# Making Sense of Math

## Fourth Six Weeks

The year is rapidly flying by and the fourth six weeks is upon us!

I hope this newsletter is helpful for parents. If you would like more explanation on any of the topics mentioned below, please feel free to contact me. I would be happy to visit with you or give you examples.

Anna Holmgreen, Director of Instruction for Math

## Direct Mailing?

If you'd like to have this newsletter emailed directly to you each six weeks, please send your email to Anna Holmgreen at aholmgreen@aliceisd.esc2.net and mention the Parent Math Newsletter!

## Kindergarten

Much of what students are working on this six weeks builds upon previous understandings of numbers. This six weeks kindergarten students are introduced to the numbers 16-20. Students are expected to:

• count forward and backward (with and without objects), as well as read, write, and represent the numbers.
• compose and decompose numbers up to 10 using objects. They instantly recognize the number being represented by a small quantity of objects.
• compare sets of objects up to 20 and generate a set of objects and pictures that is more than, less than, or equal to a given number.
• use comparative language to describe the comparison of numbers represented using objects, pictures, or numerals.
• recite numbers up to at least 100 by ones beginning with any number.
• recite numbers by tens up to at least 100 beginning with any multiple of 10 (e.g., 10, 20, 30, 40, etc.).
Students also revisit sums and minuends to 10.

They also work on the problem-solving process by working repeatedly with real-world problem situations. Students continue to distinguish between joining, separating, and part-part-whole situations and the operation needed to solve the problem. Students:

• orally explain models and representations and justify solution strategies.
• use graphing situations to represent data with numbers 0-20. Students sort and organize the data and the data is used to create real-object and picture graphs. These graphs are examined to understand the components of graphing (e.g., title, labels of categories, what each cell or picture represents, etc.)

During this unit, students extend their understanding of the base-10 place value system to include the hundreds place as they continue exploring the foundations of whole numbers up to 120. Students:

• compose and decompose numbers through 120 as so many hundreds, so many tens, and so many ones using objects, pictures, and numbers
• generate numbers that are more or less than a given number using tools (e.g., a hundreds chart, calendar, base-10 blocks, etc.).
• compare whole numbers up to 120 and represent the comparison using comparison language and comparison symbols.
• extend using place value and open number lines to order whole numbers up to 120.
• recite numbers up to 120 forward and backward by ones and tens; skip count by 2s, 5s, and 10s; and use place value patterns to determine a number that is 10 more or 10 less than a given number.
• identify pennies, nickels, dimes, and quarters by value and record the value using the cent symbol.
• exchange coins or sets of coins for other equivalent denominations.
• apply skip counting by 2s, 5s, and 10s and compound counting to determine the value of a collection of pennies, nickels, and dimes up to 120 cents.
• use data represented in bar-type and picture graphs to represent, generate, and solve problem situations involving sums and minuends up to 20 using spoken words, objects, pictorial models, and number sentences.
• explore and explain strategies to solve one-step problems involving addition, subtraction, and comparison of the data. Students are expected to use a number sentence with the unknown in any position to represent the situation.

• During this unit, students add up to four two-digit numbers or subtract two-digit numbers within 1,000 in real-world problem situations that include calculating how money saved accumulates over time with deposits and withdrawals.These problems should include numbers that require regrouping to solve the problem. In addition, students:
• make connections between representing and solving addition and subtraction problems using flexible methods, concrete and pictorial models, and number sentences to mental strategies and algorithms based on knowledge of place value and properties of operations.
• generate and solve problem situations for a given number sentence involving addition and subtraction of whole numbers within 1,000.
Students should continue to apply addition and subtraction fact strategies and work towards automatic recall and fact fluency.
• Students transition from bar-type graphs to bar graphs and from picture graphs to pictographs. Both vertical and horizontal orientations of bar graphs and pictographs with up to four categories and intervals of one or more are experienced during this unit. Students summarize the existing data, or the inferential data, in bar graphs and pictographs to draw conclusions and make predictions.
• Students also generate and solve one-step word problems based on the information in bar graphs and pictographs with intervals of one.

• During this unit, students solve one- and two-step problems involving addition and subtraction within 1,000 and multiplication and division within 100.
• Students reason through and solve real-world problem situations. Students explain their reasoning and solution strategies using expressions, equations, and precise mathematical language.
• Students solve problems involving multiplication of a two-digit number by a one-digit number and develop fluency using standard algorithms to solve addition and subtraction problems within 1,000.
• Experience real-world situations that involve various operations, including decomposing composite figures to determine area of the original figure.
• Use input-output tables and explore number pairs in tables to determine additive and multiplicative patterns that exist and represent the pattern (or process) using equations and expressions.
• Summarize a set of data using a frequency table, dot plot, pictograph, or bar graph. Students use these data representations to solve one- or two-step problems involving the categorical data represented.
• Sort and classifying two- and three-dimensional figures that may vary in size, shape, and orientation based on attributes using formal geometric language.
• Explore two-dimensional figures and subcategories of quadrilaterals, including rhombuses, parallelograms, trapezoids, rectangles, and squares.
• Decompose two congruent two-dimensional figures into parts with equal areas and express the area of each part as a unit fraction of the whole.

• During this unit, students begin the formal introduction to formulas to determine the perimeter and area of rectangles and squares. Students use models to determine the formulas for the perimeter of a rectangle (l + w + l + w or2l + 2w), including the special form for perimeter of a square (4s) and the area of a rectangle (l x w).
• Identify parallel and perpendicular lines.
• Students are expected to solve problems related to perimeter and area of rectangles where dimensions are whole numbers.
• In addition to solving problems involving length, students also solve problems that deal with measurements of intervals of time, liquid volumes, mass, and money using addition, subtraction, multiplication, or division as appropriate.
• Identify relative sizes of measurement units within the customary and metric systems, and apply this knowledge to conversion of measurements within the same measurement system, customary or metric.
• Identify points, lines, line segments, rays, angles, and perpendicular and parallel lines. These concepts are essential for the ability to classify two-dimensional figures.
• Use formal geometric language such as parallel, perpendicular, acute, obtuse, and right angle to classify two-dimensional figures.
• Additionally, students apply knowledge of right angles to identify acute, right, and obtuse triangles.
• Identify and draw one or more lines of symmetry, if they exist, for two-dimensional figures.

• 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).

• Students graph both positive and negative rational numbers in all four quadrants of the coordinate plane.
• Students are now expected to compare two rules (ex. y = ax or y = x + a) verbally, graphically, or symbolically in order to differentiate between additive and multiplicative relationships.
• Students identify independent and dependent relationships and quantities. Within this unit, students represent a given situation using verbal descriptions, tables, graphs, and equations. Also, given one representation, students should be able to create one or all of the different representations for the problem situation. For this grade level, problem situations for additive relationships may include both positive and negative rational numbers, whereas multiplicative relationships may only include integers or positive fractions or decimals.
• Students extend their knowledge of triangles and their properties to include the sum of the angles of the triangle, and how those angle measurements are related to the three side lengths of the triangle.
• Students examine and analyze the relationship between the three side lengths of a triangle and determine whether three side lengths will form a triangle using the Triangle Inequality Theorem.
• Students also decompose and rearrange parts of parallelograms (including rectangles), trapezoids, and triangles in order to model area formulas for each of the figures.
• Students write equations and determine solutions for problems dealing with area of rectangles, parallelograms, trapezoids, and triangles.
• Students expand previous knowledge of converting units within the same measurement system when determining solutions to problems involving length. Conversion processes for measurement extend beyond the use of proportions to now include dimensional analysis and conversions graphs.

• Students convert between measurement systems, including the use of proportions and the use of unit rates.
• Students are introduced to the measurement of circles as they describe pi as the ratio of the circumference of a circle to its diameter.
• The formulas for circumference and area of a circle are used to solve problems.
• Determine the area of composite figures consisting of rectangles, triangles, parallelograms, squares, quarter circles, semicircles, and trapezoids.
• Students model the relationship between the volume of rectangular prism and a rectangular pyramid.
• Students solve problems involving volume, including the volume of rectangular prisms, triangular prisms, rectangular pyramids, and triangular pyramids.
• Students also solve problems involving surface area by determining the area of the shape's net, including lateral and total surface area of a rectangular prism, rectangular pyramid, triangular prism, and triangular pyramid.

## Gr. 8

• Students extend previous knowledge of sets and subsets to order and describe relationships between sets of real numbers, which includes rational numbers and their subsets as well as irrational numbers.
• Students approximate the value of irrational numbers less than 225 and locate those approximations on a number line.
• Establish facts about the angle sum and exterior angle of triangles, the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles.
• Right triangles are examined more closely within this unit as students use models to explain the Pythagorean theorem. 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.
• Determine the volume of a cylinder in terms of its base area and height. Students are expected to model the relationship between the volume of a cylinder and a cone having both congruent bases and heights. Students connect these models to the actual formulas for determining the volume of a cylinder and cone, which directly coincides with formulas used for determining the volume of prisms and pyramids on the STAAR Grade 8 Mathematics Reference Materials.
• Students solve problems involving the volume of cylinder, cones, and spheres.
• The concept of surface area is extended from finding the sum of the areas of the faces from the net to abstract formulas for lateral and total surface area.
• Students are expected to use previous knowledge of surface area to make connections to the formulas for lateral and total surface area and determine solutions for problems involving rectangular prisms, triangular prisms, and cylinders.

## Algebra I

• Solve problems using systems of equations.
• Linear systems are formulated for the problem situations, solved by a method of choice (tables, graphs, or algebraic methods including substitution and elimination), and the reasonableness of the solutions justified in terms of the problem situations.
• Graphing calculator technologies continue to be utilized to explore the relationships within systems of equations.
• During this unit, the concepts of exponents are extended to generate and apply rules of exponents. Simplification and combination of expressions are extended to include multiplication and factoring with more complex polynomial expressions. These concepts are applied in problem situations.

## Alice I.S.D. Math Curriculum

Alice ISD strives to communicate with parents about the new ways math is being taught. Please check out the Facebook page or the district website for more information!