Problems and tasks for 6th graders
by Sybilla Beckmann, Department of Mathematics, University of Georgia
The linked problems and tasks are ones I gave (or modifications of ones I gave) to the average class of 6th graders I taught every day during the 2004/2005 academic year at Clarke Middle School, a public school in Athens, Georgia. I have organized these problems and tasks according to the grade 6 Georgia Performance Standards, which are listed below. All linked problems and tasks are copyright Sybilla Beckmann, 2004, 2005. Teachers may freely copy and use these problems and tasks with their students. The Georgia Department of Education may use these problems and tasks for the Georgia Performance Standards.
Students will understand the meaning of the four arithmetic operations as related to positive rational numbers and percents and will apply these skills in real world situations. They will also use the order of operations to evaluate expressions.
Students will understand the systems of units for measuring perimeter, area, and volume. They will also understand how to measure the volume and surface area of solid figures. Students will understand the systems of units of measuring (customary and metric) and measure quantities efficiently.
Students will further develop their understanding of geometric figures.
Students will investigate relationships between two quantities that vary.
M6D. Data Analysis and Probability
Students will represent and analyze data and make predictions from investigations. Students will also demonstrate understanding of statistics by representing, investigating, and using data.
M6P. Process Skills
Students will apply mathematical concepts and skills in the context of authentic problems and will understand concepts rather than merely following the sequence of procedures. They will also use the process standards as a way acquiring and using content knowledge.
M6P1. Using appropriate technology, students will solve problems that arise in mathematics and in other context.
a. Solve non-routine word problems using all strategies learned in previous grades.
b. Solve single and multi-step routine word problems related to all appropriate sixth grade math standards.
c. Determine the operation(s) needed to solve a problem.
d. Determine the most efficient way to solve a problem (mentally, paper/pencil, or calculator).
M6P2. Students will investigate, develop, and evaluate mathematical arguments.
M6P3. Students will use the language of mathematics to express ideas precisely.
M6P4. Students understand how mathematical ideas interconnect and build on one another and apply mathematics in other content areas.
M6P5. Students will create and use pictures, manipulatives, models and symbols to organize, record, and communicate mathematical ideas.
Terms/Symbols: positive rational numbers, factors, multiples, decompose, prime numbers, prime factorization, Fundamental Theorem of Arithmetic, GCF, LCM, evaluate, exponents, surface area, metric system of measurement, customary system of measurement, proportional relationships, right prism, cylinder, pyramid, cone, geometric solid, net, geometric figures, line symmetry, rotational symmetry, similar plane figures, scale factor, scale drawings, function, relations, varying quantities, ratio, direct proportion, proportions, proportional reasoning, frequency distributions, pictographs, histograms, bar graphs, line graphs, circle graphs, line plot, frequency table, experimental probability, theoretical probability, sampling, event, random sample, population, non-routine word problems
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