Grade Level: Grade 4

Algebraic Reasoning

Concepts
Patterns and Functions

Enduring Understandings
Patterns in tables and graphs predict outcomes.
A numeric or algebraic expression represents quantitative relationships.
Algebraic representations can be used to solve real world problems.

Skills
Classify patterns as repeating or growing.
   1.)       Construct, describe, extend and analyze a variety of patterns and trends including repeating and growing patterns.
   2.)       Explore extending and comparing arithmetic and geometric sequences.
   3.)       Develop and test generalizations of patterns and relationship.  
Demonstrate the equivalence of both sides of an equation.
   1.)       Use equations to describe the rules for number patterns and to model word problems.
   2.)       Demonstrate equivalence with the commutative, associative and distributive properties of whole numbers.   
Represent possible values using symbols.
   1.)       Use variables to represent quantities in expressions and number sentences.

Numerical & Proportional Reasoning

Concepts
Numeric Relationships, Ratios, Proportion and Number Sense

Enduring Understandings
Place value patterns are repeated in large numbers.
Computational strategies used with whole numbers can be applied to fractions and decimals.
Fractions, decimals, and percents can represent the same quantity.
Proficiency with basic facts aids in estimation and computation with larger and smaller numbers.
Estimation and approximation are useful in judging the reasonableness of answers.
The relationship between addition, subtraction, multiplication and division leads to multiple ways to solve problems.

Skills
Extend whole number place value patterns, models, and notations to include decimals, which are fractions that have denominators that are multiples of ten.
   1.)       Build place value models, draw diagrams and show equivalent representations for 2-, 3-, and 4-digit numbers in expanded and regrouped forms.
   2.)       Build models and describe tenths and hundredths using equivalent ratio, fraction and decimal notation.
Use models and pictures to reveal patterns about equivalent fractions and ratios.
   1.)       Estimate locations and label fractions on number lines and rulers.
   2.)       Build and label a variety of models to represent, compare and order fractional parts of a whole and mixed numbers and to identify ratios and equivalent fractions.
   3.)       Use counting, number patterns and grouping to identify parts of a set.   
Use fractions to represent a ratio or a division problem.
   1.)       Express a division problem as a fraction and describe the relationship between the divisor and the remainder written as a fraction.   
Make comparisons and describe quantitative relationships using ratios.
   1.)       Use models, pictures and number patterns to solve simple problems involving ratios and proportions.   
Use place value concepts and commutative and associative properties to estimate and compute.
   1.)       Use place value models, diagrams, number patterns and number lines to identify, order, round, and compare 2-, 3-, and 4-digit whole numbers to 10,000.
   2.)       Solve practical problems and extend patterns involving 10 and 100 more and less.
   3.)       Use place value concepts, number patterns, the number line, and the commutative and associative properties to develop estimation and computation strategies.
   4.)       Apply and explain a variety of estimation strategies in problem-solving situations to add and subtract 2- and 3-digit numbers with and without regrouping and money amounts less than $10.00.
   5.)       Determine and discuss the reasonableness of an answer and explain why a particular estimation strategy will result in an over or underestimate.
   6.)       Write and solve multi-step word problems, including problems with extraneous or insufficient information.  
Use number patterns, basic facts, rectangular arrays, place value models and the distributive property to multiply and divide.
   1.)       Develop fluency with multiplication and division fact families for all factors 1 through 10.
   2.)       Relate multiplication and division to models with groups and rectangular arrays and begin to identify prime and composite numbers.
   3.)       Explore the property of zero in multiplication and its implication in division.
   4.)       Identify the appropriate operation and write a word problem to match a given addition, subtraction, multiplication or division number sentence and write the matching number sentence to solve a word problem.
   5.)       Use arrays and explore using the distributive property 10 x (5 + 4) = (10 x 5) + (10 x 4) to estimate, multiply and divide 2- and 3-digit numbers by 1-digit factors.
Add and subtract fractions and mixed numbers with like denominators using models, pictures and number sentences.
   1.)       Solve problems involving the addition and subtraction of fractions with like denominators.
   2.)       Use models and pictures to estimate a reasonable answer when adding or subtracting decimals, fractions and mixed numbers.
   3.)       Write and solve word problems involving decimals, fractions and mixed numbers, identify reasonable answers, and match equations to the problems.

Geometry & Measurement

Concepts
Shapes; Geometric Comparisons; Measurement

Enduring Understandings
Relationships exist among the angles, sides, lengths, perimeters, areas, and volumes of geometric figures.
Selection of appropriate measurement tools depends on the task and degree of precision required.

Skills
Describe geometric properties of polygons and solids.
   1.)       Build, draw, describe and classify and compare two- and three-dimensional figures.
   2.)       Analyze two-dimensional shapes and determine lines of symmetry and congruence.
   3.)       Identify translations, reflections and rotations in geometric designs.
   4.)       Classify relationships as parallel or perpendicular.
Find possible pathways between two points using maps that are based on the rectangular coordinate system.
   1.)       Create and read maps and use coordinate systems to specify locations.  
Recognize that patterns exist between measurements of length, perimeter and area of squares and rectangles, as well as dollars to cents.
   1.)       Explore converting inches to feet and feet to yards.
   2.)       Solve practical problems that involve estimation and measurement of length, perimeter, area, volume, capacity, weight, and temperature.
   3.)       Explore relationships between the lengths of sides of rectangles and their areas and perimeters and generalizes the patterns as simple formulas.  
Make precise measurements and use benchmarks to estimate measures.
   1.)       Identify and use the appropriate customary and metric, and non-standard units for measuring length, perimeter, area, weight, time, temperature, volume and capacity.
   2.)       Explore converting from one unit to another when measuring time and solve problems that involve elapsed time using clocks and calendars.
   3.)       Use estimation to predict reasonable answers to measurement problems.
   4.)       Estimate, draw and measure length to the nearest inch, half-inch, quarter-inch and centimeter.

Working with Data: Probability & Statistics

Concepts
Data Relationships; Prediction; Numeric Communication

Enduring Understandings
The type of data determines how data sets can be organized, displayed, and analyzed.
Statistical measures (mean, median, range, mode) provide a numeric picture of data.
Sampling determines the validity of the relationship between experimental and theoretical probability.
Graphical representations and statistical measures can be used to make interpretations and predictions about real world events.

Skills
Organize and analyze categorical and numerical data.
   1.)       Explore a variety of ways to collect, organize, record, analyze and interpret data, identify patterns and trends.
   2.)       Construct and interpret broken line graphs, line plots, bar graphs, picture graphs, glyphs, and simple circle graphs, tables, and charts.
   3.)       Make predictions and defend conclusions based on data.
Describe what is “average” about the characteristics in a data set.
   1.)       Use the range, mode, median and mean to describe features of a data set.  
Determine fair situations and good choices based upon the likelihood of an occurrence.
   1.)       Identify possible outcomes of events using combinations (where order does not matter) and explore situations resulting in permutations (where order does matter.)
   2.)       Conduct probability experiments and express the probability based on possible outcomes, as a fraction.