Grades 6 8 Innoventure Components That Meet Common Core Mathematics Standards

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Joanna Tucker
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1 Grades 6 8 Innoventure Components That Meet Common Core Mathematics Standards Strand Ratios and Relationships The Number System Expressions and Equations Anchor Standard Understand ratio concepts and use ratio reasoning to solve problems. Apply and extend previous understandings of multiplication and division to divide fractions by fractions. Apply and extend previous understandings of arithmetic to algebraic expressions. Individual CCR Standard Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed? Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem Solve real world and mathematical problems involving the four operations with rational numbers. Use variables to represent numbers and write expressions when solving a real world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set. Use variables to represent two quantities in a realworld problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the How This is Met Through Innoventure Students will be responsible for calculating cost per unit of their product based on total materials costs. Depending on their product, students may need to convert imperial measurements to metric to create detailed drawings of the product prior to building it. They will also be building their product, which will likely involved measuring of materials for the purpose of fitting pieces together properly. Students may be building a product to scale. In doing so they will be developing an actual representation of proportionality and needing to verbally describe such proportionality. Students will be building products, which will likely involve measuring. The measurement of materials often includes fractions, including the manipulation of those fractions depending on the final measurement needed. Because building something new does not include directions, they will be first of all creating their own word problems through this activity and then needing to solve them. Students will be building a brand new product. In doing so they will be solving for variables as there will likely be more than one unknown through the process of designing and building the product. Students may be building their product to scale. If doing so, this will necessitate them being able to represent two quantities that will change in relationship to one another. Also, during the phase of building their product they may

2 Functions Geometry Define, evaluate, and compare functions. Use functions to model relationships between quantities. Solve real world and mathematical problems involving area, surface area, and volume. other quantity, thought of as the independent variable. 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 Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real world and mathematical problems. Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = l w h and V = b h to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real world and mathematical problems. need to change the relationship between two distinct parts of their mechanism, indicating a dependent and independent variable during this testing of the product. The building of a new product, without instructions, will ensure that students are completing multi step, real life mathematical problems. Through a process of trial and error as they build from scratch, they will understand better the strategic use of mathematical tools. They will also begin to use estimation and mental computation as they work on their product. Depending on the project students are creating, they may or may not be meeting this standard. Depending on the product created, area may be a key measurement of the product. Depending on the product created, volume may be a key measurement of the product. Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing Students will be creating technical drawings of their products. They will be labeling measurements of the product and representing it in as accurate a fashion as possible.

3 Statistics and Probability Summarize and describe distributions. at a different scale. Solve real world and mathematical problems involving area, volume and surface area of two and threedimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. 5. Summarize numerical data sets in relation to their context, such as by: a. Reporting the number of observations. b. Describing the nature of the attribute under investigation, including how it was measured and its units of measurement. c. Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered. As it is a technical drawing and their product is likely to be a different measurement than one represented in the drawing, they will be practicing converting a scale drawing and representing it in actuality in a different scale. When building, students may need to find a variety of geometrical measurements of their product. These products will be unique shapes, requiring students to find ways to measure the area and volume by deconstructing their product into the various geometric shapes so they are able to measure the area and volume of their products. Students will be creating a survey and recording the survey responses. The manner in which the responses are recorded will demonstrate the ability to describe and summarize statistical data. 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. Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Students will be creating and conducting a survey which will be used to infer information about a target market population to which they will be marketing their product. High School Innoventure Components That Meet Common Core Mathematics Standards

4 Strand Anchor Standard Individual CCR Standard How This is Met Through Innoventure Number and Quantity Reason quantitatively and use units to solve problems. Perform operations on matrices and use matrices in applications. Use units as a way to understand problems and to guide the solution of multi step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays. Innoventure is a multistep project that will require students to reason quantitatively and represent quantities in unit measurements. Depending on their product they may interpret their data in any manner of ways including graphs and other data displays. Algebra Functions Geometry Statistics and Probability Seeing Structure in Expressions Arithmetic with Polynomials and Rational Expressions Creating Equations Reasoning with Equations and Inequalities Interpreting Functions Building Functions Linear, Quadratic, and Exponential Models Trigonometric Functions Make geometric constructions Visualize relationships between two dimensional and three dimensional objects Summarize, represent, and interpret data on a single count or measurement Use matrices to represent and manipulate data, e.g., to represent payoffs or incidence relationships in a network. Make formal geometric constructions with a variety of tools and methods Identify the shapes of two dimensional cross sections of three dimensional objects, and identify three dimensional objects generated by rotations of two dimensional objects. Represent data with plots on the real number line Matrices may be used to manipulate data they collect as they work on their product depending on the research they do which will be unique to the project. Depending on the students individual products they are building and creating, algebraic standards may or may not be met through Innoventure. Depending on the students individual products they are building and creating, function standards may or may not be met through Innoventure. Students will build a product using a variety of tools and creating a three dimensional shape. Students will use a two dimensional technical drawing to create a three dimensional object. This will require skill in understanding the different views and cross sections of the object. Students will develop and conduct a survey. The data collected can be used and represented to meet this standard.

5 Modeling variable Make inferences and justify conclusions from sample surveys, experiments, and observational studies While there are no anchor standards for Modeling, it is an important standard for mathematical practice. Recognize the purposes of and differences among sample surveys, experiments, and observational studies; Understand statistics as a process for making inferences about population parameters based on a random sample from that population. Real world situations are not organized and labeled for analysis; formulating tractable models, representing such models, and analyzing them is appropriately a creative process. Like every such process, this depends on acquired expertise as well as creativity. Students will develop and conduct a survey. They will also be conducting testing on their product as well as observing to collect data. Innoventure is key in helping students to understand realworld situations in which they can practice modeling. They will create a solution to a real world problem, collect data about that problem and analyze how their solution will impact the problem. They must test out different products and solutions to the problem to arrive at the best one.

TenMarks Curriculum Alignment Guide: EngageNY/Eureka Math, Grade 7

TenMarks Curriculum Alignment Guide: EngageNY/Eureka Math, Grade 7 EngageNY Module 1: Ratios and Proportional Relationships Topic A: Proportional Relationships Lesson 1 Lesson 2 Lesson 3 Understand equivalent ratios, rate, and unit rate related to a Understand proportional