National STEM Standards
STEM.M. MATHEMATICS: National Council of Teachers of Mathematics (NCTM)
NCTM.1. Number and Operations
1.3. Compute fluently and make reasonable estimates.
1.3.1. Develop fluency with basic number combinations for multiplication and division and use these combinations to mentally compute related problems, such as 30 x 50.
1.3.2. Develop fluency in adding, subtracting, multiplying, and dividing whole numbers.
1.3.6. Select appropriate methods and tools for computing with whole numbers from among mental computation, estimation, calculators, and paper and pencil according to the context and nature of the computation and use the selected method or tools.
2.3. Use mathematical models to represent and understand quantitative relationships.
2.3.1. Model problem situations with objects and use representations such as graphs, tables, and equations to draw conclusions.
NCTM.11. Grade 4 Curriculum Focal Points
11.1. Number and Operations and Algebra: Developing quick recall of multiplication facts and related division facts and fluency with whole number multiplication
11.1.1. Students use understandings of multiplication to develop quick recall of the basic multiplication facts and related division facts. They apply their understanding of models for multiplication (i.e., equal-sized groups, arrays, area models, equal intervals on the number line), place value, and properties of operations (in particular, the distributive property) as they develop, discuss, and use efficient, accurate, and generalizable methods to multiply multi-digit whole numbers. They select appropriate methods and apply them accurately to estimate products or calculate them mentally, depending on the context and numbers involved. They develop fluency with efficient procedures, including the standard algorithm, for multiplying whole numbers, understand why the procedures work (on the basis of place value and properties of operations), and use them to solve problems.
NCTM.12. Connections to the Grade 4 Focal Points
12.5. Number and Operations: Building on their work in grade 3, students extend their understanding of place value and ways of representing numbers to 100,000 in various contexts. They use estimation in determining the relative sizes of amounts or distances. Students develop understandings of strategies for multi-digit division by using models that represent division as the inverse of multiplication, as partitioning, or as successive subtraction. By working with decimals, students extend their ability to recognize equivalent fractions. Students'' earlier work in grade 3 with models of fractions and multiplication and division facts supports their understanding of techniques for generating equivalent fractions and simplifying fractions.