Students understand place value of whole numbers and decimals to two decimal places, how these relate to simple fractions, and use concepts of negative numbers.

Skills: 

1.1 Read and write whole numbers in the millions. 

1.2 Order and compare whole numbers and decimals to two decimal places

1.3 Round whole numbers through the millions to the nearest ten, hundred, thousand, ten thousand or hundred thousand" 

1.4 Decide when a rounded solution is called for, and explain why this is the case. 

1.5 Interpret different meanings for fractions including parts of a whole, parts of a set, indicated division of whole numbers and quantities (and measures) between whole numbers on a number line; and relate to simple decimals on a number line. 

1.6 Write tenths and hundredths in decimal and fraction notation and know fractional/decimal equivalents for halves and fourths 

1.7 Write the fraction represented by a drawing of parts of a figure; represent a given fraction using drawings 

1.8 Use concepts of negative numbers 

1.9 Identify the relative position of fractions, mixed numbers, and decimals to two places on the number line

Students extend their use and understanding of whole numbers to addition and subtraction of simple decimals 

Skills: 

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 use rounding to judge the reasonableness of an answer 

Students solve problems involving addition, subtraction, multiplication, and division of whole numbers, including the addition and subtraction of negative numbers, and understand the relationships among the operations 

Skills: 

3.1 Demonstrate understanding of, and the ability to use, standard algorithms for addition and subtraction of multi-digit numbers 

3.2 Demonstrate understanding of, and the ability to use, standard algorithms for multiplying a multi-digit number by a two-digit number and long division for dividing a multi-digit number by a one-digit number; use relationships between them to simplify 

3.3 Solve problems involving multiplication of multi-digit numbers by two-digit numbers 

3.4 Solve problems involving division of multi-digit numbers by one-digit numbers 

Students know how to factor small whole numbers 

Skills: 

4.1 Understand that many whole numbers decompose in different ways

4.2 Know that numbers such as 2, 3, 5, 7, 11 do not have any factors except 1 and themselves, and that such numbers are called prime numbers

Students use and interpret variables, mathematical symbols and properties to write and simplify expressions and sentences 

Skills

1.1 Use letters, boxes, or other symbols to stand for any number in simple expressions or equations 

1.2 Interpret and evaluate mathematical expressions that use parentheses

1.3 Use parentheses to indicate which operation to perform first when writing expressions containing more than two terms and different operations

1.4 Use and interpret formulas to answer questions about quantities and their relationships 

1.5 Understand that an equation such as y = 3x + 5 is a prescription for determining a second number when a first number is given 

Students know how to manipulate equations 

Skills: 

2.1 Know and understand that equals added to equals are equal 

2.2 Know and understand that equals multiplied by equals are equal

Students understand perimeter and area

Skills: 

1.1 Measure the area of rectangular shapes, using appropriate units: square centimeter, square meter, square kilometer, square inches, square yard, square mile. 

1.2 Recognize that the rectangles having the same area can have different perimeters 

1.3 Understand that the same number can be the perimeter of different rectangles, each having a different area" 

1.4 Understand and use formulas to solve problems involving perimeters and are as of rectangles and squares; use these formulas to find the areas of more complex figures by dividing them into parts with these basic shapes

Students use two-dimensional coordinate grids to represent points and graph lines and simple figures

Skills: 

2.1 Draw the points corresponding to linear relationships on graph paper 

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 

Students demonstrate understanding of plane and solid geometric objects

Skills: 

3.1 Identify lines that are parallel and perpendicular 

3.2 Identify the radius and diameter of a circle 

3.3 Identify congruent figures 

3.4 Identify figures that have bilateral and rotational symmetry

3.5 Know the definitions of right angle, acute angle and obtuse angle - understand that 90, 180, 270, and 360 degrees are, respectively, associated with 1/4, 1/2 3/4 and full turns 

3.6 Visualize, describe and represent geometric solids in terms of the number and shape of faces, edges and vertices; interpret two-dimensional representations of three-dimensional objects; and draw patterns for a solid that, when folded, will make a model 

3.7 Know the definitions of different triangles 

3.8 Know the definition of different quadrilaterals 

Students organize, represent and interpret numerical and categorical data, and clearly communicate their findings

Skills: 

1.1 Formulate survey questions, systematically collect and represent data on a number line, and coordinate graphs, tables and charts 

1.2 Identify the mode for sets of categorical data, and the mode, median, and any apparent outlines for numerical data sets 

1.3 Interpret one- and two-variable data graphs to answer questions about a situation 

Students make predictions for simple probability situations 

Skills: 

2.1 Represent all possible outcomes for a simple probability situation in an organized way 

2.2 Express outcomes of experimental probability situations verbally and numerically 

Students make decisions about how to approach problems 

Skills: 

1.1 Analyze problems by identifying relationships, discriminating relevant from irrelevant information, sequencing and prioritizing information, and observing patterns 

1.2 Determine when and how to break a problem into simpler parts

Students use strategies, skills and concepts in finding solutions 

Skills: 

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 using 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 

Students move beyond a particular problem by generalizing to other situations 

Skills: 

3.1 Evaluate the reasonableness of the solution in the context of the original situation 

3.2 Note method of deriving the solution and demonstrate conceptual understanding of the derivation by solving similar problems 

3.3 Develop generalizations of the results obtained and extend them to other circumstances