NUMBER SENSE
1.0 Students understand the place value of whole numbers and decimals to two decimal places and how whole numbers and decimals relate to simple fractions. Students use the concepts of negative numbers:
KINDERGARTEN
1.0 Students understand the relationship between numbers and quantities (i.e., that a set of objects has the same number of objects in different situations regardless of its position or arrangement):
1.1 Compare two or more sets of objects (up to ten objects in each group) and identify which set is equal to, more than, or less than the other.
1.2 Count, recognize, represent, name, and order a number of objects (up to 30).
1.3 Know that the larger numbers describe sets with more objects in them than the smaller numbers have.
2.0 Students understand and describe simple additions and subtractions:
2.1 Use concrete objects to determine the answers to addition and subtraction problems (for two numbers that are each less than 10).
3.0 Students use estimation strategies in computation and problem solving that involve numbers that use the ones and tens places:
3.1 Recognize when an estimate is reasonable.
1.1 Read and write whole numbers in the millions.
Watch this animated math lesson.
Adding Roman numerals.
Subtracting Roman numerals.
Comparing Numbers
1.2 Order and compare whole numbers and decimals to two decimal places.
ASSESSMENT: Ordering and Compring Whole Numbers - Level 4
Rounding
1.3 Round whole numbers through the millions to the nearest ten, hundred, thousand, ten thousand, or hundred thousand.
Watch this animated math lesson on rounding using a number line.
1.4 Decide when a rounded solution is called for and explain why such a solution may be appropriate.
Students have direct instruction on how to estimate whole numbers and how it applies to the real world.
Students apply knowledge of estimating with whole numbers.
Fractions
1.5 Explain different interpretations of fractions, for example, parts of a whole, parts of a set, and division of whole numbers by whole numbers; explain equivalents of fractions (see Standard 4.0).
1.6 Write tenths and hundredths in decimal and fraction notations and know the fraction and decimal equivalents for halves and fourths (e.g., 1/2 = 0.5 or .50; 7/4 = 1 3/4 = 1.75).
Write tenths and hundredths in decimal and fraction notations
Draw lines to match each fraction with its equivalent decimal
1.7 Write the fraction represented by a drawing of parts of a figure; represent a given fraction by using drawings; and relate a fraction to a simple decimal on a number line.
Negative Numbers
1.8 Use concepts of negative numbers (e.g., on a number line, in counting, in temperature, in "owing").
Number Line
1.9 Identify on a number line the relative position of positive fractions, positive mixed numbers, and positive decimals to two decimal places.
2.0 Students extend their use and understanding of whole numbers to the addition and subtraction of simple decimals:
Decimal Numbers
2.1 Estimate and compute the sum or difference of whole numbers and positive decimals to two places.
2.2 Round two-place decimals to one decimal or the nearest whole number and judge the reasonableness of the rounded answer.
Rounding decimals to the nearest whole number.
Rounding decimal numbers
3.0 Students solve problems involving addition, subtraction, multiplication, and division of whole numbers and understand the relationships among the operations:
Computing Numbers
3.1 Demonstrate an understanding of, and the ability to use, standard algorithms for the addition and subtraction of multidigit numbers.
Subtract whole numbers through thousands using place-value models.
3.2 Demonstrate an understanding of, and the ability to use, standard algorithms for multiplying a multidigit number by a two-digit number and for dividing a multidigit number by a one-digit number; use relationships between them to simplify computations and to check results.
We don't multiply this way in "The States."
3.3 Solve problems involving multiplication of multidigit numbers by two-digit numbers.
3.4 Solve problems involving division of multidigit numbers by one-digit numbers.
4.0 Students know how to factor small whole numbers:
Factoring
4.1 Understand that many whole numbers break down in different ways (e.g., 12 = 4 x 3 = 2 x 6 = 2 x 2 x 3).
4.2 Know that numbers such as 2, 3, 5, 7, and 11 do not have any factors except 1 and themselves and that such numbers are called prime numbers.
Click on the apples with prime numbers as they fall from the tree.
ALGEBRA & FUNCTIONS
1.0 Students use and interpret variables, mathematical symbols, and properties to write and simplify expressions and sentences:
KINDERGARTEN
Algebra and Functions
1.0 Students sort and classify objects:
1.1 Identify, sort, and classify objects by attribute and identify objects that do not belong to a particular group (e.g., all these balls are green, those are red).
Variables
1.1 Use letters, boxes, or other symbols to stand for any number in simple expressions or equations (e.g., demonstrate an understanding and the use of the concept of a variable).
Watch this animated math lesson on finding the value of a variable.
Order of Operations
1.2 Interpret and evaluate mathematical expressions that now use parentheses.
1.3 Use parentheses to indicate which operation to perform first when writing expressions containing more than two terms and different operations.
Formulas
1.4 Use and interpret formulas (e.g., area = length x width or A = lw) to answer questions about quantities and their relationships.
1.5 Understand that an equation such as y = 3 x + 5 is a prescription for determining a second number when a first number is given.
2.0 Students know how to manipulate equations:
2.1 Know and understand that equals added to equals are equal.
2.2 Know and understand that equals multiplied by equals are equal.
MEASUREMENT & GEOMETRY
1.0 Students understand perimeter and area:
Perimeter and Area (Watch the video)
KINDERGARTEN
Measurement and Geometry
1.0 Students understand the concept of time and units to measure it; they understand that objects have properties, such as length, weight, and capacity, and that comparisons may be made by referring to those properties:
Students use non-standard units to estimate and measure.
1.1 Compare the length, weight, and capacity of objects by making direct comparisons with reference objects (e.g., note which object is shorter, longer, taller, lighter, heavier, or holds more).
1.2 Demonstrate an understanding of concepts of time (e.g., morning, afternoon, evening, today, yesterday, tomorrow, week, year) and tools that measure time (e.g., clock, calendar).
1.3 Name the days of the week.
1.4 Identify the time (to the nearest hour) of everyday events (e.g., lunch time is 12 o'clock; bedtime is 8 o'clock at night).
2.0 Students identify common objects in their environment and describe the geometric features:
2.1 Identify and describe common geometric objects (e.g., circle, triangle, square, rectangle, cube, sphere, cone).
2.2 Compare familiar plane and solid objects by common attributes (e.g., position, shape, size, roundness, number of corners).
Area & Perimeter
1.1 Measure the area of rectangular shapes by using appropriate units, such as square centimeter (cm2), square meter (m2), square kilometer (km2), square inch (in2), square yard (yd2), or square mile (mi2).
Finding the area of plane figures using grids and formulas.
1.2 Recognize that rectangles that have the same area can have different perimeters.
1.3 Understand that rectangles that have the same perimeter can have different areas.
1.4 Understand and use formulas to solve problems involving perimeters and areas of rectangles and squares. Use those formulas to find the areas of more complex figures by dividing the figures into basic shapes.
2.0 Students use two-dimensional coordinate grids to represent points and graph lines and simple figures:
The Coordinate Grid
2.1 Draw the points corresponding to linear relationships on graph paper (e.g., draw 10 points on the graph of the equation y = 3 x and connect them by using a straight line).
2.2 Understand that the length of a horizontal line segment equals the difference of the x- coordinates.
2.3 Understand that the length of a vertical line segment equals the difference of the y- coordinates.
3.0 Students demonstrate an understanding of plane and solid geometric objects and use this knowledge to show relationships and solve problems:
3.1 Identify lines that are parallel and perpendicular.
3.2 Identify the radius and diameter of a circle.
3.3 Identify congruent figures.
Symmetry
3.4 Identify figures that have bilateral and rotational symmetry.
Angles
3.5 Know the definitions of a right angle, an acute angle, and an obtuse angle. Understand that 90°, 180°, 270°, and 360° are associated, respectively, with 1/4, 1/2, 3/4, and full turns.
Using a protractor to measure angles.
Shapes
Identifying speres, cylindars, cones and cubes.
Visualize, describe, and make models of geometric solids (e.g., prisms, pyramids) in terms of the number and shape of faces, edges, and vertices.
Use nets to recognize the relationship between planes and solids.
Interpret two-dimensional representations of three-dimensional objects; and draw patterns (of faces) for a solid that, when cut and folded, will make a model of the solid.
Click on the solid figure created when the net is folded.
Know the definitions of different triangles (e.g., equilateral, isosceles, scalene) and identify their attributes.
Know the definition of different quadrilaterals (e.g., rhombus, square, rectangle, parallelogram, trapezoid).
Rotate the building until you get the right side view (see the same shape)..
STATISTICS, DATA ANALYSIS, & PROBABILITY
1.0 Students organize, represent, and interpret numerical and categorical data and clearly communicate their findings:
KINDERGARTEN
Statistics, Data Analysis, and Probability
1.0 Students collect information about objects and events in their environment:
1.1 Pose information questions; collect data; and record the results using objects, pictures, and picture graphs.
1.2 Identify, describe, and extend simple patterns (such as circles or triangles) by referring to their shapes, sizes, or colors.
Representing Data
1.1 Formulate survey questions; systematically collect and represent data on a number line; and coordinate graphs, tables, and charts.
How to read a line graph.
Circle graphs.
1.2 Identify the mode(s) for sets of categorical data and the mode(s), median, and any apparent outliers for numerical data sets.
Mean, median, and mode
1.3 Interpret one-and two-variable data graphs to answer questions about a situation.
PROBABILITY
2.0 Students make predictions for simple probability situations:
2.1 Represent all possible outcomes for a simple probability situation in an organized way (e.g., tables, grids, tree diagrams).
Determining the probability of an event and showing it as a fraction.
2.2 Express outcomes of experimental probability situations verbally and numerically (e.g., 3 out of 4; 3 /4).
MATHEMATICAL REASONING
1.0 Students make decisions about how to approach problems:
KINDERGARTEN
Mathematical Reasoning
1.0 Students make decisions about how to set up a problem:
1.1 Determine the approach, materials, and strategies to be used.
1.2 Use tools and strategies, such as manipulatives or sketches, to model problems.
2.0 Students solve problems in reasonable ways and justify their reasoning:
2.1 Explain the reasoning used with concrete objects and/ or pictorial representations.
2.2 Make precise calculations and check the validity of the results in the context of the problem.
Solving Word Problems
1.1 Analyze problems by identifying relationships, distinguishing relevant from irrelevant information, sequencing and prioritizing information, and observing patterns.
1.2 Determine when and how to break a problem into simpler parts.
2.0 Students use strategies, skills, and concepts in finding solutions:
2.1 Use estimation to verify the reasonableness of calculated results.
2.2 Apply strategies and results from simpler problems to more complex problems.
2.3 Use a variety of methods, such as words, numbers, symbols, charts, graphs, tables, diagrams, and models, to explain mathematical reasoning.
2.4 Express the solution clearly and logically by using the appropriate mathematical notation and terms and clear language; support solutions with evidence in both verbal and symbolic work.
2.5 Indicate the relative advantages of exact and approximate solutions to problems and give answers to a specified degree of accuracy.
2.6 Make precise calculations and check the validity of the results from the context of the problem.
3.0 Students move beyond a particular problem by generalizing to other situations:
3.1 Evaluate the reasonableness of the solution in the context of the original situation.
3.2 Note the method of deriving the solution and demonstrate a conceptual understanding of the derivation by solving similar problems.
3.3 Develop generalizations of the results obtained and apply them in other circumstances.
