will increase the ability to select and apply mathematical operations in a variety of contexts to _________ as measured by __________ (state scoring guide, teacher survey, performance assessments, etc.).
Compute with whole numbers. fractions, decimals and integers using paper and pencil, calculators, and computers.
Read, write, order and compare numbers to ,, numbers to ,,, rational numbers, real numbers.
Rote count to________.
Identify number of objects in a set to____________.
Identify numerals in print to ___________.
Match sets to____________.
Match/copy/write numerals to ______________.
Match a numeral to a set of objects.
Write numbers in numerals and/or words to________________.
"Count on" from___________ to__________.
Count by 's/lo's to .
Demonstrate an understanding of magnitude and relationships of numbers up to . W (). Numbers up to ,,wo (). Very large/very small numbers in the physical world.
Demonstrate numbers of different magnitude using order relations, differences, ratios. Proportions, percents, proportional change and location on the number line.
Indicate position in number sequence using ordinal number names.
Use models to demonstrate meaning and relative size of commonly used fractions.
Demonswate an understanding of and apply place value to ten-thousands, including the use of physical models.
Represent number real numbers using graphs, sketches. diagrams, and manipulatives.
Recognize. Apply and convert among equivalent farms of rational numbers.
Interpret percent as a part of and as means of comparing quantities of different sizes of changing sizes.
Order, compare. Rename, and represent numbers written as percents.
Solve percent problems.
Demonstrate an understanding of integers through applications.
Identify, name and use models m demonstrate meaning and relative size of commonly used fractions (wholes.
Halves. thirds. fourths, eighths).
Demonstrate an understanding of equivalent fractions.
Order and compare fractions with like or unlike denominators.
Solve problems involving equivalent fractions or equal ratios using proportional reasoning.
Demonstrate an understanding of the relationship between improper fractions and mixed numbers.
Add and subtract commonly-used fractions with like/unlike denominators and/or mixed-numbers.
Demonstrate an understanding of the relationships between commonly used decimals and fractions.
Order, compare, rename and represent numbers written as decimal fractions.
Represent numbers in decimal or fraction form and if scientific notation.
Demonstrate fractional and decimal concepts in a variety of contexts including linear measures, areas, sets, and money.
Add and subtract dollars and cents.
Multiply and divide dollars and cents by a whole number.
Add and subtract decimals involving tenths/hundredths/thousandths.
Multiply and divide decimals to thousandths by decimals and whole numbers.
Demonstrate an understanding of the relationship between common fractions and simple percents.
Apply concepts of ratio, proportion and percent in a wide variety of practical and other mathematical situations.
Recognize and use concepts related to multiples, factors, primes, and composites.
Use manipulatives to combine two sets and identify a sum.
Use appropriate terminology when adding two sets.
Use manipulatives to demonstrate digit addition to /.
Use rnanipulatives to remove objects in a set and identify the difference.
Use appropriate terminology when subtracting (e.g., minus, equals, difference, subtract).
Use manipulative to demonstrate single digit subtraction.
Perform whole number calculations using paper and pencil and calculators (including counting on, doubles, neighbors, and properties).
Know and use addition and subtraction fads to .
Add columns of single digits using a variety of computational strategies.
Add and subtract multi-digit numbers. Using a variety of computation strategies including algorithms such as regrouping.
Explain and use mental math strategies to compute and digit addition and subtraction problems.
Demonstrate concepts of addition. Subtraction, multiplication and division with and without calculators, using models or diagrams.
Multiply single digit numbers using a variety of strategies.
Multiply by 's through 's.
Multiply by s through 's.
Know and use the multiplication facts through 's.
Solve multiplication problems (i.e., jumps on a number, counting squares on a grid, combing rods to indicate products) using a variety of strategies. .
Relate basic division facts to inverse of the basic multiplication facts.
Know and use the division facts through 's.
Divide whole numbers with/without remainders, with -digit divisor, and with/without concrete objects.
Perform calculations on whole numbers, fractions, decimals, percents and integers using paper and pencil, calculators and/or computers.
Show place value to ___________ using concrete models.
Apply concepts of place value and grouping in whale number operations, using concrete models.
Solve simulated and real-life problems using number and numeration skills.
Compute and estimate factors to using knowledge of multiples and factors.
Select and use appropriate operations such as addition, subtraction, multiplication and division to solve problems of rational numbers.
Know when and how to use calculators to solve problems.
Explain and use strategies to mentally add, subtract, multiply and divide.
Model, explain and calculate addition. subtraction and simple multiplication with commonly used fractions and decimals using paper and pencil and calculators.
Add. subtract, multiply and divide rational numbers using mental arithmetic. Paper and pencil and calculators.
Use correct order of operations.
Compute the values of powers and roots.
Demonstrate meaning of the four basic operations using diagrams. grid paper, base or other base pieces. Tiles of other manipulates.
Check/verify that results are accurate for a problem.
Perform numeric and algebraic calculations on real numbers using paper and pencil. Calculators, and computer programs.
Demonstrate an understanding of and use a variety of models for operations on real numbers.
Estimate number of objects by matching approximate quantities.
Represent approximate quantities with a symbol.
Estimate the number of objects in a container that holds less than // objects.
Estimate solutions to problems and determine if the results are accurate.
Estimate and check answers using place-value concepts like rounding off and front-end.
Estimate addition and subtraction problems by using a variety of strategies.
Estimate whole number and fraction operations and determine the accuracy of solutions using a variety of strategies.
Estimate solutions to problems involving rational numbers real numbers and determine if the results are accurate and reasonable using a variety of strategies.
Use estimation and/or approximation to make reasonable estimates of quantities to ,.
Round one, two or three-digit numbers to nearest , , and , for addition and subtraction problems.
Round numbers from nearest hundredth to nearest ten thousands place.
Round numbers from the nearest thousandths to nearest millions place and determine when to round up, when to truncate and to which place rounding would be most useful.
Demonstrate an understanding of concept of odd and even.
Apply concepts of primes, factors and multiples in whole number and fractions.
Find, identify and sort numbers by their properties (i.e., odd, even, greater than lesser than, prime, composite, factors, and multiples).
Represent numbers in different forms using: prime factorization, expanded and scientific notation, different bases, exponential notation.
Demonstrate an understanding of properties of commutativity, distributivity and associativity to calculate mentally.
Demonstrate an understanding of properties of rational numbers, e.g., commutativity and associativity (short of formal statements).
Model the relationships among whole numbers, decimal, fraction, percent, exponent and integer operations to solve problems including the relationships involving ratio and proportions.
Solve problems using matrices.
Form and work with algebraic expressions using the properties of addition, subtraction, multiplication, division, exponentiation and root-extraction.
Identify properties of sent of numbers and of patterns using number theory concepts.