathematical ideas, individual practice, class discussion, reasoning about mathematical concepts and solving non-routine problems.In 2020, NPS middle schools adopted Desmos, a teaching and learning platform based on the Illustrative Math program. In heterogeneously grouped classrooms, students engage in interactive lessons, the Mathematical Practices and Instructional Routines in order to develop deep understanding of grade level concepts.Math Overview - Grade 6
Unit 1: Area and Surface Area
Unit 1: Area and Surface Area
Learning Targets
Learning Targets
- Calculate areas of polygons by decomposing, rearranging, and composing shapes
- Represent polyhedra with nets and calculate surface areas
Essential Questions
Essential Questions
- How can you calculate the area of a polygon?
- What strategy should you use to determine the surface of a three - dimensional figure?
Instructional Snapshot
Students will:Instructional Snapshot
- Take part in a routine called "Which One doesn't Belong" to focus on reasoning and communication skills, rather than answers
- Make sense of two strategies for determining the area of a parallelogram
- Calculate areas and observe geometric relationships between the two shapes
- Play Polygraph to develop to describe features of polygons
- Cut and fold nets to create polyhedra and calculate surface areas
Unit 2: Introducing Ratios
Unit 2: Introducing Ratios
Learning Targets
Learning Targets
- Describe a ratio relationship between two quantities and identify equivalent ratios
- Use tables, double number line diagrams and unit prices to solve problems with equivalent ratios
- Develop and use strategies to compare ratios in context
Essential Questions
Essential Questions
- What strategies are best for comparing ratios or finding equivalent ratios?
- How can you use ratios to solve real world problems?
- How is finding a unit rate useful when solving problems?
Instructional Snapshot
Students will:Instructional Snapshot
- Create pizzas using an interactive tool to explore ratio concepts
- Explore how to generate equivalent ratios in the context of balancing items on a scale
- Use a paint mixture simulator as a context for thinking about how ratios compare to one another
- Use their personal experiences and ratio reasoning to make sense of a real problem related to school lunch and lunch waste
Unit 3: Unit Rates and Percentages
Unit 3: Unit Rates and Percentages
Learning Targets
Learning Targets
- Use ratio reasoning to convert between units of measurement
- Recognize and calculate two unit rates for the same ratio relationship
- Use unit rates to solve problems involving tables of equivalent ratios
- Make connections between percentages, ratios, and rates
- Use ratio reasoning to determine unknown parts, wholes, and percentages
Essential Questions
Essential Questions
- How do you convert from one unit of measurement to another?
- What are the commonly used measurements for length, area, time, mass, or volume?
- Why does it take more of a smaller unit or fewer of a larger unit to measure the same quantity?
- How do you find a percent of a number? How do percents relate to ratios?
- How can two different unit rates for the same ratio both be useful?
Instructional Snapshot
Students will:Instructional Snapshot
- Consider distances from school given in different units of measurement
- Use equivalent ratios and unit rate to help compare speeds of model trains
- Use an interactive ice cream activity to complete custom orders, considering which unit rate is most helpful
- Play a carnival game to reason about the relationship between the percentage of winners, the number of winners, and the number of total ducks
- Use unit rates to help run a robot factory and complete a table of equivalent ratios
- Use rates and percentages to analyze characteristics of a country's population
Unit 4: Dividing Fractions
Unit 4: Dividing Fractions
Learning Targets
Learning Targets
- Interpret and create diagrams that represent dividing whole numbers by fractions
- Use a variety of strategies to calculate quotients of fractions
- Solve problems that involve dividing fractions
- Use division of fractions to compare lengths
- Solve problems about areas and volumes with fractional dimensions
Essential Questions
Essential Questions
- What are the two ways to think about a division problem?
- How can you estimate the quotient of a division problem involving fractions?
- How can you divide fractions using number sense reasoning?
- What are some different strategies or algorithms for dividing fractions and with what types of problems are they useful?
- How can you apply your understanding of multiplication and division with fractions to solve area and volume problems?
Instructional Snapshot
Students will:Instructional Snapshot
- Reason about what it means to divide by a fraction and make connections between contexts, tape diagrams, and expressions
- Develop strategies for calculating quotients of two fractions, including the use of common denominators
- Divide using an activity that manipulates the number of cookies shared to a number of plates and develop strategies for determining whether a quotient will be greater than 1, less than 1, or equal to 1
- Learn with interactive activities that offer authentic feedback as students investigate dividing a whole number by fractional divisors within a cooking recipe
- Use their creativity to write their own questions to represent division of fractions and then solve their classmates' questions using any of the strategies and tools they have learned in this unit
Unit 5: Decimal Arithmetic
Unit 5: Decimal Arithmetic
Learning Targets
Learning Targets
- Multiply and divide multi-digit decimals using a variety of strategies
- Divide multi-digit numbers with and without remainders using long division
- Use decimal operations to solve problems in context
- Use prime factorization to determine the Least Common Multiple and Greatest Common Factor of two numbers
Essential Questions
Essential Questions
- How do you use decimal arithmetic in everyday life?
- How can you use magnitude estimates to help determine products and quotients of problems involving decimals?
- How can you determine the most efficient strategy or algorithm for a problem?
Instructional Snapshot
Students will:Instructional Snapshot
- Estimate and calculate how much it costs to make dishes for different amounts of people
- Solve missing digit puzzles to practice adding and subtracting multi-digit decimals
- Develop fluency multiplying decimals by completing a scavenger hunt activity
- Use long division to calculate quotients and use decimals to represent remainders
- Analyzing relevant costs of different types of cars in order to decide which kind to purchase
Unit 6: Expressions and Equations
Unit 6: Expressions and Equations
Learning Targets
Learning Targets
- Write and solve equations of the form x+p=q and px=q
- Use the distributive property to write equivalent expressions with variables
- Evaluate numerical and variable expressions with whole number exponents
- Use tables, equations, and graphs to represent relationships
Essential Questions
Essential Questions
- How can you use tape diagrams and reasoning to figure out unknown values in an equation?
- How do balanced hangers help you solve equations?
- How can you determine the value of an equation that has a variable and an exponent for a specific value of the variable?
- What is the difference between the independent and dependent variables in a relationship?
Instructional Snapshot
Students will:Instructional Snapshot
- Use balanced hangers to represent equations and determine unknown values
- Write equivalent expressions to represent the same thing in a context
- Decide if two expressions involving exponents are equivalent and explain the reasoning
- Explore relationships between two variables using tables, equations and graphs to help customers decide what type of transportation to use
Unit 7: Positive and Negative Numbers
Unit 7: Positive and Negative Numbers
Learning Targets
Learning Targets
- Describe locations on the number line using positive and negative numbers
- Compare and order positive and negative numbers and absolute values
- Represent and solve inequalities using symbols, words and graphs
- Draw polygons given coordinates for the vertices
Essential Questions
Essential Questions
- What strategies can you use to identify and plot negative rational numbers on the number line?
- How can you compare positive and negative numbers using words and symbols?
- How can you use inequalities to describe unbalanced hangers?
- How are the locations of points in coordinate planes that differ only by one sign related?
Instructional Snapshot
Students will:Instructional Snapshot
- Compare positive and negative numbers by arranging themselves into groups based on rules related to their given number
- Apply their understanding of positive and negative numbers in the context of elevations and temperatures
- Connect verbal, symbolic and number line representations of inequalities in the context of tunnel heights, comparing weights, and sheep eating grass
- Practice what they know about coordinates to solve mazes and determine distances of polygons in the coordinate plane
Unit 8: Describing Data
Unit 8: Describing Data
Learning Targets
Learning Targets
- Create dot plots, histograms and box plots to visualize data
- Informally describe and compare data sets
- Calculate the mean and mean absolute deviation (MAD) of a data set, and use to describe and compare sets
- Calculate the quartiles, interquartile range (IQR) and range of a data set
Essential Questions
Essential Questions
- What is the difference between categorical and numerical data?
- When do you use dot plots versus histograms to represent data?
- What does the mean absolute deviation represent?
- How can you choose which measure of center best describes a data set?
Instructional Snapshot
Students will:Instructional Snapshot
- Create dot plots and histograms to visualize and compare and contrast data sets
- Play Polygraph to practice data related vocabulary
- Make connections between consistency and the mean absolute deviation in the context of basketball shots
- Use their understanding of mean and mean absolute deviation to compare salaries and consider whether pay is equal based on gender
- Explore measures of center and spread in the context of real world data sets
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