koachkorner.weebly.comkoachkorner.weebly.com/.../1/6/59167249/staar_2015_gr3_math_ana… · Web viewStudents need many experiences solving word problems that include all four problem

2015 3rd Grade STAARReporting Category 1 : Numerical Representations and Relationships3.2 (A)- compose and decompose numbers up to 100,000 as a sum of so many ten thousands, so many thousands, so many hundreds, so many tens, and so many ones using objects, pictorial models, and numbers, including expanded notation as appropriate Readiness Standard

Vocabulary: expanded notation, standard formWhen Taught? Multi-Coding: 3.1(B), (F) Cognitive Level:

Level III- Apply

Correct Answer Regional Data

Campus/ District Data

Analysis of Distracters

A/F Place Value Error- Student interprets the (8 x 100) as (8 x 1,000)

B/G Student starts with the largest place value and places the numbers in line paying no attention to what the number is being multiplied by.

C/H Place Value Error- Student interprets the (3 x 10,000) as (3 x 1,000)

*D/J Correct AnswerInstructional Implications: Expanded notation should be taught after multiplication has been introduced to the students. If place value is done at the beginning of year review expanded form and then come back to expanded notation after multiplication has been introduced.Use base ten blocks to represent numbers and have students construct how many groups of ones, how many groups of tens, how many groups of hundreds, etc…Help students connect this with expanded notation.

1 | P a g e

2015 3rd Grade STAARReporting Category 1 : Numerical Representations and Relationships3.2 (B)- describe the mathematical relationships found in the base-10 place value system through the hundred thousands place; Supporting Standard

Vocabulary: mathematical relationship, base-10, ones, tens, hundreds, thousands, ten thousands, hundred thousands, times, equalWhen Taught? Multi-Coding: 3.1(B), (G) Cognitive Level:

Level IV- Analyze




*A/F Correct AnswerB/G Multiplies incorrectlyC/H Multiplies incorrectlyD/J Multiplies incorrectly

Instructional Implications: Students need to be given opportunities to communicate their understanding about the base ten system orally and written. Using a math journal is one way to establish the routine of communicating student understanding in written form.

2 | P a g e

2015 3rd Grade STAARReporting Category 1 : Numerical Representations and Relationships3.2 (C)- represent a number on a number line as being between two consecutive multiples of 10; 100; 1,000; or 10,000 and use words to describe relative size of numbers in order to round whole numbers; and Supporting Standard

Vocabulary: number line, consecutive, multiple, distance, round, relative size, halfway, betweenWhen Taught? Multi-Coding: 3.1(A), (B), (C), (E),

(G)Cognitive Level:Level V- Evaluate




A/F Vocabulary error- Student does not understand what less than halfway or a careless error where the student didn’t read less than halfway and only saw between.

B/G Student uses the halfway mark for between 300 and 400 instead of looking for the halfway between 300 and 500.

C/H Vocabulary error- Student does not understand what less than halfway.

*D/J Correct AnswerInstructional Implications: Students should be given opportunities to create number lines themselves in a real life context and describe why they chose to the place the numbers in a particular order or place on the number line. They should be using correct mathematical language. Include questions about the students number line that reflect which multiple of ten, hundred, thousand, and ten thousand it is closest to. One way to make number lines a part of everyday life situations is using a context that includes distance: taking a road trip and running a race.

3 | P a g e

2015 3rd Grade STAARReporting Category 1 : Numerical Representations and Relationships3.2 (D)- compare and order whole numbers up to 100,000 and represent comparisons using the symbols >, <, or =. Readiness Standard

Vocabulary: compare, order, comparison, greater than, less than, equal toWhen Taught? Multi-Coding: 3.1(B), (F) Cognitive Level:

Level III- Apply




A/F Student only compares the number to the first number in the comparison statement.

*B/G Correct AnswerC/H Student only compare the number to

the first number in the comparison statement.

D/J Student only compare the number to the first number in the comparison statement.

Instructional Implications: Students need to be given opportunities to compare more than two numbers at a time and write that comparison in a single statement using comparison symbols.

4 | P a g e

2015 3rd Grade STAARReporting Category 1 : Numerical Representations and Relationships3.3 (D)- compose and decompose a fraction a/b with a numerator greater than zero and less than or equal to b as a sum of parts 1/b; Supporting Standard

Vocabulary: compose, decompose, numerator, sum, fraction, equation , unit fractionWhen Taught? Multi-Coding: 3.1(A), (B), (D), (F) Cognitive Level:

Level III- Apply




*A/F Correct AnswerB/G Student adds the denominators.C/H Student uses seven as the

denominator because it represents the total number of days in the week.

D/J Student uses seven as the denominator because it represents the total number of days in the week, and adds up denominators.

Instructional Implications: Provide opportunities for students to use manipulatives to see how a unit fraction (1/4) composes to create a common fraction (ex. ¾. ) One manipulative that works well for this is unifix cubes. It can also show how a common fraction decomposes into a unit fraction. One important aspect to note is that when working with the unifix cubes or any manipulative make sure and put it into a real life context.

5 | P a g e

2015 3rd Grade STAARReporting Category 1 : Numerical Representations and Relationships3.3 (F)- represent equivalent fractions with denominators of 2, 3, 4, 6, and 8 using a variety of objects and pictorial models, including number lines; Readiness Standard

Vocabulary: equivalent, equivalent fractions, denominator, fraction strips, diagramWhen Taught? Multi-Coding: 3.1(A), (B), (E), (F) Cognitive Level:

Level II- Understand




*A/F CorrectB/G Student only looks at the first fraction in

the list.C/H Conceptual Error- Student chooses

fractions based on a pattern. D/J Conceptual Error- Student chooses

fractions based on the numerator and denominator being a difference of 1.

Instructional Implications: Provide opportunities for students to explore equivalent fractions with non-commercial tools. For example, paper strips for folding, fraction strips without the fraction noted on them, and paper circles. Cuisenaire Rods are a commercial tool that would prepare them for questions where the picture does not have the fractions written on them as well.

6 | P a g e

2015 3rd Grade STAARReporting Category 1 : Numerical Representations and Relationships3.3 (G)- 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; and Supporting Standard

Vocabulary: equivalent, fractions, area model, number lineWhen Taught? Multi-Coding: 3.1 (B), (E), (G) Cognitive Level:

Level V- Evaluate


Campus/ District Data Analysis of Distracters

A/F Student does not pay attention the number line representation when answering the question.

*B/G Correct AnswerC/H Student does not pay attention to

the number line representation when answering the question.

D/J Student counts tick marks on the number line instead of the distance traveled. This is how they get 4/6.

Instructional Implications: Provide opportunities for students create number lines themselves. Students can begin with fractions they are familiar with when placing them on the number line. For example, a student may choose to

7 | P a g e

place one-half on the number line first and then one- fourth, because they understand that a half of a half is a fourth. The students then can recognize that two fourths is equivalent to one-half etc…Another activity to use with students is paper folding. This will represent the use of the area model for equivalent fractions.

2015 3rd Grade STAAR

8 | P a g e

Reporting Category 1 : Numerical Representations and Relationships3.3 (H)- compare two fractions having the same numerator or denominator in problems by reasoning about their sizes and justifying the conclusion using symbols, words, objects, and pictorial models. Readiness Standard

Vocabulary: compare, fraction, numerator, denominator, justify, conclusion, symbols, pictorial modelsWhen Taught? Multi-Coding: 3.1 (A),(B), (E), (F) Cognitive Level:





A/F Conceptual Error- Student thinks the larger the denominator the greater the fraction.

B/G Conceptual Error- Student thinks since numerators are the same the fractions are equivalent.

*C/H Correct AnswerD/J Student reads the first number line

as 2/3 because he/she is counting the tick marks instead of the distance.

Instructional Implications: Provide opportunities for students to compare fractions with various objects. Even though the standard does not specifically state number line, it is considered a pictorial model. Have students

9 | P a g e

communicate their reasoning about the size of the fraction compared to the whole. Students need to remember that when comparing fractions the two wholes need to be equivalent.


10 | P a g e

Reporting Category 2 : Computations and Algebraic Relationships3.4 (A)- solve with fluency one-step and two-step problems involving addition and subtraction within 1,000 using strategies based on place value, properties of operations, and the relationship between addition and subtraction; Readiness Standard

Vocabulary: addition, subtraction, strategy, place value, properties of operationsWhen Taught? Multi-Coding: 3.1 (A),(B), (F) Cognitive Level:

Level III- Apply




*A/F Correct AnswerB/G Student adds the cups of peach and

vanilla yogurt only.C/H Student does not regroup when

subtracting the total of peach and vanilla from the strawberry.

D/J Student has a subtraction error in the tens place.

Instructional Implications: Students need daily experiences in solving multi-step word problems so they can make sense of problems and persevere in solving them. They need to be able to analyze what information is needed and what operation would be most appropriate to solve the problem. Students need to understand the concepts of addition and subtraction in this problem. There should be a consistent problem solving model being used. When the standard states to use strategies based on place value, properties of operations, and the relationship between addition and subtraction, this is providing students a flexible way to calculate for the answer. The students should be looking at the numbers and deciding which strategy would be best to use for the given information.

11 | P a g e

2015 3rd Grade STAARReporting Category 2 : Computations and Algebraic Relationships3.4 (F)- recall facts to multiply up to 10 by 10 with automaticity and recall the corresponding division facts; Supporting Standard

Vocabulary: multiply, automaticity, corresponding, divisionWhen Taught? Multi-Coding: 3.1 (A),(B),

(F)Cognitive Level:Level III- Apply

Correct Answer Regional Data Campus/ District Data Analysis of Distracters*7 Correct Answer

Instructional Implications: Students need daily experiences in solving word problems so they can make sense of problems and persevere in solving them. There should be a consistent problem solving model being used. Using a representation, for example a strip diagram to organize the information is helpful for students to visualize the problem.

12 | P a g e

2015 3rd Grade STAARReporting Category 2 : Computations and Algebraic Relationships3.4 (K)- solve one-step and two-step problems involving multiplication and division within 100 using strategies based on objects; pictorial models, including arrays, area models, and equal groups; properties of operations; or recall of facts. Readiness Standard

Vocabulary: multiplication, division, strategy, pictorial model, array, equal groups, properties of operationsWhen Taught? Multi-Coding: 3.1 (A),(B), (F) Cognitive Level:

Level III- Apply




A/F Computation Error when dividing*B/G Correct AnswerC/H Multiplied the 4 boxes of recorders

times the 9 recorders in each box and then subtracted the 6 classes.

D/J Multiplied the 4 boxes of recorders times the 9 recorders in each box, but did not find how many recorders each class received.

Instructional Implications: Students need daily experiences in solving multi-step word problems so they can make sense of problems and persevere in solving them. They need to be able to analyze what information is needed and what operation would be most appropriate to solve the problem. Students need to understand the concepts of multiplication and division in this problem. There should be a consistent problem solving model being used. When the standard states to use a variety of strategies, this is providing students a flexible way to calculate for the answer. The students should be looking at the numbers and deciding which strategy would be best to use for the given information.

13 | P a g e

2015 3rd Grade STAARReporting Category 2 : Computations and Algebraic Relationships3.5 (A)- represent one- and two-step problems involving addition and subtraction of whole numbers to 1,000 using pictorial models, number lines, and equations; Readiness Standard

Vocabulary: addition, subtraction, pictorial model, number line, equationWhen Taught? Multi-Coding: 3.1 (A),(B),

(D), (F)Cognitive Level:Level III- Apply

Correct Answer Regional Data Campus/ District Data Analysis of DistractersA/F Added 11 pretzelsB/G Subtracted 20 pretzels

and added 11 pretzelsC/H Subtracted 20 pretzels*D/J Correct Answer

Instructional Implications: Students need many experiences solving word problems that include all four problem types: join, separate, part/part/whole and comparison. Students may use a strip diagram as an organizer this is considered a pictorial model that is stated in the standard. It also important that they have experiences writing equations like those in the problem above. Provide students with opportunities to develop their own word problems as well.

2015 3rd Grade STAAR14 | P a g e

Reporting Category 2 : Computations and Algebraic Relationships3.5 (B)- represent and solve one- and two-step multiplication and division problems within 100 using arrays, strip diagrams, and equations; Readiness Standard

Vocabulary: multiplication, division, array, strip diagram, equationWhen Taught? Multi-Coding: 3.1 (A),(B),

(E), (F)Cognitive Level:Level II- Understand

Correct Answer Regional Data Campus/ District Data Analysis of Distracters*A/F Correct AnswerB/G Conceptual Error- Student

adds the 14 oranges with the 7 slices.

C/H Student recognizes the array has a total of 14 and 7 in each row. There is no attention to what the question is referencing.

D/J Student recognizes the 7 in the representation that is referenced in the problem.

Instructional Implications: When students are solving problems in the classroom it is important to have them represent their understanding in various ways. Using strip diagrams as part of a problem solving model when analyzing given information will provide opportunities for students to work with them often. At times students should also be requested to represent problems using arrays.

15 | P a g e

2015 3rd Grade STAARReporting Category 2 : Computations and Algebraic Relationships3.5 (C)- describe a multiplication expression as a comparison such as 3 x 24 represents 3 times as much as 24; Supporting Standard

Vocabulary: multiplication, expression, comparisonWhen Taught? Multi-Coding: 3.1 (A),(B), (G) Cognitive Level:

Level IV- Analyze




A/F Student only looked at the expression instead of reading the entire problem.

B/G Student only looked at the expression instead of reading the entire problem.

C/H Student mixed up who the expression was representing.

*D/J Correct AnswerInstructional Implications: Provide students opportunities to create multiplication expressions and then make up their own description of the expression using comparison language.

16 | P a g e

2015 3rd Grade STAARReporting Category 2 : Computations and Algebraic Relationships3.5 (D)- determine the unknown whole number i n a multiplication or division equation relating three whole numbers when the unknown is either a missing factor or product; and Supporting Standard

Vocabulary: multiplication, division, equation, factor, productWhen Taught? Multi-Coding: 3.1 (B), (F) Cognitive Level:





A/F Interpreted the division symbol as an addition symbol

*B/G Correct AnswerC/H Interpreted the division symbol as a

subtraction symbolD/J Computational Error

Instructional Implications: Students need to have experience with the relationship between multiplication and division through visual representation such as the area model and contextual situations. Students need to have a thorough understanding of the parts of a multiplication equation and division equation and what they represent. For example: In a division problem the dividend represents the whole amount, the divisor represents the number of groups or the number in each group, and the quotient represents the amount in each group or number of groups.

17 | P a g e

2015 3rd Grade STAARReporting Category 2 : Computations and Algebraic Relationships3.5 (E)- represent real-world relationships using number pairs in a table and verbal descriptions. Readiness Standard

Vocabulary: relationship, number pair, table, verbal descriptionWhen Taught? Multi-Coding: 3.1 (A), (B), (D), (F) Cognitive Level:

Level IV-Analyze




A/F Student pays attention to first column only

*B/G Correct AnswerC/H Student pays attention to first two

columns onlyD/J Student does not pay attention to

the number of display casesInstructional Implications: Students need to be flexible in looking across and down to see that each display holds 10 sunglasses and it increases by 10 for each display noted. Some students may be paying attention to the wrong

18 | P a g e

information, for example, increasing by 10 without regards to the number of display cases listed. Students need opportunities to generate their own tables using real life examples.


19 | P a g e

Reporting Category 3 : Geometry and Measurement3.6 (A)- classify and sort two- and three-dimensional figures, including cones, cylinders, spheres, triangular and rectangular prisms, and cubes, based on attributes using formal geometric language; Readiness Standard

Vocabulary: classify, sort, two- dimensional figure, three-dimensional figure, cones, cylinders, spheres, triangular prism, rectangular prism, cube, attribute, formal geometric languageWhen Taught? Multi-Coding: 3.1 (B), (E), (F) Cognitive Level:

Level IV- Analyze




A/F Careless error and vocabulary errorB/G Mistakes a pentagon for a hexagonC/H Mistakes a quadrilateral for a

pentagon*D/J Correct Answer

Instructional Implications: Provide opportunities for students to focus on the attributes of two-dimensional and three-dimensional shapes and promote the development of appropriate geometric language. Students need to be familiar with different attributes of shapes. Students need to be exposed to regular and irregular shapes. One example of this is that students need to know that a pentagon can be any shape with 5 sides it doesn’t always have to look like a house.

20 | P a g e

2015 3rd Grade STAARReporting Category 3 : Geometry and Measurement3.6 (C)- determine the area of rectangles with whole number side lengths in problems using multiplication related to the number of rows times the number of unit squares in each row; Readiness Standard

Vocabulary: area, rectangle, multiplication, row, unit squaresWhen Taught? Multi-Coding: 3.1 (A), (B), (F) Cognitive Level:

Level III- Apply


Campus/ District Data Analysis of Distracters

*A/F Correct AnswerB/G Adds all of the numbers in the

problem togetherC/H Adds 5 + 5 + 4 + 4D/J Adds the 5 rows with 4 tiles

Instructional Implications: Beginning instruction with area students should have opportunities to use concrete items such as color tiles to determine the area of different rectangles. This can then be connected to arrays in which students have been using with multiplication. Also, students should have been using an area model while working on multiplication which will transition well with this standard.

21 | P a g e

2015 3rd Grade STAARReporting Category 3 : Geometry and Measurement3.6 (D)- decompose composite figures formed by rectangles into non-overlapping rectangles to determine the area of the original figure using the additive property of area; and Supporting Standard

Vocabulary: decompose, composite figure, rectangle, non-overlapping rectangles, area, figure, additive property of area, diagram, composedWhen Taught? Multi-Coding: 3.1 (A), (B),

(E), (F)Cognitive Level:Level III- Apply

Correct Answer Regional Data Campus/ District Data Analysis of Distracters*42 Correct Answer

Instructional Implications: Students need experiences decomposing composite figures formed by rectangles to determine area. Beginning instruction can utilize color tiles to construct different composite figures and then determining the area of different rectangles within them using the additive property of area.

22 | P a g e

2015 3rd Grade STAARReporting Category 3 : Geometry and Measurement3.6 (E)- 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 and recognize that equal shares of identical wholes need not have the same shape. Supporting Standard

Vocabulary: decompose, congruent, two-dimensional, figure, equal, area, unit fraction, equal shares, identicalWhen Taught? Multi-Coding: 3.1 (B), (E), (G) Cognitive Level:

Level IV- Evaluate




A/F Conceptual error with fractions. Student does not pay attention that the rectangles are the same size and both represent fourths. Student thinks because the area that is shaded is thicker then it must be greater.

B/G Conceptual error with fractions. Student does not pay attention that the rectangles are the same size and both represent fourths. Student thinks because the area that is shaded is longer then it must be greater.

*C/H Correct AnswerD/J Conceptual error

Instructional Implications: This can be taught while teaching fraction concepts with students. It should not be introduced until fractions have been covered in the classroom. Paper folding is one way to help students develop this

23 | P a g e

concept. Using graph paper can also help students see how when dividing two congruent shapes into the same number of equal parts differently the area of each unit fraction is equivalent.

24 | P a g e

2015 3rd Grade STAARReporting Category 3 : Geometry and Measurement3.7 (B)- determine the perimeter o f a polygon or a missing length when given perimeter and remaining side lengths in problems; Readiness Standard

Vocabulary: perimeter, polygon, length, unitWhen Taught? Multi-Coding: 3.1 (B), (E), (F) Cognitive Level:

Level III- Apply




A/F Student visualizes instead of using calculations to figure out the answer.

B/G Adds one of each side length 8 + 7*C/H Correct AnswerD/J Adds the sides that are given, but

does not find the answer to the question.

Instructional Implications: Students need hands on experiences finding perimeters of objects. Include examples with a given perimeter and side lengths to determine a missing length.

25 | P a g e

2015 3rd Grade STAARReporting Category 3 : Geometry and Measurement3.7 (D)- determine when it is appropriate to use measurements of liquid volume (capacity) or weight; Supporting Standard

Vocabulary: appropriate, measurement, liquid volume, capacity, weightWhen Taught? Multi-Coding: 3.1 (A), (B), (C), (F) Cognitive Level:

Level I- Remember




A/F Weight unit of measurement*B/G Correct AnswerC/H Length unit of measurementD/J Weight unit of measurement

Instructional Implications: Students need hands-on experiences measuring liquid capacity and weight. They need to understand what they are being asked to measure and the relative size of the unit as it compares to an object being measured.


26 | P a g e

Reporting Category 4 : Data Analysis and Personal Financial Literacy3.8 (A)- summarize a data se t with multiple categories using a frequency table, dot plot, pictograph, or bar graph with scaled intervals; and Readiness Standard

Vocabulary: summarize, data set, multiple, categories, frequency table, dot plot, pictograph, bar graph, scaled intervalsWhen Taught? Multi-Coding: 3.1 (A), (B), (D), (F) Cognitive Level:

Level III- Analyze




*A/F Correct AnswerB/G Student only pays attention to the

first two students.C/H Student does not pay attention to

the scale and interprets it as going by 10

D/J Student increases the number sold for each student to the next multiple of 10 if it does not land exactly on one.

Instructional Implications: Students need to have experience with various scales on the frequency axis. When looking at the axis, students should observe where the range begins and ends as well as the intervals between the lines.

27 | P a g e

2015 3rd Grade STAARReporting Category 4 : Data Analysis and Personal Financial Literacy3.9 (B)- describe the relationship between the availability or scarcity of resources and how that impacts cost; Supporting Standard

Vocabulary: relationship, scarcity, resources, costWhen Taught? Multi-Coding: 3.1 (A), (B), (G) Cognitive Level:

Level IV: Evaluate




A/F Student only reads the first part of the statement.

B/G Student does not interpret the situation correctly with what the bad weather did to the peach trees.

*C/H Correct AnswerD/J Student associates the word

decrease with fewer.Instructional Implications:

Have students role play situations that involve scarcity of resources. Make cards with different situations involving scarcity of resources (similar to the STAAR example) and

draw one when lining up to go somewhere and have students think-pair share how they would describe the relationship in the situation.

28 | P a g e

2015 3rd Grade STAARReporting Category 4 : Data Analysis and Personal Financial Literacy3.9 (D)- explain that credit is used when wants or needs exceed the ability to pay and that it is the borrower’s responsibility to pay it back to the lender, usually with interest; and Supporting Standard

Vocabulary: credit, borrower, lender, interestWhen Taught? Multi-Coding: 3.1 (A), (B), (G) Cognitive Level:

Level IV: Evaluate




A/F Vocabulary error with the word interest.

B/G Vocabulary error with the word interest.

C/H Vocabulary error with the word interest.

*D/J Correct AnswerInstructional Implications:

Give opportunities to students to specify and communicate their ideas about borrowing, lending and interest throughout the year.

Have students role play being a borrower or a lender. Use classroom management ideas to incorporate borrowing, lending, and interest. For

example, if a student needs to borrow a pencil they can pay you back with the pencil and interest depending on how much time they kept the pencil.

29 | P a g e

30 | P a g e

Documents

koachkorner.weebly.comkoachkorner.weebly.com/.../1/6/59167249/staar_2015_gr3_math_ana… · Web viewStudents need many experiences solving word problems that include all four problem