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
- 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.
- 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 smaller units require more units to measure and 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.
- 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 multiplication and division that is similar to the inverse relationship between addition and subtraction.
- 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.
- Students solve one- and two-step, real-world problem situations that include 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 represent problems and solutions. Students analyze a variety of solutions in order to justify and evaluate the reasonableness of a solution.
- Students represent equivalent fractions and compare fractions with denominators of 2, 3, 4, 6, and 8 presented in real-world situations.
- Students determine the corresponding fraction less than or equal to one when given a specific point on a 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 partitioning an object or a set of objects among two or more recipients using pictorial representations of fractions.
- Students use multiplication related to the number of rows times the number of unit squares in each row to determine the area of rectangles and squares with 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.
- Students revisit and solidify essential understandings of fractions. They 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 improper fractions as sums of unit fractions, students decompose fractions into sums of fractions with the same denominator using 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 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, students 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
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
- Students estimate to determine sums, differences, products, and quotients.
- 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 four-digit dividends and two-digit whole number divisors, with quotients limited to the hundredths. Simplifying numerical expressions is revisited as a means for students to communicate their solution process and to solve problem situations involving decimals.
- 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 with unequal denominators using concrete objects, pictorial models, and properties of operations to build to the expectation to add and subtract positive rational numbers fluently.
- Students use concrete objects and pictorial models to multiply a whole number by a unit fraction and 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
- Students solve and represent problem situations involving ratios and rates with 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 find the whole given a part and the percent, to find the part given the whole and the percent, and to 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.
a multiplicative comparison of two different quantities where the measuring unit is different for each quantity
a multiplicative comparison of two quantities
the common multiplicative ratio between pairs of related data which may be represented as a unit rate
- Students model and solve one-variable, two-step equations and inequalities with concrete and pictorial models and algebraic representations.
- Solutions to equations and inequalities are represented on number lines and given values are used to determine if they make an equation or inequality true.
- Students are expected to write an inequality to represent conditions or constraints within a problem and then, conversely, 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 to solve problems.
- Students determine the area of composite figures consisting of rectangles, triangles, parallelograms, squares, quarter circles, semicircles, and trapezoids.
- Students also solve problems involving the volume of rectangular and triangular prisms and pyramids.
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
- 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 the unit rate and slope of a line that represents a proportional linear situation.
- Students are expected to identify the values of x and y that simultaneously satisfy two linear equations in the form y = mx + b from the intersections of the graphed equations. Students must also verify these values algebraically with the equations that represent the two graphed linear equations
- Students identify proportional and non-proportional linear functions in mathematical and real-world problems.
- Students continue to examine characteristics of linear relationships through the lens of trend lines that approximate the relationship between bivariate sets of data.
- 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.
- Scatterplots are constructed from bivariate sets of data and used to describe the observed data. Observations include questions of association such as linear, non-linear, or no association.
- Within a scatterplot, students use the trend line of a linear proportional relationship to interpret the slope of the line that models the relationship as the unit rate of the scenario.
data relating two quantitative variables that can be represented by a scatterplot
data with finite and distinct values, no inclusive of in-between values
Proportional and Non-proportional
- Data is analyzed using various models, including graphs, tables, verbal representations, and algebraic generalizations. 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.
- Quadratic equations 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.
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 analyze the characteristics of the linear functions in terms of the problem situation.
- Students formulate questions that are solved by equations, inequalities, and systems of equations.
- Students justify predictions in terms of the problem situations. Students create displays and present their findings.