Making Sense of Math

A Word Before We Start....

How does the picture on the left make you feel? Do you agree? Perhaps the statement, "I Love Math" the total opposite of how you feel!

The intention of this newsletter has always been to communicate with parents about topics being taught in math this year. There are many changes this year with new SEs (student expectations). Things are being taught in very different ways than you or I learned them.

These ways may seem strange, but they DO help students understand the WHY behind the process. You can see a bit more about that in the video below.

If you have questions about math, please feel free to email me (aholmgreen@aliceisd.esc2.net) or give my office a call

(664-0981, ext. 81).

I would love to discuss these new strategies with you or perhaps create a video that explains them. Perhaps you have questions about the STAAR test this year.

If you can think of more we can do to be of help, please let me know!

Anna Holmgreen

Director of Instructional Services for Math

Why is Math Different Now

A page has been created to give info about math. I have shared many posts and ideas for teaching math on this site.

Click this link: Alice ISD Mathematics to see the page.

Kindergarten

This six weeks students explore two-dimensional figures, three-dimensional figures and count coins.

• Two-dimensional (flat) figures studied include circles, triangles, rectangles, and squares as special rectangles.
• Students determine the number of sides and vertices for each shape and use these attributes to discern different shapes from one another. Color, texture, and size are not defining attributes of shapes.
• Informal (such as sides and corners) and formal (such as edges and vertices) language is used interchangeably as students identify the attributes of two-dimensional shapes.
• Students distinguish between regular (sides and corners appear equal) or irregular figures (sides and corners appear different or unequal).
• Students also develop spatial reasoning and visualization skills to create circles, triangles, rectangles, and squares using a variety of materials and drawings.
• Students use their knowledge of two-dimensional shapes to identify three-dimensional solids (cylinders, cones, spheres and cubes).
• Students learn that three-dimensional figures have different names than two-dimensional figures (cube not square for example).
• Students also classify and sort a collection of three-dimensional objects and a mixed collection of two- and three-dimensional figures based on their geometric attributes rather than other features such as orientation, color, texture, or size.
• Students explore traditional and special edition pennies, nickels, dimes, and quarters.
• Students use sorting and classifying skills to discern distinguishing features and identify U.S. coins by name. The emphasis in Kindergarten is on identification only and not on value, relationships, or counting collections.

During this six weeks 1st graders work with two and three-dimensional figures, fractions and time.

• Students use formal and informal geometric language to describe the attributes that identify and define circles, triangles, rectangles, squares, rhombuses, and hexagons.
• Students distinguish between attributes that define a two-dimensional figure (sides, vertices) and attributes that do not define a two-dimensional figure (size, color, orientation, texture, etc.) as they sort and classify a collection of two-dimensional shapes.
• They also examine if figures are regular (the sides are equal in length and if the corners are square) and irregular (sides are not the same length).
• Students create and manipulate representations of shapes, as they create circles, triangles, rectangles, squares, rhombuses, and hexagons using drawings and a variety of materials.
• Students compose two-dimensional shapes by joining two, three, or four figures to produce a target shape in more than one way if possible.
• Students partition shapes into two or four parts and describe the resulting parts using words rather than fraction notation.
• Students identify shapes partitioned into two or four equal parts as examples of halves and fourths and figures partitioned into two or four unequal parts as non-examples of halves and fourths.
• Students tell time to the half hour by making connections between one-half of a circle and one-half of the face of an analog clock. Students study digital clocks learning that the number(s) to the left of the colon represents the hour and the numbers to the right of the colon represents the minutes. Students begin to associate the relationship of half of 60 on a number line to half of an hour on a digital clock.
• Students relate the fractional language of time such as “one-thirty is half past one” as they become proficient with telling time to the half hour on both analog and digital clocks.
• Students end the six weeks studying three-dimensional figures, including spheres, cones, cylinders, rectangular prisms (including cubes), and triangular prisms. Students distinguish between attributes that define three-dimensional figures (edges, faces, and vertices) and attributes that do not define three-dimensional figures (size, color, texture, orientation, etc.). Students use formal geometric language to describe defining geometric attributes.

Second graders focus on measurement this six weeks. They are measuring time and also focusing on linear measurement.
• Students read and write time to the nearest one-minute increment using digital and analog clocks.
• Students understand that time is a measurement attribute used to describe the length of time increments.
• Students make connections between the marked and unmarked increments on a number line to the face of an analog clock in order to read time to the nearest minute.
• Students explore the continuous nature of time measurement as it applies to the rotation of hands on an analog clock and the rotation of the digits on a digital clock.
• Students use previous knowledge of fractions and their relationship between common terms used for describing time, such as “a quarter to,” “a quarter past,” or “half-past.” As students explore the concept of a 24 hour day, they are able to distinguish between a.m. and p.m. as they record time. Students are also exposed to a variety of common terms related to a.m. and p.m. (such as sunrise, sunset, dawn, dusk, evening, etc.) and common activities related to each time period.
• Students explore length using concrete models of standard units (inch, foot, yard, centimeter, meter, etc.) in the customary and metric measurement systems.
• Students use concrete tools to measure distances and record the measure to the nearest whole unit.
• Students review locating whole numbers on a number line and extend their understanding to representing whole number distances from zero or any given location on the number line. The relationship between the number line and standard measuring tools is applied as students transition to determining length to the nearest whole unit using rulers, yardsticks, meter sticks, and measuring tapes.
• Students apply their understanding of length, including estimating lengths, to problem-solving situations. Students use benchmarks to estimate solutions (e.g., a finger joint on a thumb is approximately 1 inch, the width of tip of a finger is approximately 1 centimeter, etc.) and use actual measurements to solve problems involving adding and/or subtracting lengths, including finding the distances around the outer edges of objects.

Third graders are working on fractions and measurement this six weeks.

• Students represent equivalent fractions with denominators of 2, 3, 4, 6, and 8 using objects, pictorial models (including strip diagrams and area models), and number lines.
• Students explain that two fractions are equivalent if and only if they are both represented by the same point on the number line or represent the same portion of a same size whole for an area model.
• Students learn the role of the numerator and the role of the denominator. Understandings of the numerator and denominator assist students when comparing fractions.
• Strategies that students begin to develop when comparing fractions include comparing the size of the numerators when the denominators are the same, comparing the size of the denominators when the numerators are the same, and comparing the size of parts and the number of equal sized parts considered when the numerators and/or denominators are not the same.
• Students begin developing the understanding that the smaller the number in the denominator, the larger the size of equal pieces and the larger the number in the numerator, the more equal size pieces being considered.
• Students develop an understanding that although a fraction is composed of a number in the numerator and a number in the denominator, together they represent a single value. Students also justify the comparison of fractions using symbols, words, objects, and pictorial models.
• Students determine the area of rectangles and squares with whole number side lengths by multiplying the number of rows by the number of unit squares in each row.
• Students extend their knowledge of area to determining the area of composite figures by decomposing composite figures into non-overlapping rectangles and determining the area of the original figure.
• Students determine the perimeter of polygons with given side lengths as well as by measuring side lengths with both customary and metric measures.
• They also find a missing length when given the perimeter of a polygon and the remaining side lengths.
• Students determine and use appropriate customary and metric units of measure, including distinguishing between fluid ounces for measuring liquid volume (capacity) and ounces for measuring weight, and determine liquid volume (capacity) and weight in problem situations. Students do not convert between units of measure.
• In this unit, students also solve problems involving addition and subtraction of time intervals in minutes using pictorial models and tools such as analog or digital clocks and number lines. When solving time problems, students should experience situations that require knowing there are 60 minutes in one hour.

This six weeks 4th graders work on geometry and measuring angles (a new skill this year).

• During this unit, students illustrate the measure of an angle as the part of a circle whose center is at the vertex of the angle that is "cut out" by the rays of the angle.
• They learn that a circle is comprised of 360 degrees.They also illustrate degrees as the units used to measure an angle.
• Using a protractor, students determine the approximate measures of angles in degrees to the nearest whole number and also draw angles of a specified measure.
• Given one or both angle measures, students determine the measure of an unknown angle formed by two non-overlapping adjacent angles.
• The concepts of complementary and supplementary angles are embedded within the study of adjacent angles. Within this unit, all angle measures are limited to whole numbers.

Math Muscle...Problem Solving Opportunities

Students in 5-8th grade have an additional opportunity each week to solve problems. These are problems created by the Director of Instructional Services for Math and sent out to teachers. Students work these on a voluntary basis, but those who turn in papers and meet a criteria are given the opportunity to win a prize.

The picture shown here is an example of a recent Math Muscle and the video solution is below.

5th grade students work this six weeks with different forms of data.

• Students represent categorical data with bar graphs and frequency tables.
• Numerical data, including data sets of measurements in fractions or decimals, is represented with dot plots or stem-and-leaf plots.
• Students are introduced to scatterplots as a means to represent discrete paired data.
• Students utilize all of these graphical representations to solve one- and two-step problems.

Students in 6th grade study financial literacy and explore analysis of data.

• Students compare the features and costs of checking accounts and debit cards offered by different local financial institutions.
• They examine fees associated with both checking accounts and debit cards, and they balance a check register associated to a checking account.
• Students also distinguish between credit cards and debit cards. The information included within a credit report is examined and students are expected to explain why it is important to have a positive credit history.
• Students describe the value of credit reports to both the borrower and to the lenders. The salaries of various career choices are explored and the correlation between the salary and required levels of education is analyzed. Students consider this relationship as they calculate the effects of different annual salaries on lifetime income. Various methods to pay for college are examined, including savings, grants, scholarships, student loans, and work-study.
• During this unit, students extend previous knowledge of data representations including dot plots and stem-and-leaf plots, and are formally introduced to histograms, box plots, and percent bar graphs. (Please view the video below to learn about box-plots!)
• Students use graphical representations to describe the shape, center, and spread of the data distribution. Descriptions of shape, center, and spread include skewed right, skewed left, symmetric, mean, median, mode, range, and interquartile range.
• Students also summarize numeric data with numerical summaries, including the measures of center and the measures of spread.
• Categorical data is summarized numerically with the mode and the percent of values in each category and summarized graphically with a percent bar graph. Students also distinguish between situations that yield data with and without variability.
Box Plots • 7th grade students work with solving problems using data represented in bar graphs, dot plots, and circle graphs this six weeks.
• Students use data from random samples to make inferences about a population and compare two populations based on data from random samples, including informal comparative inferences about differences between the two populations.
• Two groups of numeric data are compared using comparative dot plots or box plots by describing their shapes, centers, and spreads. Descriptions of shape, center, and spread include skewed right, skewed left, symmetrical, mean, median, mode, range, and interquartile range.
• Percents are also incorporated within this unit as students calculate the components of a personal budget in conjunction with circle graphs and bar graphs.

This unit reviews concepts previously covered this year and also work with the new financial literacy expectations.
• During this unit, students extend their understanding of solving equations to model and solve one-variable equations with variables on both sides of the equal sign.
• Students use data from a table or graph to determine the rate of change or slope and the y-intercept.
• Students specifically examine the relationship between the unit rate and slope of a line that represents a proportional linear situation.
• Students must identify functions using sets of ordered pairs, tables, mappings, and graphs.
• During this unit, students continue to examine characteristics of linear relationships through the lens of trend lines that approximate the relationship between bivariate sets of data.
• Observations include questions of association such as linear, non-linear, or no association.
• Students use trend lines that approximate the linear relationship between bivariate sets of data to make predictions.
• Students extend concepts of similarity to dilations on a coordinate plane as they compare and contrast a shape and its dilation(s).
• The concept of proportionality is revisited as 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 a dilation on a coordinate plane.
• Properties of orientation and congruence are examined as students generalize the properties as they apply to rotations, reflections, translations, and dilations of two-dimensional figures on a coordinate plane.
• 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 use the Pythagorean Theorem and its converse to solve problems and apply these understandings to the coordinate plane as they determine the distance between two points on the coordinate plane.
• Financial literacy contexts such as calculating and comparing simple and compound interest rates and how those rates affect earnings in a savings account or the total cost of repaying a loan or credit card are embedded in this unit.
• During this unit, students extend their understanding of percent and formulas to compare interest rates, including simple and compound interest, and loan lengths.
• Students investigate the effect of the cost of credit and the total cost of repaying that credit, whether it be with credit cards or loans.
• They will also use an online calculator to compare different payment methods. Students compare the advantages and disadvantages of various payment methods and analyze situations that constitute financial responsibility and irresponsibility.
• Lastly, students estimate the cost of attending a two-year and four-year college and devise a savings plan to pay for the total estimated costs for the first year of attendance.
Dilation

Algebra 1

• During this unit, students analyze quadratic functions by investigating transformations of the quadratic parent function, including reflections in the x-axis, vertical dilations, and vertical translation. Students also analyze the characteristics of the quadratic function and apply quadratic functions to model real-life situations.
• During this unit, students solve quadratic equations using tables, graphs, and algebraic methods (factoring and quadratic formula).
• Students explore the relationships between the x-intercepts and zeros of the quadratic function as well as the real roots and solutions of the quadratic equation. Students use quadratic equations to model and solve problem situations throughout the unit.

Math Dictionaries

I try my best to define words I think parents may need when discussing math with their children. Hopefully you find these useful.

I am going to include some links below to additional online math resources.

Note: If you see "Maths" it isn't a spelling error--that's how they say it in England and Australia!