# Making Sense of Math

### 3rd Six Weeks AISD Parent Newsletter • 2016-2017

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/9k100

Second Six Weeks: https://www.smore.com/v4qx7

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

## Would you like this newsletter emailed to you?

## Acing Math

Some handouts were given, but here is the link where you can find the whole resource.

## Kindergarten

- 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 tha****n 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*.

**See the video below 1st grade info for information on decomposing numbers.**

## Addend The number being added or joined with another number. | ## Minuend The number from which another number will be subtracted. | ## Number Sentence A mathematical statement consisting of numbers, an operation and an equality or inequality symbol. |

## Kinder and 1st Grade Interactive Activities for Computer and iPad

Octa's Rescue practice counting.

Ten Frames - students build number sense and number recognition.

Break Apart - this activity from Greg Tang Math helps students break apart numbers to help add.

Place Value - Help build place value with these interactives.

## First Grade

- 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"

## Open Number Line An empty number line where tick marks are used to indicate landmarks of numbers. | ## Decomposing Numbers Click the link below for a short video. | ## Open Number Line Click the link below for a short video. |

## Second Grade

- 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.

Fractions are the big idea in the next unit. Students:

- 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. Students partition into 2, 4 and 8 equal 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**.

## 3rd Grade

**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. (Ex: Three-fourths = one-fourth + one-fourth + one-fourth)
- 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.

The next unit deals with future financial security as students explore how skills and education needed for jobs may impact 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.

## Denominator The part of the fraction written below the fraction bar that tells the total number of equal parts in a whole or set. | ## Numerator The part of the fraction written above the fraction bar that tells the number of fractional parts being specified. | ## Unit fraction A fraction with a numerator of one. |

## Denominator

## Numerator

## Dividend, Divisor, Quotient The dividend is the number being divided. The divisor is the number you divide by and the quotient is the answer after you divide. | ## Charitable giving Charitable giving is donating to an organization that collects money, goods, or services to groups in need/ | ## Interest A fee paid for the use of someone else's money. Interest paid...money paid for delaying payment. Interest earned...money earned for investing. |

## Dividend, Divisor, Quotient

The divisor is the number you divide by and the quotient is the answer after you divide.

## Charitable giving

## Fourth Grade

During this unit, students with concepts previously learned to:

- solve one-, two-, or multi-step problems involving addition and subtraction of whole numbers and decimals to the hundredths place,
- multiplication of whole numbers up to two-digit factors and up to four-digit factors by one-digit factors,
- division of whole numbers up to four-digit dividends by one-digit divisors with remainders in appropriate contexts.
- This unit further requires students to represent problems using an input-output table and numerical expressions to generate a number pattern that follows a given rule. These identified rules incorporate an algebraic understanding of the relationship of the values in the resulting sequence and their position in the sequence.

The next unit involves geometry

- identify points, lines, line segments, rays, angles and parallel and perpendicular lines.
- classify two dimensional figures using the presence or absence of parallel or perpendicular lines and presence or absence of angles of a specified size.
- identify and draw lines of symmetry and
- identify acute, right and obtuse angles.

## Parallel Lines Lines are parallel if they are always the same distance apart and never meet. | ## Perpendicular Lines Perpendicular lines are those at right angles (90º) to each other. | ## Line SegmentA |

## Line of Symmetry If you can reflect (or flip) a figure over a line and the figure appears unchanged, then the figure has reflection symmetry or line symmetry. The line that you reflect over is called the line of symmetry. A line of symmetry divides a figure into two mirror-image halves. | ## Right Angle A right angle is one that measures 90º. See the definitions below 5th grade for examples of acute, right and obtuse angles. |

## Line of Symmetry

**line**and the figure appears unchanged, then the figure has reflection

**symmetry**or

**line symmetry**. The

**line**that you reflect over is called the

**line of symmetry**. A

**line of symmetry**divides a figure into two mirror-image halves.

## Fifth Grade

- Explore volume as a three-dimensional measure. Students use objects and pictorial models to develop the formulas for volume of a rectangular prism (
*V*=*l*x*w*x*h*and*V*=*Bh*), including the special form for the volume of a cube (*V*=*s*x*s*x*s*). - Students use Reference Chart formulas to represent and solve problems related to perimeter and/or area and volume.
- Classify two-dimensional figures based on the presence or absence of
**parallel**or**perpendicular**lines or angles of a specified size to formally classify two-dimensional figures into sets and subsets using graphic organizers. - Solve problems by calculating conversions within a measurement system.
- Students are introduced to the coordinate plane and its key attributes including the axes and origin. Students graph ordered pairs in the first quadrant of the coordinate plane. Although graphing is limited to the Quadrant I of the coordinate plane, ordered pairs may include any positive rational number, including fractions and decimals.
- Students are expected to graph ordered pairs in the first quadrant of the coordinate plane that are generated from number patterns or an input-output table.
- Number patterns are examined closely as students recognize the difference between
*additive*and*multiplicative*numerical patterns when given in a table or graph. Students use input-output tables and graphs to generate numerical patterns when given a rule in the form*y = ax*(multiplicative numerical pattern) or*y = a + x*(additive numerical pattern).

## Ordered Pair ordered pairs are pairs of numbers. When plotting ordered pairs, the first number is the x-coordinate and the second number is the y-coordinate. | ## Multiplicative and Additive Relationships Multiplicative and Additive Relationships are identified often in input-output tables. To determine the relationship, you must look at the relationship between the x and y variables. |

## Ordered Pair

## Sixth Grade

This six weeks...

- Sixth grade students are formally introduced to proportional reasoning with the building blocks of
**ratios**,**rates**, and**proportions**. - Students generate equivalent forms of
**fractions**,**decimals**, and**percents**using**ratios**, including problems that involve money. - They solve and represent problem situations involving ratios and rates with
**scale factors**,**tables**,**graphs**, and**proportions**. - Students also represent real-world problems involving ratios and rates, including
**unit rates**, while converting units within a measurement system.

Students solve real-world problems using part, percent and whole.

- They find the
**whole**when given part and percent. - Find the
**part**given the whole and the percent. - Find the
**percent**given the part and the whole.

**The concept of proportionality is vital to future understanding of upcoming math concepts in this grade and beyond.**

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.

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.

## Coefficient, Constant, Variable Coefficient - a number multiplied by a variable (4x - 4 is coefficient) Constant - a value that doesn't appear with a variable Variable - a letter or symbol that represents a number | ## Exponent The exponent of a number says how many times to use that number in a multiplication. It is written as a small number to the right and above the base number. In this example: 82 = 8 × 8 = 64 (The exponent "2" says to use the 8 two times in a multiplication.) | ## Prime Factorization Decomposing a number to show it as the product of only prime numbers. Remember, a prime number is one whose only factors are one and itself. (7 is prime because its only factors are 1 and 7.) |

## Coefficient, Constant, Variable

Constant - a value that doesn't appear with a variable

Variable - a letter or symbol that represents a number

## Exponent

It is written as a small number to the right and above the base number.

In this example: 82 = 8 × 8 = 64

(The exponent "2" says to use the 8 two times in a multiplication.)

## Ratio A ratio is a multiplicative comparison of two quantities. For instance, suppose you were going on a field trip and students and teachers were split into groups. There are 20 students and 4 teachers, so each teacher has 5 students. The teacher to student ratio is 1:5 or 1 to 5. | ## Rate A rate is a multiplicative comparison of two different quantities where the measuring unit is different for each quantity. For instance, miles per gallon is considered a rate. The number of people per square mile is also a rate. | ## Scale Factor Scale factor is the multiplicative ratio between two sets of data. For example, suppose School A has 5 sixth grade classes and School B has 10 sixth grade classes. The scale factor comparing A to B is 2. |

## Ratio

**multiplicative comparison**of two quantities. For instance, suppose you were going on a field trip and students and teachers were split into groups. There are 20 students and 4 teachers, so each teacher has 5 students. The teacher to student ratio is 1:5 or 1 to 5.

## Rate

The number of people per square mile is also a rate.

## Seventh Grade

Seventh graders are studying proportional reasoning with ratios and rates through the lens of **constant rates of change**.

- Students are expected to represent constant rates of change given
**pictorial**,**tabular**,**verbal**,**numeric**,**graphical**and**algebraic representations**, including*d = rt*. - Students solve problems involving ratios, rates, and percents.
- They calculate unit rates from rates and determine the constant of proportionality within mathematical and real-world problems.
- Students use proportions and unit rates to convert units between customary and metric measurements.
- Students are also solving problems involving
**percent increase**,**percent decrease**, and**financial literacy**and identify the components of a personal budget.

- Students use data with two variables, to determine constant rates of change given pictorial, tabular, verbal, numeric, graphical and algebraic representations.
- Students are formally introduced to the slope intercept form of equations,
*y*=*mx*+*b*, to represent linear relationships.

## Eighth Grade

S*y*-intercept to **represent proportional and non-proportional linear situations. **Students

- distinguish between proportional and non-proportional linear situations.
- examine the relationship between the unit rate and slope of a line that represents a proportional linear situation
- Students examine graphs of linear equations and the intersection of graphed equations and identify the values of x and y. Students must also verify these values algebraically with the equations.

They use this understanding to explain how small amounts of money, without interest, invested regularly grow over time.

Students also examine how periodic savings plans can be used to contribute to the cost of attending a two-year or four-year college after estimating the financial costs associated with obtaining a college education.

Students are formally introduced to **functions** and must identify functions using sets of ordered pairs, tables, mappings, and graphs.

**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.

## Bivariate data Data for two variables---often represented by a scatterplot. Example: Ice cream sales versus the temperature on that day. The two variables are Ice Cream Sales and Temperature. | ## Discrete data Data that can only take certain values. There is no in-between (for example, you can't have half a student). | ## Linear Relationship A relationship with a constant rate of change represented by a graph that forms a straight line. |

## Bivariate data

Example: Ice cream sales versus the temperature on that day. The two variables are Ice Cream Sales and Temperature.

## Discrete data

## Scatterplot The data is displayed as a collection of points, each having the value of one variable determining the position on the horizontal axis and the value of the other variable determining the position on the vertical axis | ## Scale Factor An image that is transformed by either enlarging or reducing, depending on the scale factor. | ## Scale Factor The common multiplicative ratio between two sets of data. In the picture, the scale factor from the smaller to the larger would be 2, because the corresponding side on the larger is two times the smaller. |

## Scatterplot

## Scale Factor

## Correlation The description between two sets of data. In a linear equation there are three possibilities: positive linear correlation, negative linear correlation and no correlation. | ## Trend Line The line that best fits the data on a scatterplot. |