Resources 6th Grade Math Quarter 1 Check-Ins (2017-18)

The following resources provide an opportunity to address the standards assessed on this quarter’s check-in. Ratios & Proportional Relationships 6.RPUnderstand ratio concepts and use ratio reasoning to solve problems.6.RP.3 Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. a. Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the

tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios. b. Solve unit rate problems including those involving unit pricing and constant speed.

Tasks from Illustrative Mathematics

Ticket BoothHunger Games versus DivergentRunning at a Constant SpeedWhich detergent is a better buy?

Lesson from Mathematics Assessment Project

Using Proportional ReasoningThis lesson unit is intended to help you assess how well students are able to reason proportionally when comparing the relationship between two quantities expressed as unit rates and/or part-to-part ratios. In particular, it will help you assess how well students are able to:

Describe a ratio relationship between two quantities. Compare ratios expressed in different ways. Use proportional reasoning to solve a real-world problem.

The Number System 6.NSApply and extend previous understandings of multiplication and division to divide fractions by fractions.6.NS.1 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.

Tasks from Illustrative Mathematics

Traffic JamDan’s Division StrategyReciprocity

Lesson from Mathematics Assessment Project

Interpreting Multiplication and DivisionThis lesson unit is designed to help students to interpret the meaning of multiplication and division. Many students have a very limited understanding of these operations and only recognize them in terms of ‘times’ and ‘share’. They find it hard to give any meaning to calculations that involve non-integers. This is one reason why they have difficulty when choosing the correct operation to perform when solving word problems.

Compute fluently with multi-digit numbers and find common factors and multiples.6.NS.3 Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.

Tasks from Illustrative Mathematics

Reasoning about Multiplication and Division and Place Value, Part 1Reasoning about Multiplication and Division and Place Value, Part 2Jayden’s SnacksAdding Base Ten Numbers, Part 1Adding Base Ten Numbers, Part 2Adding Base Ten Numbers, Part 3

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Lesson from Mathematics Assessment Project

Using Standard Algorithms for Number OperationsThis lesson unit is intended to help students to make sense of standard algorithms for addition, subtraction, multiplication, and division of positive integers. In particular it should assist them in the following areas:

Improving conceptual understanding of why and how the algorithms work. Developing procedural fluency in carrying out the algorithms. Becoming more able to spot unreasonably sized answers and to debug errors in

procedures.

Expressions & Equations 6.EEApply and extend previous understandings of arithmetic to algebraic expressions.6.EE.1 Write and evaluate numerical expressions involving whole-number exponents.

Tasks from Illustrative Mathematics

The Djinni’s OfferExponent Experimentation 1Exponent Experimentation 2

Lesson from Mathematics Assessment Project

Representing the Laws of ArithmeticThis lesson unit is intended to help you assess how well students are able to:

Perform arithmetic operations, including those involving whole-number exponents, recognizing and applying the conventional order of operations.

Write and evaluate numerical expressions from diagrammatic representations and identify equivalent expressions.

Apply the distributive and commutative properties appropriately. Use the method for finding areas of compound rectangles.

Geometry 6.GSolve real-world and mathematical problems involving area, surface area, and volume.6.G.1 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.

Tasks from Illustrative Mathematics

Painting a BarnFinding Areas of PolygonsAreas of Special Quadrilaterals

Lessons from Utah Middle School Math Project

Section 5.1: Area of PolygonsThis section revolves around finding the area of right triangles, other triangles, special quadrilateral, and polygons. Students begin their work with area by finding area of figures on a graph and counting out unit squares. They learn that when confronted with irregular figures they can decompose and rearrange the figures into shapes that they can easily find the area of. A lot of work is done in this section with developing methods and formulas for finding the area of parallelograms, triangles, and trapezoids. Students do this by finding the area of several different examples of these shapes through transformations and then generalize their methods. Once students are familiar with finding area they turn to finding missing measurements. They use the relationship between a polygon’s dimensions and its area to do so. They use their knowledge of finding area to answer question related to real-world applications and finally work with finding the area of irregular figures by decomposing these figures into triangles, rectangles, and/or trapezoids.

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