# Making Sense of Math

### AISD Parent Newsletter for Math

## Why This Newsletter?

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

Third Six Weeks: https://www.smore.com/btntg

Fourth Six Weeks: https://www.smore.com/kvgpe

FIfth Six Weeks: https://www.smore.com/s9wzh

Please contact Anna Holmgreen, Director of Instruction for Math, if you have questions.

**THE BLUE BOX BELOW TAKES YOU TO A SURVEY ABOUT POSSIBLE WORKSHOPS FOR PARENTS. PLEASE TAKE A MINUTE TO TAKE THE SURVEY!**

Please click this link to take a short survey about potential workshops to help you help your child with math!

## A Word About the Last Six Weeks

## Elementary Math

## Kindergarten

- identifying measurable attributes of objects, including
**length**,**capacity**, and**weight**. - describing the differences of the attributes between two objects using
**comparative****language**. (less than, more than, lighter than, lightest, longer than, longest, etc.) - Students also work on
**counting**,**problem****solving**, and**graphing**. - Counting now involves an understanding of the relationship between the numbers in the counting sequence.
- Students begin to understand how numbers increase by one during the forward count or decrease by one during the backward count. Because of this understanding, students are able to
**count forward**and**backward**easily**without**the use of objects. - Students transition to reading, writing, and representing numerals
**without**objects or pictures. - Students also transition from one-to-one correspondence to working with
**number****relationships**. These mathematical relationships are applied when students generate and**compare sets of objects**or**compare written numerals**using comparative language. - Students
**instantly recognize quantities**as they compose and decompose numbers. - Students are able to explain the strategies used to
**solve problems with sums and minuends to 10.** - Numeracy concepts extend into
**graphing**. Students draw conclusions about data in both real-object and picture graphs.

## 1st Grade

- Students use
**concrete**,**non-standard measuring tools**(paper clips, cubes, etc.) to measure the length of objects and determine the length of objects to the nearest whole unit and describe the length using numbers and unit labels. - Students also measure the length of an object using two different units of measure and begin to recognize that
and*smaller units require more units to measure**larger sized units require fewer units to measure.* - Students will generate and
**solve****addition**and**subtraction****problems****within 20**using a variety of objects, pictorial models, and strategies. - Students will apply basic fact strategies and properties of operations (additive identity, associative property of addition, and commutative property of addition) to
**add**and**subtract****two**or**three****numbers**, including determining the unknown when the unknown may be any one of three or four terms in the equation. - Students will
**represent**and**explain**their**solution strategies using words, objects, pictorial models, and number sentences**, including explaining the role of the equal sign in an equation.

## 2nd Grade

- Students
**model**,**create**, and**describe****multiplication**and**division**situations where**equal grouping**is involved. - Students use
**repeated addition**or**skip counting**to determine the total number of objects and describe these situations using language such as “3 equal groups of 5 is 15.” - Students extend the understanding of equal grouping situations to include determining the
**area of a rectangle**. - Students discover the relationship between a variety of equal group models and the
**arrangement of the objects**in**rows and columns**to determine area. - Students also use
**concrete**and**pictorial****models**to**represent****problem****situations**such as “15 separated into 3 equal groups makes 5 in each group” or “15 separated into equal groups of 5 makes 3 groups.” - Students begin to see the
**inverse****relationship**and**multiplication**that is similar to the inverse relationship between addition and subtraction.**division** - Students revisit and solidify essential understandings of
**fractions**. - Students
**partition objects into equal parts**and**naming the parts,**including halves, fourths, and eighths,**using words**rather than symbols (e.g., one-half or 1 out of 2 equal parts rather than ). - Students recognize the
**inverse relationship**between the**number of parts**and**the size of each part**and explain this relationship using appropriate mathematical language. - Students determine
**how many parts it takes to equal one whole**, and use this understanding to count fractional parts.

## 3rd Grade

- Students solve
, real-world problem situations that include**one**- and**two**-**step****interpreting categorical data from a graph**(frequency tables, dot plots, pictographs, and bar graphs). - Select appropriate tools, models (pictorial models, number lines, arrays, area models, equal group models), and equations to
. Students analyze a variety of solutions in order to justify and**represent problems and solutions**of a solution.**evaluate the reasonableness** - Students represent
with denominators of*equivalent fractions*and*compare fractions***2, 3, 4, 6**, and**8**presented in real-world situations. - Students determine the
when given a specific point on a**corresponding fraction less than or equal to one****number line**and use number lines and other objects to represent equivalent fractions. - They also explain that two
*fractions are***equivalent**if and only if they**both represent the same point on the number line**or represent the**same portion of a same size whole**for an area model. - Students
.**compare two fractions**with**like numerators**or**like denominators**in problems by reasoning about their sizes and**justify**their**conclusions**using symbols, words, objects, and pictorial models - Students also solve real-world problem situations involving
or a set of objects among two or more recipients using pictorial representations of fractions.*partitioning an object* - Students use multiplication related to the
**number of rows times the number of unit squares**in each row towith whole unit side lengths. Students also explore the relationship between the perimeters of many different polygonal figures (including regular and irregular figures) in order to generalize a method for finding the perimeter of any polygon or the side length of a polygon when given the perimeter and the remaining side lengths.*determine the area of rectangles and squares*

## 4th Grade

- Students revisit and solidify essential understandings of
**fractions**. They relate their understanding of, and**decimal numbers to fractions that name tenths and hundredths****represent both types of numbers as distances from zero on a number line.** - Along with representing fractions, including improper fractions as
**sums of unit fractions**, studentsusing*decompose fractions into sums of fractions with the same denominator**concrete*and*pictorial**models*and record their results with symbolic representations. - Students 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
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, students**reasonableness****compare two fractions with different numerators and different denominators and represent those comparisons using the symbols >, <, or =.** - Solve
**one-, two-, or multistep problems**. - Students apply concepts of addition and subtraction of whole numbers and decimals to solve problems, including situations involving calculating profit.
- Students apply concepts of multiplication and division of whole numbers to solve problems, including division situations that require
*interpreting remainders*. - Students also demonstrate
**solving problems involving intervals of time and money**. **Financial understandings**are discussed and examined by comparing**advantages**and**disadvantages**of**saving**operations; distinguishing between**fixed**and**variable****expenses**; describing how to allocate a weekly allowance among spending, saving, including for college, and sharing; and describing the basic purpose of financial institutions, including keeping money safe, borrowing money, and lending.

## Associative Property of Addition If three or more addends are added, they can be grouped in any order, and the sum will remain the same | ## Commutative Property of Addition if the order of the addends are changed, the sum will remain the same | ## Improper Fraction A fraction that has a numerator larger than the denominator. Improper fractions represent quantities greater than one. |

## Associative Property of Addition

## Commutative Property of Addition

## Least Common Denominator the least common multiple of the denominators of two or more fractions | ## Least Common Multiple (LCM) the smallest multiple that two or more numbers have in common | ## Least Common Numerator the least common multiple of the numerators of two or more fractions |

## Intermediate Math

## 5th Grade

**Students revisit and solidify essential understandings of**

*decimals*.- Students
to determine sums, differences, products, and quotients.**estimate** - They solve situations involving
**addition**and**subtraction**of**decimals****through the thousandths**. - Students
**represent multiplication and division**involving products and quotients using**concrete objects**,**pictorial models**, and**area models**.**Factors may include decimals through the thousandths place as long as the product is only through the hundredths place**.**Division**is limited to. Simplifying numerical expressions is revisited as a means for students to communicate their solution process and to solve problem situations involving decimals.**four-digit dividends**and**two-digit whole number divisors**, with**quotients limited to the hundredths**

**Students revisit and solidify essential understandings of fractions.**

- Students
**estimate**to determine solutions to mathematical and real-world problems involving**addition**,**subtraction**,**multiplication**, and**division**. - Students represent and solve
**addition and subtraction of fractions**withto build to the expectation to add and subtract positive rational numbers fluently.**unequal****denominators****using concrete objects, pictorial models, and properties of operations** - Students use concrete objects and pictorial models to
and**multiply a whole number by a unit fraction***divide a whole number by a unit fraction and a unit fraction by a whole number.*

## Associative Property of Multiplication If three or more factors are multiplied, they can be grouped in any order, and the product will remain the same | ## Commutative Property of Multiplication If the order of the factors are changed, the product will remain the same | ## Distributive Property of Multiplication If multiplying a number by a sum of numbers, the product will be the same as multiplying the number by each addend and then adding the products together |

## Associative Property of Multiplication

## Commutative Property of Multiplication

## Order of Operations the rules of which calculations are performed first when simplifying an expression | ## Divide a whole number by unit fraction | ## Dividing a fraction by a whole number |

## 6th Grade

**Students revisit and solidify essential understandings of proportionality.**

- Students solve and represent problem situations involving
and**ratios**with**rates****scale****factors, tables, graphs, and proportions**. - They represent real-world problems involving ratios and rates, including unit rates, while
**converting units within a measurement system**. - They solve real-world problems to
, to*find the whole given a part**and the percent*, and to*find the part given the whole and the percen*t**find the percent given the part and the whole, including the use of concrete and pictorial models.**

**During this unit, students revisit and solidify essential understandings of equations.**

- Students represent two-variable algebraic relationships, including
**additive**and**multiplicative**relationships, in the form of verbal descriptions, tables, graphs, and equations in the form*y = kx or y = x + b*, and model and solve one-variable, one-step equations that represent problems, including geometric concepts. - Students should also
**solve equations with positive rational number constants**or**coefficients**with an algebraic model. - Students determine the
*sum of the angles of the triangle and how those angle measurements are related to the three side lengths of the triangle*. - Students
*write equations and determine solutions to problems related to area of rectangles, parallelograms, trapezoids, and triangles*.

## Rate a multiplicative comparison of two different quantities where the measuring unit is different for each quantity | ## Ratio a multiplicative comparison of two quantities | ## Scale Factor the common multiplicative ratio between pairs of related data which may be represented as a unit rate |

## Middle School

## 7th Grade

**Students revisit and solidify essential understandings of algebra.**

- Students
with concrete and pictorial models and algebraic representations.**model and solve one-variable, two-step equations and inequalities** to equations and inequalities**Solutions****are represented on number lines and given values are used to determine if they make an equation or inequality true.**- Students are expected to
or constraints within a problem and then, conversely,**write an inequality to represent conditions****when given an inequality out of context, students are expected to write a corresponding real-world problem to represent the inequality.**

**Students revisit and solidify essential understandings of geometry.**

- Students use the
*formulas for circumference and area of a circle* - Students determine the area
**of**consisting of rectangles, triangles, parallelograms, squares, quarter circles, semicircles, and trapezoids.*composite figures* - Students also solve problems involving the
*volume of rectangular and triangular prisms and pyramids.*

## Composite Figure | ## Inequality a mathematical statement composed of algebraic and/or numeric expressions set apart by an inequality symbol | ## Coefficient and Constant Coefficient - a number that is multiplied by a variable Constant - a fixed value that does not appear with a variable |

## 8th Grade

**Students revisit and solidify essential understandings of algebra.**

- Students extend their previous understandings of
*slope and y-intercept*to**represent**.*proportional and non-proportional linear situations*with*tables*,*graphs*, and*equations* - Students specifically
**examine the relationship**between thethat represents a proportional linear situation.**unit rate and slope of a line** - Students are expected to
**identify the values of**that simultaneously satisfy two linear equations in the form*x*and*y**y*=*mx*+*b**from the intersections of the graphed equations*. Students must also*verify these values algebraically* - Students
*identify proportional and non-proportional linear functions* - Students continue to
through the lens of**examine****characteristics of linear relationships**that approximate the relationship between bivariate sets of data.**trend lines** - Students contrast graphical representations of bivariate sets of data that suggest linear relationships with bivariate sets of data that do not suggest a linear relationship.
are constructed from bivariate sets of data and used to describe the observed data. Observations include questions of association such as**Scatterplots**,**linear**-**non**, or**linear****no association.**- Within a scatterplot, students use the
of the line that models the relationship as the unit rate of the scenario.*trend line of a linear proportional relationship to interpret the slope*

## Bivariate Data data relating two quantitative variables that can be represented by a scatterplot | ## Discrete data data with finite and distinct values, no inclusive of in-between values | ## Proportional and Non-proportional |

## Algebra 1

**During this unit, students analyze a variety of real-world situations involving**

*linear*,*quadratic*,*exponential*, and*inverse*functions.- Data is analyzed using various models, including
,**graphs**,**tables****verbal**, and*representations***algebraic**. Characteristics of the function are defined in terms of the problem situation. Linear equations, inequalities, and systems of equations are used to determine solutions to problem situations involving linear functions.**generalizations** are used to determine solutions to problem situations involving quadratic functions. Tables and graphs are used to make predictions in problem situations involving exponential and inverse functions. Students make and justify predictions and conclusions in terms of the problem situation.**Quadratic equations**

**During this unit, students apply the concepts of linear functions to analyze collected data from a real-world situation**.

- Students
*represent the collected data using tables, graphs, verbal descriptions, and algebraic generalizations*. - Students
in terms of the problem situation.*analyze the characteristics of the linear functions* - Students
*formulate questions that are solved by equations, inequalities, and systems of equations*. - Students
in terms of the problem situations. Students create displays and present their findings.*justify predictions*