3-5.1.1 Develop an understanding of multiplication and division concepts and strategies for basic multiplication facts and related division facts.
3-220.127.116.11 Develop concepts of multiplication and division through the use of different representations (e.g. equal-sized groups, arrays, area models, and skip counting on number lines for multiplication, and successive subtraction, partitioning, and sharing for division).
3-18.104.22.168 Use commutative, associative, and distributive properties to develop strategies and generalizations to solve multiplication problems. These strategies will evolve from simple strategies (e.g. times 0, times 1, doubles, count by fives) to more sophisticated strategies, such as splitting the array.
3-22.214.171.124 Apply their understanding of models for multiplication (i.e. equal-sized groups, arrays, area models), place value, and properties of operations (in particular, the distributive property) as they develop, discuss, and use efficient, accurate, and generalizable methods to multiply multidigit whole numbers.
3-126.96.36.199 Apply their understanding of models for division (partitioning, successive subtraction) place value, properties, and the relationship of division to multiplication as they develop, discuss, and use efficient, accurate, and generalizable procedures to find quotients involving multidigit dividends.
3-188.8.131.52 Select and apply appropriate strategies (mental computation, number sense and estimation) for estimating products and quotients or determining reasonableness of results, depending on the context and numbers involved.
3-184.108.40.206 Understand decimal notation as an extension of the base-ten system of writing whole numbers through place-value patterns and models (place-value charts and base-ten blocks) from tenths to hundredths and thousandths, depending on grade level.
3-220.127.116.11 Connect and extend their understanding of fractions to modeling, reading and writing decimals (tenths, hundredth and thousandths), that are greater than or less than 1, identifying equivalent decimals, and comparing and ordering decimals. Connect fractions (initially halves, fourths, and tenths, and then fifths, thirds, and eighths) and their equivalent decimals through representations including word names, symbols and models (10 x 10 grids and number lines).
3-5.2.1 Represent and analyze patterns and relationships involving multiplication and division to introduce multiplicative reasoning.
3-18.104.22.168 Build a foundation using multiplicative contexts for later understanding of functional relationships with such statements as, "The number of legs is 4 times the number of chairs" or "A quarter is five times the value of a nickel."
3-22.214.171.124 Make generalizations by reasoning about the structure of the pattern to determine if the patterns are nonnumeric growing, repeating, or multiplicative patterns.
3-5.2.2 Identify the commutative, associative, and distributive properties and use them to compute with whole numbers.
3-126.96.36.199 Explore the commutative and associative properties through models and examples to determine which properties hold for multiplication and division facts and develop increasingly sophisticated strategies based on these properties and the distributive property to solve multiplication problems involving basic facts.
3-188.8.131.52 Use properties of addition and multiplication to multiply and divide whole numbers and understand why these algorithms work.
3-184.108.40.206 Relate two-dimensional shapes to three-dimensional shapes and analyze properties of polyhedral solids, describing them by the number of edges, faces, or vertices as well as the types of faces.
3-220.127.116.11 Understand attributes and properties of two-dimensional space through building, drawing and analyzing two-dimensional shapes and use the attributes and properties to solve problems, including applications involving congruence and symmetry.
3-18.104.22.168 Recognize area as an attribute of two-dimensional regions and that they can quantify area by finding the total number of same-sized units of area that cover the shape without gaps or overlaps.
3-22.214.171.124 Recognize volume as an attribute of three-dimensional space and understand they can quantify volume by finding the total number of same-sized units of volume that fill the space without gaps or overlaps.
3-126.96.36.199 Learn to collect data using observations, surveys and experiments and propose conjectures.
3-188.8.131.52 Design simple experiments to examine their conjectures and justify their conclusions.
3-184.108.40.206 Design investigations to address a question and consider how data collection methods affect the nature of the data set.
3-220.127.116.11 Examine the role of sample size has in predictions about data.
3-5.4.4 Predict the probability of simple experiments and test predictions.
3-18.104.22.168 Examine the probability of experiments that have only a few outcomes, such as game spinners (i.e., how likely is it that the spinner will land on a particular color?), by first predicting the probability of the desired event and then exploring the outcome through experimental probability.