# Making Sense of Math

### AISD Parent Newsletter for the 3rd six weeks

Each six weeks teachers meet together to analyze the Student Expectations (SEs) being taught. They meet with a consultant and discuss what is taught and how to teach it. These meetings are called "Rollouts". Consider this newsletter a "Parent Rollout".

This newsletter is intended to give parents an idea of what is being covered each six weeks in math and what their students should be learning.

Here are links to the first two six weeks newsletters. Please visit them to access vocabulary you may need.

First Six Weeks: https://www.smore.com/h71kx

Second Six Weeks: https://www.smore.com/v8edc

aholmgreen@aliceisd.esc2.net

## Would you like this newsletter emailed to you?

If you'd like to have this newsletter emailed directly to you each six weeks, please send your email to Anna Holmgreen at aholmgreen@aliceisd.esc2.net and mention the Parent Math Newsletter!

## Kindergarten

Kinder students have been working with the numbers 1-15. In this six weeks they are introduced to the numbers 11-15.

• Students count forward and backward to 15 with and without objects, as well as read, write, and represent the numbers.
• Students also compose and decompose numbers up to 10 using objects and pictures
• They compare sets of objects up to 15 using comparative language and generate a set of objects and pictures that is more than, less than, or equal to a given number.
• When given a number up to 15, students are expected to generate a number that is one more than or one less than the number.
• Students are expected to recite numbers up to 90 by ones beginning with any number.

In the second unit students develop the foundation of operations.

• Students use concrete objects, pictorial models, and acting out a situation to model and represent joining and separating problems involving sums and minuends up to 10.
• Students record their solution using a number sentence and orally explain their solution strategy.
• As students model, represent, and solve addition and subtraction problems, they begin to develop an understanding of the problem solving process that includes understanding the context of the problem situation and the question being asked, forming a plan or strategy, and using the plan or strategy to determine a solution.

During this unit, students extend their knowledge of the base-10 number system by using objects and manipulatives to form multiple groups of tens and ones up to 99.

• Students compose and decompose numbers through 99 (tens and ones) using concrete objects (base-10 blocks, place value disks, etc.), pictorial models, and numerical representations (e.g., expanded form and standard form).
• Students use place value relationships to generate numbers that are more or less than a given number using tools such as a hundreds chart and/or base-10 blocks.
• Students compare whole numbers up to 99 and represent the comparison using comparative language and symbols.
• Students use open number lines to represent the order of numbers.

During the next unit, students continue delving deeply into the place value system.

• Discover numerical patterns in the number system using Various representations (e.g., linking cubes, straw bundles, base-10 blocks, place value disks, hundreds charts, and open number lines)
• Students use place value patterns to determine the sum up to 99 of a multiple of 10 and a one digit number, as well as determining a number that is 10 more or 10 less than a given number.
• Students develop the understanding of cardinal numbers (numbers that tell "how many"

Students analyze attributes of two-dimensional shapes and three-dimensional solids in order to develop generalizations about their properties. Students:

• classify and sort polygons with 12 or fewer sides by identifying the number of sides and number of vertices.
• examine if the sides are equal in length, and if the corners are square.
• use attributes based on formal geometric language to classify and sort three-dimensional solids, including spheres, cones, cylinders, rectangular prism (including cubes as special rectangular prisms), and triangular prisms.
• compose two-dimensional shapes and three-dimensional solids with given properties or attributes.
• decompose two-dimensional shapes into equal or unequal parts and use geometric attributes to identify and name the resulting parts.

In the next unit, students continue to develop spatial visualization skills. They:

• analyze the resulting parts to determine if equal parts exist and name the fractional parts using words rather than symbols (e.g., one-half or 1 out of 2 equal parts rather than).
• discover and explain the relationship between the number of fractional parts used to make a whole and the size of the parts.
• Using concrete models, students recognize how many parts it takes to equal one whole, and use this understanding to count fractional parts beyond one whole.
• Students make connections between counting whole numbers and counting fractional parts as well as extend their understanding of hierarchical inclusion, meaning each prior number in the counting sequence is included in the set as the set increases, to include the sequence of fractional parts.

Students work with fractions less than one in this unit. They understand the numerator as the part and the denominator as the whole. This unit works with denominators of 2, 3, 4 6, and 8.

• Fractions are represented using concrete objects, pictorial models (including strip diagrams), and number lines.
• Students explain the unit fraction as one part of a whole that has been partitioned into 2, 3, 4, 6, or 8 parts and use this understanding to compose and decompose a fraction as a sum of unit fractions.
• Additionally, students represent fractions as halves, fourths, and eighths as distances from zero on the number line. They must also determine a corresponding fraction when given a specified point on a number line.
• Students also solve problems that involving partitioning an object or a set of objects among two or more recipients using pictorial representations of fractions.

During the next unit, students extend their understanding of multiplication and division and the mathematical relationships between these operations.

• They represent multiplication and division of a two-digit number by a one-digit number using arrays, area models, strip diagrams, and equations.
• Students use the commutative (3 x 2 = 2 x 3), associative [ (2 x 3) x 4 = 2 x (3 x 4) ], and distributive [ 2 x (3 +2) = (2 x 3) + (2 x 2) ] properties of multiplication,
• mental math,
• partial products, and the
• standard multiplication algorithm to represent and solve one- and two-step multiplication and division problem situations within 100.

Multiplication problems include determining area of rectangles.

The last unit deals with future financial security as students explore how skills and education needed for jobs may impact potential income. They also deal with how scarcity of resources may impact cost. Students discuss decisions related to planned and unplanned spending including the responsibilities of using credit.

Students list reasons to save and explain the benefits of saving (e.g., saving for college, surviving hard financial times, being prepared for unforeseen expenses, setting goals, etc.). Students also identify decisions regarding charitable giving.

Students relate their understanding of decimal numbers to fractions that name tenths and hundredths, and represent both types of numbers as distances from zero on a number line.

• Along with representing fractions (including those that represent values greater than one) as sums of unit fractions, students decompose fractions into sums of fractions with the same denominator using concrete and pictorial models and record the results with symbolic representations.
• Students represent and solve addition and subtraction of fractions with equal denominators using objects and pictorial models that build to the number line and properties of operations.
• Students evaluate the reasonableness of those sums and differences using benchmark fractions 0, , and 1, referring to the same whole.
• Using a variety of methods to determine equivalence of two fractions underlies students’ abilities to compare two fractions with different numerators and different denominators and represent those comparisons using symbols.

During the second unit, students represent data on a frequency table, dot plot, or stem-and-leaf plot marked with whole numbers and fractions.

Students examine the characteristics of each data representation, as well as compare the similarities and differences between them. This allows students to solve one- and two-step problems using data in whole number, decimal, and fraction form in a frequency table, dot plot, or stem-and-leaf plot.

In this six weeks students add, subtract, multiply and divide numbers including whole numbers and fractions.
• This unit has them add and subtract positive rational numbers fluently to include fractions.
• Students continue to estimate solutions in mathematical and real-world problems. Concrete objects, pictorial models, and properties of operations are used to represent and solve problems involving adding and/or subtracting fractions with unequal denominators referring to the same whole.
• Students also continue to simplify numerical expressions that involve adding and subtracting fractions with unequal denominators.

In the next unit, students represent a product of whole number and a fraction referring to the same whole using concrete and pictorial models, including area models and strip diagrams.

• Students continue to estimate solutions in mathematical and real-world problems.
• Concrete and pictorial models, including area models and strip diagrams, are also used to represent the division of a whole number by a unit fraction and the division of a unit fraction by a whole number.
• Students also continue to simplify numerical expressions that involve all operations with whole numbers, decimals, and fractions, respectively.

During this unit, students transition from using order of operations without exponents, to simplifying numerical expressions using order of operations with exponents, and to generating equivalent numerical expressions.

• Prime factorization is introduced as a means to generate equivalent numerical expressions. Students should recognize that when a number is decomposed into prime and composite factors, the product of the factors is equivalent to the original number.

In this unit they are formally introduced to algebraic expressions.

• Students investigate generating equivalent numerical and algebraic expressions using the properties of operations which include the inverse, identity, commutative, associative, and distributive properties.
• Concrete models, pictorial models, and algebraic representations are used to determine if two expressions are equivalent.
• Students should distinguish between and expression and an equation.
• Equations within this unit are limited to one-variable, one-step equations.
• Constants or coefficients of one-variable, one-step equations may include positive rational numbers or integers.
• Students are expected to write a one-variable, one-step equation as well as write a corresponding real-word problem when given a one-variable, one-step equation.

Concrete models, pictorial models, and algebraic representations are used again as students model and solve one-variable, one-step equations that represent problems, including geometric concepts.

• Students are expected to represent their solution on a number line as well as determine if a given value(s) make(s) the one-variable, one-step equation true.

• During this unit students are introduced to algebraic inequalities.
• Constants or coefficients of one-variable, one-step inequalities may include positive rational numbers or integers.
• Students are expected write a one-variable, one-step inequality as well as write a corresponding real-word problem when given a one-variable, one-step inequality.
• Concrete models, pictorial models, and algebraic representations are used again as students model and solve one-variable, one-step inequalities that represent problems, including geometric concepts.
• Students are expected to represent their solution on a number line as well as determine if a given value(s) make(s) the one-variable, one-step inequality true.

During this unit, students extend concepts of proportionality to two-dimensional figures as they solve mathematical and real-world problems involving similar shapes and scale drawings. Students generalize the critical attributes of similarity which include examining the multiplicative relationship within and between similar shapes.

During this unit, students extend the use of proportional reasoning to solve problems as they are formally introduced to probability concepts.

• Students use various representations including lists, tree diagrams, tables, and the Fundamental Counting Principle to represent the sample spaces for simple and compound events.
• Students select, design, develop, and use various methods to simulate simple and compound events. Students are expected to distinguish between theoretical and experimental data and find the probabilities of a simple event.
• Students analyze and describe the relationship between the probability of a simple event and its complement. Probabilities may be represented as a decimal, fraction, or percent.
• Data and sample spaces are used to determine experimental and theoretical probabilities to simple and compound events.
• Data from experiments, experimental data, theoretical probability, and random samples are used to make qualitative and quantitative inferences about a population. Qualitative and quantitative predictions and comparisons from simple experiments are used to solve problems.

During this unit, students examine characteristics of linear relationships through trend lines that approximate the relationship between bivariate sets of data.

• Students contrast graphical representations of linear and non-linear relationships.
• Scatterplots are constructed from bivariate sets of data and used to describe the observed data.

Observations include questions of association such as linear (positive or negative trend), non-linear, or no association. Students continue to represent situations with tables, graphs, and equations in the form y = kx or y = mx + b, where b ≠ 0. Within a scatterplot that represents a linear relationship, students use the trend line to make predictions and interpret the slope of the line that models the relationship as the unit rate of the scenario.

During this unit, students develop transformational geometry concepts as they examine orientation and congruence of transformations.

• Students extend concepts of similarity to dilations on a coordinate plane as they compare and contrast a shape and its dilation(s).
• Students generalize the ratio of corresponding sides of a shape and its dilation as well as use an algebraic representation to explain the effect of dilation(s) on a coordinate plane.
• Students generalize the properties as they apply to rotations, reflections, translations, and dilations of two-dimensional figures on a coordinate plane. Students must distinguish between transformations that preserve congruence and those that do not.
• Students are expected to use an algebraic representation to explain the effect of translations, reflections over the x- or y- axis, dilations when a positive rational number scale factor is applied to a shape, and rotations limited to 90°, 180°, 270°, and 360°.
• The relationship between linear and area measurements of a shape and its dilation are also examined as students model the relationship and determine that the measurements are affected by both the scale factor and the dimension (one- or two-dimensional) of the measurement.
• Students are expected to generalize when a scale factor is applied to all of the dimensions of a two-dimensional shape, the perimeter is multiplied by the same scale factor while the area is multiplied by the scale factor squared.

## Algebra 1

During this unit, students learn multiple methods for writing equations of lines. They also continue their exploration of linear functions focusing on data collection and the analysis of scatterplots, trend lines, and linear correlation. Students make interpretations, predictions, and critical judgments from the functional relationships based on the data.

During the next unit, students are introduced to solving linear systems using concrete models, tables, graphs, and algebraic methods including substitution and combination. Reasonableness of the solution is justified using various methods.