Math problem-solving skills at Green Bank Elementary-Mid Grade progress in complexity across the grades, building upon foundational concepts. Here's a comparison based on the sources:
Grade 1:
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Focus on basic skills like identifying numbers to 99 and 999, comparing numbers to 100
, and identifying value of coins.●
Introduction to measurement, including measuring length, and estimating length with nonstandard measures.
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Reasoning logically and identifying outcomes are introduced.
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Computation begins with addition and subtraction.
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Identifying equivalent amounts of money is an early skill.
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Students learn to identify models divided into equal parts.
Grade 2:
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Number sense expands to identifying numbers up to 1000, and identifying numbers from expanded notation
.●
Counting skills advance with skip counting
.●
Money skills develop further with counting coins and determining change.
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Measurement skills include measuring length and determining elapsed time.
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Students learn about fractions.
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Students learn to identify place value.
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Students learn to recognize the commutative property
and identity element.●
Reasoning logically continues.
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Computation includes subtraction with regrouping and two and three digit addition.
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Students begin to identify plane figures and components of figures.
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Students learn about geometric patterns.
Grade 3:
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Students begin to work with number sentences that represent inverse operations and the commutative property of multiplication.
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Multiplication is introduced, with an understanding of it as repeated addition.
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Students are expected to interpret bar graphs, tally charts and solve problems with non-routine strategies.
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They begin to compare and order fractions, and decimal fractions.
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They learn to estimate using front-end estimation and compatible numbers.
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Geometric skills include identifying congruent figures, components of figures, and completing geometric patterns.
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They learn about length, area and time.
Grade 4:
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Students learn to compare numbers and sets to 9999 and order numbers to the same value
. They also name numbers to 9999.
●
Place value skills include identifying the place value of a digit in a whole number.
●
Measurement skills include estimating and measuring length using customary and metric units, reading thermometers, comparing areas and identifying elapsed time.
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Money skills expand to counting and trading coins and bills, and identifying correct change.
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They learn to solve problems using non-routine strategies, and to identify missing information.
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Students learn to identify the operations needed to solve problems.
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They learn about probability including identifying the most and least likely outcomes, and making predictions from a sampling.
●
They are introduced to number sentences that represent the inverse operation of a given number.
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Students work with fractions, including identifying a fraction model that is part of a group.
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They learn to identify symmetry and coordinate locations.
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They are introduced to decimals, including identifying the place value of a digit in a decimal fraction.
Grade 5:
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Students work with equivalent fractions and learn to compare and order decimals.
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They work with alternative representations of fractions and decimals.
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They learn to identify the place value of a digit in a decimal.
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They learn to identify a number that is 100 more or 100 less than a given number.
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They learn to identify missing elements in geometric patterns and numeric patterns.
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Students are taught about probability and learn to predict outcomes and use combinations and permutations.
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They learn to solve problems using non-routine strategies and identify missing information.
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They learn to convert between units within the same system.
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They are introduced to measures of central tendency and dispersion.
●
They learn to compare areas.
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Students use estimation in problems with decimals and money.
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They learn to determine measurements indirectly from scale drawings.
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They are introduced to transformations (translations, rotations, reflections).
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They learn to classify polygons.
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They learn to extrapolate from line graphs, bar graphs and tables.
Grade 6:
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Students work with number sentences representing inverse operations.
●
They learn to identify equivalent fractions and alternative representations of fractions.
●
They learn to identify the place value of a digit in a decimal.
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Students learn to determine combinations and permutations and identify probabilities.
●
They work with measures of central tendency and dispersion and extrapolate from a circle graph.
●
They are expected to solve problems using non-routine strategies.
Grade 7:
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Students learn to solve linear equations, and evaluate linear expressions
.
●
They learn to identify equivalent expressions representing the associative property
.
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Students learn to identify integers on a number line
.
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They work with numbers expressed in scientific notation, and identify powers and square roots
.
●
They learn to solve problems involving rate or proportion and find the output of functions
.
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Students learn to identify probabilities and to determine combinations and permutations, and predict outcomes
.
●
They learn to identify missing information.
●
They learn to read and interpret tables and multiple-line graphs, and to extrapolate from tables.
●
They learn to calculate volume, circumference, and to measure length.
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They learn to identify parallel and perpendicular lines.
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They work with alternative representations of decimals and fractions.
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They learn to classify polyhedrons and angles.
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They learn to determine measurements indirectly from scale drawings.
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They learn to identify radius and diameter.
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They learn to distinguish between prime numbers and other numbers.
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They learn to identify integers greater than or less than negative numbers.
Grade 8:
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Students learn to identify an algebraic expression equivalent to a problem expressed in words and the meaning in words of an algebraic equation.
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They learn to use a statistical sampling to make a prediction and to use a pie graph to make predictions.
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They learn to determine combinations and permutations and to identify probabilities.
●
Students learn to solve problems using non-routine strategies and identify missing information.
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They learn to extrapolate from bar graphs, read scattergrams and stem-and-leaf charts.
●
They work with measures of central tendency and dispersion.
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Students learn to calculate area and volume and identify radius and diameter.
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They work with alternative representations of fractions.
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They learn to classify polyhedrons.
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They learn to distinguish between prime numbers and other numbers
.
In summary, math problem-solving at Green Bank progresses from basic number recognition and counting in the early grades to more complex concepts such as algebra, geometry, and statistics by grade 8. Each grade level builds upon previous knowledge, introducing new skills and reinforcing existing ones, moving from concrete to abstract reasoning, while working with increasingly difficult numbers and operations.
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