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2015 5th Grade STAAR

Reporting Category 1: Numerical Representations and Relationships

5.2(B) compare and order two decimals to thousandths and represent comparisons using the symbols >, <, or =; and

Vocabulary: table, compares

When Taught? Multiple Coding: 5.1 (A) apply mathematics to problems arising in everyday life, society, and the workplace;5.1 (B) use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution;5.1 (E) create and use representations to organize, record, and communicate mathematical ideas;5.1 (F) analyze mathematical relationships to connect and communicate mathematical ideas; and

Cognitive Level:

Analyze

Correct Answer Regional Data Campus/ District

Analysis of Distracters

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Data

A Compares the number from right to left instead of left to right.

*B Correct Answer

C The number on the left has more decimal places appearing to some to have a larger value.

D Not identifying the thousandths place as significant.

Instructional Implications:

Students need to be able to:

use an appropriate problem solving plan to solve problems find the information to use from a table instead of giving it to them in a word problem understand place value and the meaning of greater than and less than symbols


5.4 (E) describe the meaning of parentheses and brackets in a numeric expression

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Vocabulary: expression, parentheses

When Taught? Multiple Coding: 5.1 (B) use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution5.1 (G) display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication

Cognitive Level:

Evaluate

Correct Answer Regional Data Campus/ District Data


*A Correct Answer

B Following only the multiplication/division, then addition/subtraction in order of operations, leaving out the first two steps; parentheses and exponents.

C This is a working from the left to the right understanding and not applying order of operations.

D This is a working from the left to the right understanding and not applying order of operations.


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In order to solve problem such as this, students need to:

understand order of operations and that parentheses or brackets should always be done first be exposed to various problems with parenthesis and/or brackets to fully understand the

order in which to solve problem be given opportunities to communicate that in various ways, not just solving the problem


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5.4(F) simplify numerical expressions that do not involve exponents, including up to two levels of grouping;

Vocabulary: expression

When Taught? Multiple Coding: 5.1 (B) use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution5.1 (F) analyze mathematical relationships to connect and communicate mathematical ideas

Cognitive Level:

Analyze



*A Correct Answer

B Multiplied, divided then added to 36, does not understand parentheses or brackets application.

C Worked from left to right, ignoring the order of operations.

D Did the first two steps, but did not divide by 6.


Students need to:

understand the order of operations fully to be able to successfully

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be exposed to many problems that encompass multiple operations the operations should be varied in the location in which they come in the problem be exposed to problems where they have to do more than one set of parentheses

Reporting Category 2: Computations and Algebraic Relationships

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5.3 (D) represent multiplication of decimals with products to the hundredths using objects and pictorial models, including area models

Vocabulary: equation

When Taught? Multiple Coding: 5.1 (B) use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution5.1 (D) communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate5.1 (F) analyze mathematical relationships to connect and communicate mathematical ideas

Cognitive Level:

Analyze

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A Applies to the whole number system instead of the rational number system for decimals, did not read the “hundredths mode” in the question.

B Uses “hundredths” to indicate the numbers that are being multiplied, instead of the model. Or does not understand that one row or column represents 0.1 not 0.01.

*C Correct Answer

D Same as answer B distractor, but the answer fits the problem for answer D, however does not fit the model in the question.


Students need to:

understand how to model place value on a 100 chart do problems with concrete examples of modeling multiplication of decimals on a 100 chart

using an area model connect equations to the model and be able to identify what the model is displaying given

only the model, as well as being able to model what the equation is asking

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5.3 (E) ) solve for products of decimals to the hundredths, including situations involving money, using strategies based on place-value understandings, properties of operations, and the relationship to the multiplication of whole numbers

Vocabulary:

When Taught? Multiple Coding: 5.1 (A) apply mathematics to problems arising in everyday life, society, and the workplace5.1 (B) use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution5.1 (F) analyze mathematical relationships to connect and communicate mathematical ideas

Cognitive Level:

Analyze



A Decimal placement is wrong.

B Added numbers instead of multiplied.

*C Correct Answer

D Multiplied by 1 twice and added the numbers

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together, instead of multiplying by 10 and 1 or 11.


Students need to:

be able to use an appropriate problems solving model that incorporates analyzing the given information in a question

be given word problems that incorporate decimals, especially using money and be able to understand strategies or the algorithm of how to multiply decimals by whole numbers in real-life situations

to be exposed to problems that don’t have key word in them so that they can understand situations that require them to multiply without those key words


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5.3 (F) represent quotients of decimals to the hundredths, up to four-digit dividends and two-digit whole number divisors, using objects and pictorial models, including area models;


When Taught? Multiple Coding: 5.1 (B) use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution5.1 (D) communicate mathematical ideas, reasoning, and their implications using multiple

Cognitive Level:

Analyze

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representations, including symbols, diagrams, graphs, and language as appropriate5.1 (F) analyze mathematical relationships to connect and communicate mathematical ideas



A Total number is incorrect 2.5 not 2.6, also us multiplying not dividing.

*B Correct Answer

C Applying to whole numbers instead of rational numbers, decimals, also is indicating multiplication instead of division.

D 2.06 is not the original model, indicating that they do not understand one column models 0.1; calculation are correct for the equation in answer D, but does not match the model displayed in the question.


Students need to:

be able to evaluate a problem and the relationships between the numbers in the problem or model

model how to multiply and divide on a 100 grid in regards to an array model for decimals model, as well as identify what is being modeled when given a picture of a 100 grid. use concrete models until they are very clear on how to do this on their own using paper and

pencil.

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5.3 (G) solve for quotients of decimals to the hundredths, up to four-digit dividends and two-digit whole number divisors, using strategies and algorithms, including the standard algorithm;

Vocabulary: saving


Cognitive Level:

Analyze



*A Correct answer

B Divided 96 by 7 and used the remainder as the cents.

C Divided, but added a zero between the 7 and 4 or

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inverted the numbers in the quotient

D Calculation error


Students need to:

use a problem solving model to analyze given information in a word problem and be able to solve it appropriately

successfully divide decimals using the traditional algorithm of long division or using strategies of partial products to determine quotients

identify the operation of division not given key words

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5.3 (H) represent and solve addition and subtraction of fractions with unequal denominators referring to the same whole using objects and pictorial models and properties of operations

Vocabulary: fraction

When Taught? Multiple Coding: 5.1 (A) apply mathematics to problems arising in everyday life, society, and the workplace5.1 (B) use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution5.1 (E) create and use

Cognitive Level:

Analyze

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representations to organize, record, and communicate mathematical ideas5.1 (F) analyze mathematical relationships to connect and communicate mathematical ideas



A Does not understand the fractional value indicated by the various sizes, only counted the shaded regions

*B Correct answer.

C Counted shaded to number of pieces, does not understand the fractional value indicated by the sizes or that they are out of the whole amount of paper.

D Only looked at the first month and not the other months.


Students need to

be able to use a problem solving model appropriately be able to identify various fractional pieces without identification of what those pieces

represent numerically ie: 1/8, ¼, ½ as displayed in the question work with models and fractional pieces where they have to determine what portion of the

whole is being displayed understand how to make equivalent fractions from models, as well as adding fractions with

various denominators


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5.3 (I) represent and solve multiplication of a whole number and a fraction that refers to the same whole using objects and pictorial models, including area models

Vocabulary: chart

When Taught? Multiple Coding: 5.1 (A) apply mathematics to problems arising in everyday life, society, and the workplace5.1 (B) use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution5.1 (E) create and use representations to organize, record, and communicate mathematical ideas5.1 (F) analyze mathematical relationships to connect and communicate mathematical ideas

Cognitive Level:

Analyze

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A Subtracted 24 and 6.

B Did not apply the fraction to the number of flights only used the 4 in the numerator

*C Correct Answer.

D Found 2/6 of 24, not 4/6.


Students need to

be able to use a problem solving model appropriately understand how to use a table and get the information from the table as necessary understand how and when to multiply a fractions by a whole number; either using the

traditional algorithm, or strategies. be given problems using a model first and develop understanding before moving to the

traditional algorithm.

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5.3 (K) add and subtract positive rational numbers fluently; and

Vocabulary: total, less


Cognitive Level:

Analyze



*A Correct answer.

B Regrouping or decomposing calculation error.

C Added all the numbers in the problem, instead of subtracting $0.75.

D Regrouping or decomposing calculation error.


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Students need to

understand how to use a problem solving model appropriately where they are able to analyze given information in a problem

be able to identify what operation is identified in the question and know what to do, especially with problems involving multiple steps.

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5.3 (L) divide whole numbers by unit fractions and unit fractions by whole numbers.

Vocabulary:


Cognitive Level:

Analyze



A Added 5 and 15.

B Divided 15 by 5.

C Multiplied 15 by 6 and not 5.

*D Correct answer.


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Students need to

be able to use a problem solving model appropriately and be able to analyze information in a question

be able to identify what operation is to be used given certain situations understand how to divide fractions and whole numbers divide fractions and whole numbers with models but also know how to do the algorithm be exposed to multiple problems of this type so that they develop a deep understanding of

what operation to use when key words are not included.

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5. 4 (B) represent and solve multi-step problems involving the four operations with whole numbers using equations with a letter standing for the unknown quantity


When Taught? Multiple Coding: 5.1 (A) apply mathematics to problems arising in everyday life, society, and the workplace5.1 (B) use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution5.1 (D) communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate5.1 (F) analyze mathematical relationships to connect and communicate mathematical ideas

Cognitive Level:

Analyze



A Added the number in the box and the number of boxes instead of multiplying.

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*B Correct answer.

C Subtracted the number of baseballs instead of multiplying and divided 8 instead of subtracting it.

D Added the number of baseballs, instead of subtracting.


Students need to

be able to use a problem solving model appropriately. be solving problems with multiple steps be able to write equations that go along with the word problems, when they have multiple

steps encounter word problems that match the given equation and equations that match various

statements where they have to choose the correct situation

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5.4 (C) generate a numerical pattern when given a rule in the form y = ax or y = x + a and graph

Vocabulary: ordered pairs, coordinate plane, satisfy, equation

When Taught? Multiple Coding: 5.1 (B) use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution5.1 (D) communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate

Cognitive Level:

Analyze

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5.1 (F) analyze mathematical relationships to connect and communicate mathematical ideas



A Added two to each x value instead of 3.

B Inverted the x and y values in the equation giving them the wrong values in the table.

*C Correct Answer

D N/A


Students need to

be able to read a graph plot points on a coordinate grid understand how to put numbers into an equation, solve the equation for those various points

and then be able to identify which table has the corresponding outputs When teaching this concept best practice is to have various problems that include different

representations and have the students identify what goes together.

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Reporting Category 3: Geometry and Measurement

5.4 (H) represent and solve problems related to perimeter and/or area and related to volume

Vocabulary: base, rectangular prism, length, width, area, square inches, place value

When Taught? Multiple Coding: 5.1 (B) use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution5.1 (C) select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques, including mental math, estimation, and number sense as appropriate, to solve problems5.1 (F) analyze mathematical relationships to connect and communicate mathematical ideas

Cognitive Level:

Analyze


Analysis of Distracters: N/A

195


Students need to

understand how to find area of a rectangle understand that the base of a rectangular prism is a rectangle know what the length and width of a rectangle are and how they are used in the formula Reading a formula chart would be ideal in this situation so they need to be familiar with that

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resource so they can refer to it. Another important component of this question is how to answer using the grid when filling in

the answer on the answer document. They need to understand that the decimal if fixed and they have to put the answer in the

correct place value in order to get the answer right. Exposure to questions that have answers using a grid are crucial to ensure that students know

what to do when they come to answering in this fashion.


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5.5 (A) classify two-dimensional figures in a hierarchy of sets and subsets using graphic organizers based on their attributes and properties

Vocabulary: graphic organizer, polygons, section, classify

When Taught? Multiple Coding: 5.1 (A) apply mathematics to problems arising in everyday life, society, and the workplace5.1 (B) use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution5.1 (E) create and use

Cognitive Level:

Analyze

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representations to organize, record, and communicate mathematical ideas5.1 (F) analyze mathematical relationships to connect and communicate mathematical ideas



A Only identifies the polygons that have two sets of parallel lines, did not identify the one that also has perpendicular lines.

B Does not understand the definition of parallelogram, having two sets of parallel sides.

C Only chose the shapes with slanted lines, or having one set of parallel lines, not the one with perpendicular lines.

*D Correct answer.


Students need to

understand how to use a graphic organizer understand the relationship for polygons, specifically quadrilaterals and the similarities and

differences that classify them into sets and subsets know the characteristics that classify a specific quadrilateral using those characteristics.

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5.8 graph in the first quadrant of the coordinate plane ordered pairs of numbers arising from mathematical and real-world problems, including those generated by number patterns or found in an input-output table

Vocabulary: ordered pairs, vertices, trapezoid, vertex

When Taught? Multiple Coding: 5.1 (B) use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution5.1 (E) create and use representations to organize, record, and communicate mathematical ideas5.1 (F) analyze mathematical relationships to connect and communicate mathematical ideas

Cognitive Level:

Analyze

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A Did not plot points to trapezoid, picked a point in between the last two given in the question.

B Possibly added and or subtracted previous coordinates.

*C Correct answer.

D Made a triangle and not a trapezoid.


Students need to

understand how to graph coordinate pairs on a coordinate grid understand what a trapezoid is and how to go about finding the remaining point when given

three other points, understanding the characteristic that trapezoids have one set of parallel sides

These types of questions should not only be focused on trapezoids, but all polygons.

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Reporting Category 4: Data Analysis and Personal Financial Literacy

5.9 (A) represent categorical data with bar graphs or frequency tables and numerical data, including data sets of measurements in fractions or decimals, with dot plots or stem-and-leaf plots

Vocabulary: measurements, dot plot

When Taught? Multiple Coding: 5.1 (A) apply mathematics to problems arising in everyday life, society, and the workplace5.1 (B) use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution5.1 (D) communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols,

Cognitive Level:

Analyze

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diagrams, graphs, and language as appropriate5.1 (F) analyze mathematical relationships to connect and communicate mathematical ideas



A Missing 1, ¾ dot.

B Missing 1, ¾ dot and 1, 7/8 dot.

C Missing 1, 1 dot.

*D Correct answer.


Students need to

understand what a dot plot is how to plot points on a dot plot They also need to understand how to extrapolate on a scale without given points; those that

fall between other points Students need to be exposed to various problems that require them to plot points when the

value is not explicitly stated on the dot plot.

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5.9 (B) represent discrete paired data on a scatterplot

Vocabulary: scatterplot, data, table

When Taught? Multiple Coding: 5.1 (A) apply mathematics to problems arising in everyday life, society, and the workplace5.1 (B) use a problem-solving model that incorporates analyzing given information, formulating a

Cognitive Level:

Analyze

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plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution5.1 (D) communicate mathematical ideas, reasoning, and their implication using multiple representations, including symbols, diagrams, graphs and language as appropriate5.1 (F) analyze mathematical relationships to connect and communicate mathematical ideas



*A Correct answer.

B Graphed (3, 12) instead of (3, 11) and is missing (1,5).

C Graphed (3,14) instead of (4, 14).

D Did not graph (3,11).


Students will need to

understand what a scatterplot is how to plot points on a coordinate grid be exposed to data given in a table and then plotting it in the scatterplot, using the

information given for the x and y values One strategy could be to display the scatterplot and have them find the matching table or vice

versa; display the table and find the corresponding scatterplot.

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5.9 (C) solve one- and two-step problems using data from a frequency table, dot plot, bar graph, stem-and-leaf plot, or scatterplot

Vocabulary: frequency table, prefer, frequency, tally, data

When Taught? Multiple Coding: 5.1 (A) apply mathematics to problems arising in everyday life, society, and the workplace5.1 (B) use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution5.1 (E) create and use representations to organize, record, and communicate

Cognitive Level:

Analyze

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mathematical ideas5.1 (F) analyze mathematical relationships to connect and communicate mathematical ideas



A Just picked the highest frequency.

B Added the first three numbers in the table not the highest frequency.

C Added all frequencies instead of highest three.

*D Correct answer.


Students need to

understand how to use a problem solving model and how to analyze given information in the question

understand how to read and interpret a frequency table and understand that the tallies and frequency is the same value

use the tables and interpret what the question is asking ie: understand how to total the number of the three highest values

Teachers need to expose students to various type of questions that ask student to interpret and find specific values and how to combine/subtract those values when appropriate.


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5.10 (A) define income tax, payroll tax, sales tax, and property tax

Vocabulary: tax, income tax, payroll tax, sales tax, property tax

When Taught? Multiple Coding: 5.1 (A) apply mathematics to problems arising in everyday life, society, and the workplace5.1 (F) analyze mathematical relationships to connect and communicate mathematical ideas

Cognitive Level:

Analyze



A Does not understand the difference between income tax and property tax.

B Does not understand the difference between payroll tax and property tax.

C Does not understand the difference between sales tax and property tax.

*D Correct answer.


Students need to

understand each of the various taxes that they explore in the personal financial literacy standards

be given different tax types and then be able to identify which tax it goes with

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5.10 (B) explain the difference between gross income and net income

Vocabulary: gross income, net income, tax, income, earns, wages, employer, deductions,

When Taught? Multiple Coding: 5.1 (G) display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication

Cognitive Level:

Evaluate



A Does not understand the difference between gross income and net income.

B Does not understand the difference between gross income and net income.

C Does not understand the difference between gross income and net income.

*D Correct answer.


Students need to

understand the difference between gross income and net income and what defines them as such

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5.10 (E) describe actions that might be taken to balance a budget when expenses exceed income

Vocabulary: expenses, income, balance budget

When Taught? Multiple Coding: 5.1 (A) apply mathematics to problems arising in everyday life, society, and the workplace5.1 (B) use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution5.1 (G) display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication

Cognitive Level:

Evaluate



A Does not understand how expenses and income work together.

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B Does not understand how expenses and income work together.

*C Correct Answer.

D Does not understand how expenses and income work together.


Students need to

understand the difference between expenses and income understand what it means to increase and decrease those expenses and how that impacts a

balanced budget be able to apply this understanding in context to real life questions.

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5.10 (F) balance a simple budget

Vocabulary: budget, paycheck, balanced, car payment, expenses, income, house payment, utilities, groceries, gas, insurance, retirement savings

When Taught? Multiple Coding: 5.1 (A) apply mathematics to problems arising in everyday life, society, and the workplace5.1 (B) use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution5.1 (E) create and use representations to organize, record, and communicate mathematical ideas5.1 (F) analyze mathematical relationships to connect and communicate mathematical ideas

Cognitive Level:

Analyze

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A Added the work paychecks together.

*B Correct answer.

C Did not regroup correctly leaving in $200 and then subtracted from the income to get $500.

D Added all the expenses together and did not subtract from the income.


Students need to

be able to use a problem solving model that includes analyzing given data read a chart of given information understand the difference between income and expenses understand that income is to be added when you are putting it into a budget understand that expenses are subtracted from a budget understand when given a list of expenses and income how and when to add and subtract

those values

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