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. These problems and tasks address portions of the Georgia Performance Standard M6N1, which is shown 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.
M6N1. Students will understand the meaning of the four arithmetic operations as related to positive rational numbers and percents using these concepts to solve problems.
a. Use factors and multiples.
b. Decompose numbers into their prime factorization (Fundamental Theorem of Arithmetic)
c. Determine the greatest common factor (GCF) and the least common multiple (LCM) for a set of numbers.
d. Multiply and divide fractions and mixed numbers.
e. Use fractions, decimals, and percents interchangeably.
f. Solve problems involving fractions, decimals, and percents and justify the process.
g. Evaluate expressions using order of operations including exponents.
REMARKS: M6N1d and M6N1e. Only terminating decimal fractions should be used.
Multiplying multiples of 10:
Fractions on number lines, equivalent fractions, comparing fractions, what fractions mean:
Mixed numbers and improper fractions:
Adding and subtracting mixed numbers:
Relating fractions and decimals:
Percents, decimals, and fractions:
Multiplying fractions (why we multiply fractions the way we do, when we multiply fractions and when we don't):
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