M.1.2.6 Add and subtract within 1000, concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, and ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds. M.1.3.6 Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. M.1.4.6 Understand ordering and absolute of rational numbers. Interpret statements of inequality as statements the relative position of two numbers on a number line diagram. interpret, and explain statements of order for rational numbers in real-world contexts. Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a situation. Distinguish comparisons of absolute value from statements about order. M.1.2.7 Use value understanding and properties of operations to add and subtract. Mentally add 10 or 100 to a given number 100-900, and mentally subtract 10 or 100 from a given number M.1.3.7 Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use exponents to denote powers of 10. M.1.4.7 Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate.
appropriately when multiplying or dividing quantities. M.1.3.15 Add and subtract numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. M.1.4.15 Analyze proportional relationships and use them to solve and mathematical problems. Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. M.1.3.16 Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem. M.1.4.16 Recognize and represent proportional relationships between quantities. Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. Represent proportional relationships by equations. Explain what a (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate. M.1.3.17 Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Understand a fraction a / b as a multiple of 1 / b. Understand a multiple of a / b as a multiple of 1 / b, and use this understanding to multiply a fraction by a whole number. word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction models and equations to represent the problem. M.1.4.17 Use proportional relationships to solve multistep ratio and percent problems. world
M.4.3.5 Investigate chance processes. Develop an understanding of events as certain, impossible, likely, or unlikely to Understand that probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. M.4.4.5 Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a two-way Construct and interpret a two-way table summarizing data on two categorical variables collected from the same subjects. Use relative frequencies calculated for row or columns to describe possible association between two variables. M.4.3.6 Investigate chance processes. Determine the probability of basic events (e.g., in the results of tossing a coin, rolling a die, or drawing cards from a deck of cards, chance of baby being born on a certain day of week, etc.) and express the likelihood of an occurrence as a ratio, fraction, or percent. M.4.4.6 Use random sampling to draw inferences about a population. Understand that statistics can be used to gain information about a population by examining a sample of the population. Understand that random sampling tends to produce representative samples and support valid inferences. Use data from a random sample to draw inferences a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. M.4.4.7 Draw informal comparative inferences about two populations. Informally assess the degree of visual overlap of two numerical data distributions with similar variability, measuring the difference between the centers by expressing it as a multiple of a measure of variability. Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. M.5 Algebraic Thinking: Students will develop and apply concepts of basic algebra, patterns, relationships, expressions, equations, and functions to explore, analyze, and solve mathematical and real-life problems. M.5.1 Level 0.0-1.9 M.5.2 Grade Level 2.0-3.9 M.5.3 Grade Level 4.0-5.9 M.5.4 Grade Level 6.0-8.9