# Making Sense of Math

## Why this newsletter? - A message from Anna Holmgreen, Director of Instruction for Mathematics

This year we continue with instruction of the math standards that were revised last year. The state has rearranged the skills to various grade levels and parents may find that things seem more complex than when they were in elementary school!

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.

aholmgreen@aliceisd.esc2.net

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## Kindergarten

In Kindergarten during the first six weeks, students are developing an understanding of the numbers 0-5. Students:

• count forward and backward and reciting numbers up to 30 (beginning with any number).
• compose and decompose numbers up to 5, which means they break apart the number. For example 5 can be represented as 1 and 4, 2 and 3, 1 and 1 and 3, etc. Composing and decomposing numbers is a critical part of number sense.
• name one more or one less than a given number and compare and order numbers.
• model and explain strategies to add and subtract to 5.
• use concrete objects and pictures to act out joining and separating and begin using a number sentence (2 + 3 = 5).

First graders begin the year collecting, sorting and organizing data and representing that information using picture and bar-type graphs to draw conclusions and answer questions from the data.

Next students move on to subitizing, which means instantly recognizing a quantity of a small group of objects. Students:

• explore composing and decomposing quantities to 10 to investigate addition and subtraction operations.
• use words, objects, pictorial models and number sentences to represent and solve real-world problems.
• understand that the expressions on each side of an equals sign represent the same value.

Finally in the first six weeks, students begin telling time to the hour using both digital and analog clocks. This is the first time students have been introduced to the concept.

Students in second grade begin the year extending their understanding of the base-10 system to include the thousands period and numbers up to 1,200. Students:

• compose and decompose numbers through 1,200 as a sum of so many one thousands, so many hundreds, so many tens and so many ones using concrete objects, picture models and numeral representations
• use hundreds charts and base-10 blocks and compare whole numbers
• use number lines to locate, name and order numbers
Students also address patterns and relationships in numbers. This includes basic addition and subtraction facts, fact families, odd and even numbers, place value and value of coins.

Third grade addresses composing and decomposing numbers, but they are responsible for numbers up to 100,000. Students:
• identify their base-10 relationships through the hundred thousands place and compare and order these numbers.
• use concrete objects, pictorial models, and numerical representations to compose and decompose numbers as so many ten thousands, so many thousands, so many hundreds, so many tens and so many ones.
• begin to describe the mathematical relationship between digits in a number (one hundred is 10 tens, one thousand is 10 hundreds, etc.)
• estimate, solve and represent one- and two-step addition and subtraction problems.
• use number lines and place value relationships to round numbers to the nearest 10 or 100.
• use their estimation and mental math strategies to justify the reasonableness of their solutions. These concepts are extended by determining the value of a collection of coins and bills and determining the perimeter of a polygon.

Fourth graders begin the year by extending their understanding of place value patterns. They:

• represent the value of digits through one billion (whole numbers) and decimals to the hundredths using expanded notation and numerals.
• compare and order whole numbers and represent their comparisons using symbols (< or >). When ordering three or more numbers they will include descriptors (greatest/least, ascending/descending, fastest/slowest, etc.)
• locate numbers on a number line
• represent decimals using concrete and visual models (number lines, decimal grids, base-10 blocks) and money
• round numbers in the hundred thousands place using their choice of strategies.
• analyze real-life problem situations to identify vocabulary that indicates estimation (about, close, approximately, etc.).
• make connections between place value and the standard algorithms for adding and subtracting. This includes adding and subtracting decimals including tenths and hundredths.
• examine at the purpose of financial institutions in their financial literacy lessons.
• determine products of a number by 10 or 100 using properties of operations and place value understandings.
• use strategies (mental math, partial products, and the commutative, associative and distributive properties) as well as algorithms to multiply up to a four-digit number by a one-digit number and to multiply a two-digit number by a two-digit number.
• represent problem situations using strip diagrams and with equations with a letter standing for an unknown quantity.

## Intermediate -5th and 6th Grade

During the first six week students in fifth grade work on becoming fluent in solving whole number addition, subtraction, and multiplication problems and proficient in solving whole number division problems. Students:
• estimate to determine solutions using all operations with whole numbers in real-world problems.
• multiply a 3-digit number by a 2-digit number and divide a 4-digit number by a 2-digit divisor.

Students who are not already fluent in their multiplication facts need to practice those to help in problem solving.

In the second unit, students are developing algebraic understanding. They will be introduced to properties of prime and composite numbers. They also:

• examine grouping symbols and solve multi-step problems using an equation with a letter representing an unknown.

These first two units develop important concepts which will be used all year.

Students in sixth grade begin their year generating equivalent forms of fractions, decimals and percents as well as solving real-world problems involving fractions, decimals and percents (including money). Sixth graders:

• use concrete and pictorial models to represent multiples of benchmark fractions and percents. Percents less than or greater than 100% are studied as well as percents with fractional or decimal values.
• work with various forms of numbers including negative numbers
• locate a number on a number line and use the location to compare and order a set of values
• classify numbers as counting numbers, whole numbers, integers, or rational numbers

## Middle School - Gr. 7, 8

Students in grade 7 begin working the year working with sets of rational numbers and solving equations. Students:

• use a visual representation to organize and display the relationship of the sets and subsets of rational numbers, which include counting (natural) numbers, whole numbers, integers, and rational numbers.
• fluently add, subtract, multiply, and divide various forms of positive and negative rational numbers which include integers, decimals, fractions, and percents converted to equivalent decimals or fractions for multiplying or dividing.
• begin working with the new personal financial literacy skills by creating and organizing a financial assets and liabilities record, constructing a net worth statement, calculating sales tax for a given purchase, and calculating income tax for earned wages.

In the next unit, students work with equations and geometry concepts. Students:

• model and solve one-variable, two-step equations and inequalities with concrete and pictorial models and algebraic representations.
• represent solutions to equations and inequalities on number lines and given values are used to determine if they make an equation or inequality true.
• write an equation or inequality to represent conditions or constraints within a problem
• when given an equation or inequality out of context, they are expected to write a corresponding real-world problem to represent the equation or inequality.
• write and solve equations using geometry concepts, including the sum of the angles in a triangle, and angle relationships.
• use equations and inequalities to include problem situations involving monetary incentives such as sales, rebates, or coupons.
• Financial literacy aspects such as calculating and comparing simple and compound interest as well as utilizing a family budget estimator to determine the minimum household budget needed for a family to meet its basic needs is also explored.

The 8th graders also begin the year studying sets and subsets of rational numbers. They:

• use a visual representation, such as a Venn diagram, to describe the relationships between the sets and subsets.
• order a set of rational numbers that arise from mathematical and real-world situations.
• convert between standard decimal notation and scientific notation for both positive and negative numbers and with values greater than and less than one
• order numbers and find the mean to calculate the mean absolute deviation of up to 10 data points
• describe the data by comparing each data point to the mean absolute deviation
• students describe the spread and shape of data by looking at its difference from the mean
• develop the notion that random samples of a population with known characteristics is representative of a population from which it was selected
• explore appropriate methods for simulating such samples.

Finally in unit 3, students:

• extend their understanding of solving equations to model and solve one-variable equations with variables on both sides of the equal sign
• write one-variable equations or inequalities with variables on both sides to represent problems using rational numbers coefficients and constants
• write a corresponding real-world problem for a one-variable equation or inequality with variables on both sides
• calculate and compare simple and compound interest rates and how those rates affect earnings and total cost in repaying a loan or credit card