Mathematics

Earlier grades (6)(12)

• Grade 1 1.3.D Apply fact strategies within 20
  Close

  Prerequisites

  1. 1.3.C · Grade 1Compose 10 from two or more addends

  1.3.D · Grade 1

  Apply fact strategies within 20

  apply basic fact strategies to add and subtract within 20, including making 10 and decomposing a number leading to a 10

  Example

  1. Ask for 8 + 5 and listen for whether they take 2 off the 5 to make 10 first.
  2. Ask for 13 - 5 and listen for whether they come down to 10 first and take the other 2 after.

  19 TAC §111.3

  Part of the adding and subtracting topic

• Grade 1 1.3.E Explain add and subtract strategies to 20
  Close

  Prerequisites

  1. 1.3.D · Grade 1Apply fact strategies within 20

  1.3.E · Grade 1

  Explain add and subtract strategies to 20

  explain strategies used to solve addition and subtraction problems up to 20 using spoken words, objects, pictorial models, and number sentences

  Example

  1. After they answer 7 + 8, ask them to say out loud how they got there.
  2. Ask them to show that same 7 + 8 with counters, then write it as a number sentence.

  19 TAC §111.3

  Part of the adding and subtracting topic

• Grade 1 1.3.F Generate, solve stories for number sentences
  Close

  Prerequisites

  1. 1.3.B · Grade 1Solve join, separate, compare problems to 20

  1.3.F · Grade 1

  Generate, solve stories for number sentences

  generate and solve problem situations when given a number sentence involving addition or subtraction of numbers within 20

  Example

  1. Write 12 - 5 = 7 and ask them to invent a story the sentence answers.
  2. Write 6 + 9 = 15 and ask for a story where the 9 is something arriving, not something already there.

  19 TAC §111.3

  Part of the adding and subtracting topic

• Grade 1 1.5.D Model addition and subtraction problems to 20
  Close

  Prerequisites

  1. 1.3.B · Grade 1Solve join, separate, compare problems to 20

  1.5.D · Grade 1

  Model addition and subtraction problems to 20

  represent word problems involving addition and subtraction of whole numbers up to 20 using concrete and pictorial models and number sentences

  Example

  1. Tell them 7 birds were on a wire and 5 more landed. Ask for the drawing and the number sentence first.
  2. Put 15 stones out, say 6 got carried off, and ask for the model and the number sentence before the answer.

  19 TAC §111.3

  Part of the adding and subtracting topic

• Grade 1 1.5.F Determine the unknown in any term
  Close

  Prerequisites

  1. 1.5.E · Grade 1Equal sign means the same value

  1.5.F · Grade 1

  Determine the unknown in any term

  determine the unknown whole number in an addition or subtraction equation when the unknown may be any one of the three or four terms in the equation

  Example

  1. Write 8 + [ ] = 15 and ask for the missing number.
  2. Write [ ] - 4 = 9, where the unknown starts the sentence instead of ending it.
  3. Write 5 + 3 = [ ] + 6 and ask for the missing number in the one with four terms.

  19 TAC §111.3

  Part of the adding and subtracting topic

• Grade 1 1.5.G Add and subtract using operation properties
  Close

  1.5.G · Grade 1

  Add and subtract using operation properties

  apply properties of operations to add and subtract two or three numbers

  Example

  1. Ask for 7 + 4, then 4 + 7, and ask why the answer did not move.
  2. Ask for 8 + 2 + 5 and watch whether they take the 8 and the 2 first.

  19 TAC §111.3

  Part of the adding and subtracting topic

• Grade 2 2.4.A Automatic addition and subtraction within 20
  Close

  Prerequisites

  1. 1.3.D · Grade 1Apply fact strategies within 20

  2.4.A · Grade 2

  Automatic addition and subtraction within 20

  recall basic facts to add and subtract within 20 with automaticity

  Example

  1. Ask 9 + 6 and 14 - 8 with no paper. Listen for an answer in a couple of seconds, not a count.

  19 TAC §111.4

  Part of the adding and subtracting topic

• Grade 2 2.4.B Up to four two-digit addends, and subtraction
  Close

  Prerequisites

  1. 1.5.G · Grade 1Add and subtract using operation properties
  2. 2.2.A · Grade 2Compose and decompose numbers to 1,200
  3. 2.4.A · Grade 2Automatic addition and subtraction within 20

  2.4.B · Grade 2

  Up to four two-digit addends, and subtraction

  add up to four two-digit numbers and subtract two-digit numbers using mental strategies and algorithms based on knowledge of place value and properties of operations

  Example

  1. Ask for 23 + 41 + 12 + 30 in one go, all four at once.
  2. Ask for 62 - 47 and listen for whether they can explain the borrowing, not just do it.

  19 TAC §111.4

  Part of the adding and subtracting topic

• Grade 2 2.4.C One- and multi-step word problems within 1,000
  Close

  Prerequisites

  1. 1.3.B · Grade 1Solve join, separate, compare problems to 20
  2. 2.4.B · Grade 2Up to four two-digit addends, and subtraction

  2.4.C · Grade 2

  One- and multi-step word problems within 1,000

  solve one-step and multi-step word problems involving addition and subtraction within 1,000 using a variety of strategies based on place value, including algorithms

  Example

  1. Two legs of a drive run 235 miles and 148 miles. Ask how far that is altogether, then how much farther to 500.
  2. A jar holds 412 beads and 175 come out. Ask how many are left, then ask them to check it a different way.

  19 TAC §111.4

  Part of the adding and subtracting topic

• Grade 2 2.4.D Write and solve problems from number sentences
  Close

  Prerequisites

  1. 1.3.F · Grade 1Generate, solve stories for number sentences
  2. 2.4.C · Grade 2One- and multi-step word problems within 1,000

  2.4.D · Grade 2

  Write and solve problems from number sentences

  generate and solve problem situations for a given mathematical number sentence involving addition and subtraction of whole numbers within 1,000

  Example

  1. Write 300 - 125 = 175 and ask them to invent a story that the sentence answers.

  19 TAC §111.4

  Part of the adding and subtracting topic

• Grade 2 2.7.C Represent and solve problems with any unknown
  Close

  Prerequisites

  1. 1.5.D · Grade 1Model addition and subtraction problems to 20
  2. 1.5.F · Grade 1Determine the unknown in any term

  2.7.C · Grade 2

  Represent and solve problems with any unknown

  represent and solve addition and subtraction word problems where unknowns may be any one of the terms in the problem

  Example

  1. Say "the drive was some number of miles, then 40 more, and ended at 130," and ask for the first number.
  2. Give a second story where the missing number is the one that changed in the middle, not the one at the start or the end.

  19 TAC §111.4

  Part of the adding and subtracting topic

• Grade 2 2.10.C Write and solve one-step graph problems
  Close

  Prerequisites

  1. 1.3.F · Grade 1Generate, solve stories for number sentences
  2. 2.10.A · Grade 2Bars and pictures stand for data points

  2.10.C · Grade 2

  Write and solve one-step graph problems

  write and solve one-step word problems involving addition or subtraction using data represented within pictographs and bar graphs with intervals of one

  Example

  1. Have them redraw the same counts with one square per vehicle, then ask them to make up a word problem about it and solve it.

  19 TAC §111.4

  Part of the adding and subtracting topic

• Grade 3 3.4.A Add and subtract fluently within 1,000
  Close

  Prerequisites

  1. 2.4.C · Grade 2One- and multi-step word problems within 1,000

  3.4.A · Grade 3

  Add and subtract fluently within 1,000

  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

  Example

  1. A sign says 462 miles to the next park. After 175 miles, ask how far is left, then ask again after another 130.
  2. Ask for 703 - 268 and listen for whether they can explain the regrouping, not just do it.

  19 TAC §111.5

  Part of the adding and subtracting topic

• Grade 3 3.4.B Estimate with rounding or compatible numbers
  Close

  Prerequisites

  1. 3.2.C · Grade 3Round whole numbers using a number line

  3.4.B · Grade 3

  Estimate with rounding or compatible numbers

  round to the nearest 10 or 100 or use compatible numbers to estimate solutions to addition and subtraction problems

  Example

  1. Before adding 287 and 412, ask them to round each to the nearest 100 and say roughly what to expect.
  2. Ask them to round 68 and 34 to the nearest 10 before subtracting, then ask how close the estimate landed.

  19 TAC §111.5

  Part of the adding and subtracting topic

• Grade 3 3.4.E Represent multiplication facts several ways
  Close

  Prerequisites

  1. 3.4.D · Grade 3Total objects in equal groups or arrays

  3.4.E · Grade 3

  Represent multiplication facts several ways

  represent multiplication facts by using a variety of approaches such as repeated addition, equal-sized groups, arrays, area models, equal jumps on a number line, and skip counting

  Example

  1. Ask them to show 4 x 6 three ways: as repeated addition, as an array, and as equal jumps on a number line.
  2. Ask them to skip count by fours up to 24 and say how many jumps it took.

  19 TAC §111.5

  Part of the adding and subtracting topic

• Grade 3 3.5.A Represent addition and subtraction to 1,000
  Close

  Prerequisites

  1. 2.4.C · Grade 2One- and multi-step word problems within 1,000

  3.5.A · Grade 3

  Represent addition and subtraction to 1,000

  represent one- and two-step problems involving addition and subtraction of whole numbers to 1,000 using pictorial models, number lines, and equations

  Example

  1. Give a two-step story about a drive and ask for the equation before the answer.
  2. Ask them to draw the same story on a number line: 340 miles, then 155 more, then how far short of 600.

  19 TAC §111.5

  Part of the adding and subtracting topic

• Grade 3 3.7.C Add and subtract time intervals in minutes
  Close

  Prerequisites

  1. 2.9.G · Grade 2Time to the minute, am or pm

  3.7.C · Grade 3

  Add and subtract time intervals in minutes

  determine the solutions to problems involving addition and subtraction of time intervals in minutes using pictorial models or tools such as a 15-minute event plus a 30-minute event equals 45 minutes

  Example

  1. A fuel stop takes 25 minutes and the next stop takes 40. Ask how long both come to together.
  2. A hike is planned for 50 minutes and 15 have gone by. Ask them to show the rest on a clock face and say how many minutes are left.

  19 TAC §111.5

  Part of the adding and subtracting topic

Earlier grades (2)(4)

• Grade 1 1.4.C Count pennies, nickels, dimes to find value
  Close

  Prerequisites

  1. 1.4.A · Grade 1Identify coins by value, relate them
  2. 1.5.B · Grade 1Skip count twos, fives, tens to 120

  1.4.C · Grade 1

  Count pennies, nickels, dimes to find value

  use relationships to count by twos, fives, and tens to determine the value of a collection of pennies, nickels, and/or dimes

  Example

  1. Slide 8 pennies across the table and ask them to count by twos to the total.
  2. Put out 6 nickels and ask them to count by fives.
  3. Put out 4 dimes and 3 pennies and ask them to count the dimes by tens before picking up the pennies.

  19 TAC §111.3

  Part of the counting topic

• Grade 1 1.5.B Skip count twos, fives, tens to 120
  Close

  Prerequisites

  1. 1.5.A · Grade 1Recite forward and backward within 120

  1.5.B · Grade 1

  Skip count twos, fives, tens to 120

  skip count by twos, fives, and tens to determine the total number of objects up to 120 in a set

  Example

  1. Pour out a jar of buttons, ask them to push the buttons into groups of 10, and count by tens to the total.
  2. Lay out 30 pennies in pairs and ask for the total by twos.
  3. Ask them to count a page of tally marks by fives.

  19 TAC §111.3

  Part of the counting topic

• Grade 2 2.3.C Count parts to and beyond one whole
  Close

  Prerequisites

  1. 2.3.A · Grade 2Partition and name halves, fourths, eighths

  2.3.C · Grade 2

  Count parts to and beyond one whole

  use concrete models to count fractional parts beyond one whole using words and recognize how many parts it takes to equal one whole

  Example

  1. Break two crackers into fourths, lay out five of the pieces, and ask them to count the parts aloud: one fourth, two fourths, and on past the whole.
  2. Ask how many eighths it takes to make one whole.

  19 TAC §111.4

  Part of the counting topic

• Grade 2 2.9.F Find rectangle area with square unit models
  Close

  Prerequisites

  1. 1.7.B · Grade 1Length is same-size units, end to end

  2.9.F · Grade 2

  Find rectangle area with square unit models

  use concrete models of square units to find the area of a rectangle by covering it with no gaps or overlaps, counting to find the total number of square units, and describing the measurement using a number and the unit

  Example

  1. Draw a rectangle four tiles by six tiles, ask them to cover it with no gaps or overlaps, and say the area as a number and a unit.

  19 TAC §111.4

  Part of the counting topic

• Grade 3 3.4.E Represent multiplication facts several ways

Earlier grades (1)(4)

• Grade 1 1.6.G Partition into two and four equal parts
  Close

  1.6.G · Grade 1

  Partition into two and four equal parts

  partition two-dimensional figures into two and four fair shares or equal parts and describe the parts using words

  Example

  1. Hand over a tortilla and ask them to split it into two fair shares, then name one piece out loud.
  2. Fold a square of paper into four equal parts and ask what one part is called.

  19 TAC §111.3

  Part of the fractions topic

• Grade 2 2.3.A Partition and name halves, fourths, eighths
  Close

  Prerequisites

  1. 1.6.G · Grade 1Partition into two and four equal parts

  2.3.A · Grade 2

  Partition and name halves, fourths, eighths

  partition objects into equal parts and name the parts, including halves, fourths, and eighths, using words

  Example

  1. Hand them a sandwich and ask for fourths, then ask them to name one piece in words.
  2. Fold a sheet of paper into eighths and ask what one part is called.

  19 TAC §111.4

  Part of the fractions topic

• Grade 2 2.3.B More parts, smaller parts; fewer, larger
  Close

  Prerequisites

  1. 2.3.A · Grade 2Partition and name halves, fourths, eighths

  2.3.B · Grade 2

  More parts, smaller parts; fewer, larger

  explain that the more fractional parts used to make a whole, the smaller the part; and the fewer the fractional parts, the larger the part

  Example

  1. Ask which is bigger, a half of a cracker or an eighth of the same cracker, and why.

  19 TAC §111.4

  Part of the fractions topic

• Grade 2 2.3.C Count parts to and beyond one whole
• Grade 3 3.3.A Represent fractions up to one whole
  Close

  Prerequisites

  1. 2.9.C · Grade 2A number as distance from any location
  2. 3.3.C · Grade 3Explain the unit fraction 1/b

  3.3.A · Grade 3

  Represent fractions up to one whole

  represent fractions greater than zero and less than or equal to one with denominators of 2, 3, 4, 6, and 8 using concrete objects and pictorial models, including strip diagrams and number lines

  Example

  1. Cut one paper strip into thirds and another into sixths, and ask them to shade two thirds on the first and five sixths on the second.
  2. Draw a number line from 0 to 1 and ask them to mark one half, then three fourths, then seven eighths.

  19 TAC §111.5

  Part of the fractions topic

• Grade 3 3.3.B Determine the fraction at a number-line point
  Close

  Prerequisites

  1. 3.3.A · Grade 3Represent fractions up to one whole

  3.3.B · Grade 3

  Determine the fraction at a number-line point

  determine the corresponding fraction greater than zero and less than or equal to one with denominators of 2, 3, 4, 6, and 8 given a specified point on a number line

  Example

  1. Draw a line from 0 to 1 divided into eighths, mark one point on it, and ask them to name the fraction that sits there.
  2. Do it again with the line divided into halves, then thirds, then fourths, then sixths.

  19 TAC §111.5

  Part of the fractions topic

• Grade 3 3.3.C Explain the unit fraction 1/b
  Close

  Prerequisites

  1. 2.3.A · Grade 2Partition and name halves, fourths, eighths

  3.3.C · Grade 3

  Explain the unit fraction 1/b

  explain that the unit fraction 1/b represents the quantity formed by one part of a whole that has been partitioned into b equal parts where b is a non-zero whole number

  Example

  1. Fold a sheet into six equal parts, point at one part, and ask what to call it and why the six matters.
  2. Ask what the bottom number of one eighth is telling them about the whole.

  19 TAC §111.5

  Part of the fractions topic

• Grade 3 3.3.D Compose and decompose a/b into 1/b parts
  Close

  Prerequisites

  1. 3.3.C · Grade 3Explain the unit fraction 1/b

  3.3.D · Grade 3

  Compose and decompose a/b into 1/b parts

  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

  Example

  1. Ask them to write three fourths as a sum of fourths.
  2. Break a cracker into sixths, put five pieces on the table, and ask what fraction is there and how many one-sixths it took.

  19 TAC §111.5

  Part of the fractions topic

• Grade 3 3.3.E Partition objects into fractional shares
  Close

  Prerequisites

  1. 2.6.B · Grade 2Division as separating into equivalent sets
  2. 3.3.A · Grade 3Represent fractions up to one whole

  3.3.E · Grade 3

  Partition objects into fractional shares

  solve problems involving partitioning an object or a set of objects among two or more recipients using pictorial representations of fractions with denominators of 2, 3, 4, 6, and 8

  Example

  1. Cut one granola bar so three people get equal shares, and ask them to name one share.
  2. Draw three sandwiches shared fairly among eight people and ask them to shade what one person gets.

  19 TAC §111.5

  Part of the fractions topic

• Grade 3 3.3.F Represent equivalent fractions with models
  Close

  Prerequisites

  1. 3.3.A · Grade 3Represent fractions up to one whole

  3.3.F · Grade 3

  Represent equivalent fractions with models

  represent equivalent fractions with denominators of 2, 3, 4, 6, and 8 using a variety of objects and pictorial models, including number lines

  Example

  1. Fold one strip into halves, one into fourths, and one into eighths, line all three up, and ask which shaded pieces match.
  2. Draw two number lines from 0 to 1, one in thirds and one in sixths, and ask for a point that lands on both.

  19 TAC §111.5

  Part of the fractions topic

• Grade 3 3.3.G Explain when two fractions are equivalent
  Close

  Prerequisites

  1. 3.3.F · Grade 3Represent equivalent fractions with models

  3.3.G · Grade 3

  Explain when two fractions are equivalent

  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

  Example

  1. Mark two fourths and one half on the same number line and ask them to say why those are the same number.
  2. Shade one fourth of one circle and two eighths of a same-size circle, and ask whether the shaded amount is equal and how they can tell.

  19 TAC §111.5

  Part of the fractions topic

• Grade 3 3.3.H Compare fractions: same numerator/denominator
  Close

  Prerequisites

  1. 2.3.B · Grade 2More parts, smaller parts; fewer, larger
  2. 3.3.A · Grade 3Represent fractions up to one whole

  3.3.H · Grade 3

  Compare fractions: same numerator/denominator

  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

  Example

  1. Ask which is bigger, three eighths or five eighths, and why.
  2. Ask which is bigger, two thirds or two eighths, and ask them to write the symbol between them.

  19 TAC §111.5

  Part of the fractions topic

• Grade 3 3.6.E Decompose figures into unit-fraction parts
  Close

  Prerequisites

  1. 3.3.C · Grade 3Explain the unit fraction 1/b
  2. 3.6.D · Grade 3Find area by decomposing composite figures

  3.6.E · Grade 3

  Decompose figures into unit-fraction parts

  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

  Example

  1. Cut two identical squares of paper into fourths, one with straight cuts and one with diagonals, and ask whether every piece is still one fourth.
  2. Ask them to name one piece as a fraction of the whole square, then ask whether equal shares are always the same shape.

  19 TAC §111.5

  Part of the fractions topic

• Grade 3 3.7.A Halves, fourths, and eighths on number lines
  Close

  Prerequisites

  1. 3.3.A · Grade 3Represent fractions up to one whole

  3.7.A · Grade 3

  Halves, fourths, and eighths on number lines

  represent fractions of halves, fourths, and eighths as distances from zero on a number line

  Example

  1. Draw a line from 0 to 2 and ask them to mark one half, then three fourths, then seven eighths, measuring from zero each time.
  2. Point at five eighths on the line and ask how far that is from zero, not which tick it sits on.

  19 TAC §111.5

  Part of the fractions topic

Earlier grades (4)(9)

• Grade 1 1.1.D Communicate ideas, reasoning, implications
  Close

  1.1.D · Grade 1

  Communicate ideas, reasoning, implications

  communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate

  Example

  1. Ask them to show 7 + 6 two ways: as a drawing, and as a number sentence.
  2. Ask them to tell you in one sentence what a bar graph on a visitor-center wall is saying.

  19 TAC §111.3

  Part of the graphs and data topic

• Grade 1 1.8.A Collect, sort, organize up to three categories
  Close

  1.8.A · Grade 1

  Collect, sort, organize up to three categories

  collect, sort, and organize data in up to three categories using models/representations such as tally marks or T-charts

  Example

  1. On a drive, ask them to keep tally marks for three things: cars, trucks, and motorcycles.
  2. Ask them to set the T-chart up before the counting starts, with a heading written over each column.

  19 TAC §111.3

  Part of the graphs and data topic

• Grade 1 1.8.B Make picture and bar-type graphs from data
  Close

  Prerequisites

  1. 1.8.A · Grade 1Collect, sort, organize up to three categories

  1.8.B · Grade 1

  Make picture and bar-type graphs from data

  use data to create picture and bar-type graphs

  Example

  1. Turn the tally into a picture graph, one small drawing per vehicle.
  2. Ask them to redraw the same counts as bars, one square per vehicle.

  19 TAC §111.3

  Part of the graphs and data topic

• Grade 1 1.8.C Ask, answer, and conclude from graphs
  Close

  Prerequisites

  1. 1.8.B · Grade 1Make picture and bar-type graphs from data

  1.8.C · Grade 1

  Ask, answer, and conclude from graphs

  draw conclusions and generate and answer questions using information from picture and bar-type graphs

  Example

  1. Ask which bar is tallest, and how many more it holds than the shortest one.
  2. Ask them to make up a question their own graph can answer, then answer it.

  19 TAC §111.3

  Part of the graphs and data topic

• Grade 2 2.1.D Communicate math in multiple representations
  Close

  2.1.D · Grade 2

  Communicate math in multiple representations

  communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate

  Example

  1. Ask them to show 24 + 18 two ways: with a drawing, and with numbers.
  2. Ask them to explain a subtraction out loud, without pointing at the page.

  19 TAC §111.4

  Part of the graphs and data topic

• Grade 2 2.10.A Bars and pictures stand for data points
  Close

  Prerequisites

  1. 1.8.B · Grade 1Make picture and bar-type graphs from data

  2.10.A · Grade 2

  Bars and pictures stand for data points

  explain that the length of a bar in a bar graph or the number of pictures in a pictograph represents the number of data points for a given category

  Example

  1. Show a bar graph and ask what the height of one bar means.

  19 TAC §111.4

  Part of the graphs and data topic

• Grade 2 2.10.B Four categories in pictographs and bar graphs
  Close

  Prerequisites

  1. 1.8.B · Grade 1Make picture and bar-type graphs from data

  2.10.B · Grade 2

  Four categories in pictographs and bar graphs

  organize a collection of data with up to four categories using pictographs and bar graphs with intervals of one or more

  Example

  1. Ask them to count four kinds of vehicle at a rest stop, then build a bar graph with an interval of two.

  19 TAC §111.4

  Part of the graphs and data topic

• Grade 2 2.10.C Write and solve one-step graph problems
• Grade 2 2.10.D Draw conclusions and predictions from graphs
  Close

  Prerequisites

  1. 1.8.C · Grade 1Ask, answer, and conclude from graphs
  2. 2.10.C · Grade 2Write and solve one-step graph problems

  2.10.D · Grade 2

  Draw conclusions and predictions from graphs

  draw conclusions and make predictions from information in a graph

  Example

  1. Ask what the graph suggests would happen if you counted again tomorrow, and why.

  19 TAC §111.4

  Part of the graphs and data topic

• Grade 3 3.1.D Communicate ideas in multiple representations
  Close

  3.1.D · Grade 3

  Communicate ideas in multiple representations

  communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate

  Example

  1. Ask them to show 6 x 7 two ways: with a drawing, and with a number sentence.
  2. Ask them to explain a division out loud, without pointing at the page.

  19 TAC §111.5

  Part of the graphs and data topic

• Grade 3 3.8.A Summarize data in tables and scaled graphs
  Close

  Prerequisites

  1. 2.10.B · Grade 2Four categories in pictographs and bar graphs

  3.8.A · Grade 3

  Summarize data in tables and scaled graphs

  summarize a data set with multiple categories using a frequency table, dot plot, pictograph, or bar graph with scaled intervals

  Example

  1. Count four kinds of vehicle at a rest stop, then ask them to put the counts in a frequency table and a dot plot.
  2. Ask them to draw a bar graph of the same counts with each square standing for five.

  19 TAC §111.5

  Part of the graphs and data topic

• Grade 3 3.8.B Solve problems from categorical data displays
  Close

  Prerequisites

  1. 2.10.C · Grade 2Write and solve one-step graph problems
  2. 3.8.A · Grade 3Summarize data in tables and scaled graphs

  3.8.B · Grade 3

  Solve problems from categorical data displays

  solve one- and two-step problems using categorical data represented with a frequency table, dot plot, pictograph, or bar graph with scaled intervals

  Example

  1. Show a pictograph where one symbol stands for 10 and ask how many more there are of one category than another.
  2. Off the same graph, ask a two-step question: how many in two categories together, then how many fewer that is than a third.

  19 TAC §111.5

  Part of the graphs and data topic

Earlier grades (4)(10)

• Grade 1 1.7.A Use tools to measure object length
  Close

  1.7.A · Grade 1

  Use tools to measure object length

  use measuring tools to measure the length of objects to reinforce the continuous nature of linear measurement;

  Example

  1. Hand over a tape measure and ask for the length of the picnic table, then the bench beside it.
  2. Watch whether they line the end of the object up with the zero on the tape rather than with the first number they see.

  19 TAC §111.3

  Part of the measurement topic

• Grade 1 1.7.B Length is same-size units, end to end
  Close

  1.7.B · Grade 1

  Length is same-size units, end to end

  illustrate that the length of an object is the number of same-size units of length that, when laid end-to-end with no gaps or overlaps, reach from one end of the object to the other

  Example

  1. Ask them to measure a book with color tiles laid end to end, and watch for gaps and overlaps.
  2. Slide one tile out of the middle of the finished row and ask what the measurement says now.

  19 TAC §111.3

  Part of the measurement topic

• Grade 1 1.7.C Measure with two unit sizes, explain why
  Close

  Prerequisites

  1. 1.7.B · Grade 1Length is same-size units, end to end

  1.7.C · Grade 1

  Measure with two unit sizes, explain why

  measure the same object/distance with units of two different lengths and describe how and why the measurements differ

  Example

  1. Have them walk the length of a hallway in their own steps, then walk it in yours, and ask why the two counts came out different.

  19 TAC §111.3

  Part of the measurement topic

• Grade 1 1.7.D Describe length using number and whole unit
  Close

  Prerequisites

  1. 1.7.B · Grade 1Length is same-size units, end to end

  1.7.D · Grade 1

  Describe length using number and whole unit

  describe a length to the nearest whole unit using a number and a unit

  Example

  1. After they measure a leaf, ask for the answer as a number and a unit, not a number on its own.
  2. When the end of the object lands between two marks, ask which whole one is nearer.

  19 TAC §111.3

  Part of the measurement topic

• Grade 2 2.9.A Find length with models of standard units
  Close

  Prerequisites

  1. 1.7.A · Grade 1Use tools to measure object length
  2. 1.7.B · Grade 1Length is same-size units, end to end

  2.9.A · Grade 2

  Find length with models of standard units

  find the length of objects using concrete models for standard units of length

  Example

  1. Ask them to measure the picnic table with inch tiles laid end to end, no gaps.

  19 TAC §111.4

  Part of the measurement topic

• Grade 2 2.9.B Bigger units, fewer units needed
  Close

  Prerequisites

  1. 1.7.C · Grade 1Measure with two unit sizes, explain why

  2.9.B · Grade 2

  Bigger units, fewer units needed

  describe the inverse relationship between the size of the unit and the number of units needed to equal the length of an object

  Example

  1. Measure the same table in paper clips and then in shoes, and ask why the bigger unit gave the smaller number.

  19 TAC §111.4

  Part of the measurement topic

• Grade 2 2.9.D Use measuring tools to the nearest mark
  Close

  Prerequisites

  1. 1.7.D · Grade 1Describe length using number and whole unit
  2. 2.9.A · Grade 2Find length with models of standard units

  2.9.D · Grade 2

  Use measuring tools to the nearest mark

  determine the length of an object to the nearest marked unit using rulers, yardsticks, meter sticks, or measuring tapes

  Example

  1. Hand over a ruler and ask for the length of a leaf to the nearest marked unit.
  2. Watch whether they line the object up with zero rather than with the end of the ruler.

  19 TAC §111.4

  Part of the measurement topic

• Grade 2 2.9.E Solve length problems, including estimates
  Close

  Prerequisites

  1. 2.9.D · Grade 2Use measuring tools to the nearest mark

  2.9.E · Grade 2

  Solve length problems, including estimates

  determine a solution to a problem involving length, including estimating lengths

  Example

  1. Ask them to guess the length of the trail sign before measuring, then measure it.
  2. Ask which of two trails is longer, and by roughly how much, without working it out exactly.

  19 TAC §111.4

  Part of the measurement topic

  what we did

• Grade 2 2.9.F Find rectangle area with square unit models
• Grade 2 2.10.A Bars and pictures stand for data points
• Grade 3 3.7.B Find perimeter or a missing side length
  Close

  Prerequisites

  1. 2.4.B · Grade 2Up to four two-digit addends, and subtraction
  2. 2.7.C · Grade 2Represent and solve problems with any unknown
  3. 2.9.D · Grade 2Use measuring tools to the nearest mark

  3.7.B · Grade 3

  Find perimeter or a missing side length

  determine the perimeter of a polygon or a missing length when given perimeter and remaining side lengths in problems

  Example

  1. Ask them to measure every side of the picnic table and say the distance all the way around.
  2. Say a four-sided figure has a perimeter of 30 inches and three sides of 9, 6, and 9 inches, and ask for the fourth side.

  19 TAC §111.5

  Part of the measurement topic

• Grade 3 3.7.D Decide when to measure volume or weight
  Close

  Prerequisites

  1. 3.7.E · Grade 3Measure liquid volume or weight

  3.7.D · Grade 3

  Decide when to measure volume or weight

  determine when it is appropriate to use measurements of liquid volume (capacity) or weight

  Example

  1. Hold up a water jug and a bag of apples and ask which one you would weigh and which one you would measure by volume.
  2. Ask which of the two tells you more about what fits in a cooler, and why.

  19 TAC §111.5

  Part of the measurement topic

Earlier grades (5)(9)

• Grade 1 1.4.A Identify coins by value, relate them
  Close

  1.4.A · Grade 1

  Identify coins by value, relate them

  identify U.S. coins, including pennies, nickels, dimes, and quarters, by value and describe the relationships among them

  Example

  1. Lay out a penny, a nickel, a dime, and a quarter, and ask them to name each one and say what it is worth.
  2. Ask how many pennies make a nickel, how many nickels make a dime, and how many nickels make a quarter.

  19 TAC §111.3

  Part of the money topic

• Grade 1 1.4.B Write coin values with the cent symbol
  Close

  1.4.B · Grade 1

  Write coin values with the cent symbol

  write a number with the cent symbol to describe the value of a coin

  Example

  1. Hand over a dime and ask them to write what it is worth with the cent sign.
  2. Do the same with a quarter, and watch where the cent sign lands.

  19 TAC §111.3

  Part of the money topic

• Grade 1 1.9.A Money earned is income
  Close

  1.9.A · Grade 1

  Money earned is income

  define money earned as income

  Example

  1. Ask what to call the money someone gets for doing a job.
  2. Ask whether money out of a birthday card counts as income, and what the difference is.

  19 TAC §111.3

  Part of the money topic

• Grade 1 1.9.B Income buys goods, services; wants or needs
  Close

  Prerequisites

  1. 1.9.A · Grade 1Money earned is income

  1.9.B · Grade 1

  Income buys goods, services; wants or needs

  identify income as a means of obtaining goods and services, oftentimes making choices between wants and needs

  Example

  1. At a gas stop, ask which things on the shelf are wants and which are needs.
  2. Ask how the money someone earns turns into a loaf of bread and a haircut, and which of the two is a service.

  19 TAC §111.3

  Part of the money topic

• Grade 1 1.9.C Spending versus saving
  Close

  1.9.C · Grade 1

  Spending versus saving

  distinguish between spending and saving

  Example

  1. Give them a jar, ask which coins are for today and which are for later, and ask what each pile is called.

  19 TAC §111.3

  Part of the money topic

• Grade 2 2.5.A Coin collection value up to one dollar
  Close

  Prerequisites

  1. 1.4.C · Grade 1Count pennies, nickels, dimes to find value

  2.5.A · Grade 2

  Coin collection value up to one dollar

  determine the value of a collection of coins up to one dollar; and

  Example

  1. Hand over three quarters, two dimes, and a nickel and ask for the total. It is one dollar.
  2. Lay out two quarters, a dime, and a nickel and ask what it comes to. It is 65 cents.

  19 TAC §111.4

  Part of the money topic

• Grade 2 2.5.B Name coin values with money symbols
  Close

  Prerequisites

  1. 1.4.B · Grade 1Write coin values with the cent symbol
  2. 2.5.A · Grade 2Coin collection value up to one dollar

  2.5.B · Grade 2

  Name coin values with money symbols

  use the cent symbol, dollar sign, and the decimal point to name the value of a collection of coins.

  Example

  1. Lay out three quarters, a dime, and two pennies, then ask them to write what it comes to two ways: with the cent sign, and with a dollar sign and a decimal point.

  19 TAC §111.4

  Part of the money topic

• Grade 2 2.11.A Calculate how savings grow over time
  Close

  Prerequisites

  1. 1.9.C · Grade 1Spending versus saving

  2.11.A · Grade 2

  Calculate how savings grow over time

  calculate how money saved can accumulate into a larger amount over time

  Example

  1. Ask what saving a nickel a day comes to after a week.

  19 TAC §111.4

  Part of the money topic

• Grade 2 2.11.B Saving instead of spending
  Close

  2.11.B · Grade 2

  Saving instead of spending

  explain that saving is an alternative to spending

  Example

  1. Offer a small thing now or a bigger thing in a month, and ask them to explain the choice rather than just make it.

  19 TAC §111.4

  Part of the money topic

• Grade 3 3.4.C Find the value of coins and bills
  Close

  Prerequisites

  1. 2.5.A · Grade 2Coin collection value up to one dollar

  3.4.C · Grade 3

  Find the value of coins and bills

  determine the value of a collection of coins and bills

  Example

  1. Hand over two dollar bills, three quarters, and four dimes and ask for the total.
  2. Empty the change out of the cup holder onto the seat and ask what it comes to.

  19 TAC §111.5

  Part of the money topic

• Grade 3 3.9.A Explain how human capital earns income
  Close

  Prerequisites

  1. 1.9.A · Grade 1Money earned is income

  3.9.A · Grade 3

  Explain how human capital earns income

  explain the connection between human capital/labor and income

  Example

  1. Ask what a ranger does all day and how that work turns into a paycheck.
  2. Ask what a person would learn or practice to get paid more for the same hours.

  19 TAC §111.5

  Part of the money topic

• Grade 3 3.9.C Identify costs and benefits of spending
  Close

  Prerequisites

  1. 2.11.B · Grade 2Saving instead of spending

  3.9.C · Grade 3

  Identify costs and benefits of spending

  identify the costs and benefits of planned and unplanned spending decisions

  Example

  1. After a gas-station stop, go down the receipt and ask which things were planned and which were not.
  2. Point at the unplanned one and ask what it was good for, and what you gave up to buy it.

  19 TAC §111.5

  Part of the money topic

• Grade 3 3.9.E List saving reasons and savings-plan benefits
  Close

  Prerequisites

  1. 2.11.A · Grade 2Calculate how savings grow over time

  3.9.E · Grade 3

  List saving reasons and savings-plan benefits

  list reasons to save and explain the benefit of a savings plan, including for college

  Example

  1. Ask for three reasons to leave money in the jar instead of spending it, and whether college is one of them.
  2. Ask what saving $5 a week comes to by the end of a month, and what that pile is for.

  19 TAC §111.5

  Part of the money topic

• Grade 3 3.9.F Identify decisions about money and giving
  Close

  3.9.F · Grade 3

  Identify decisions about money and giving

  identify decisions involving income, spending, saving, credit, and charitable giving

  Example

  1. Read out five choices — taking a job, buying a snack, putting money in a jar, borrowing from you, dropping a coin in a donation box — and ask which is income, spending, saving, credit, and charitable giving.
  2. Hand over $10 of chore money and ask them to say what part is for spending, what part is for saving, and what part is for giving away.

  19 TAC §111.5

  Part of the money topic

Earlier grades (2)

• Grade 2 2.6.A Multiplication as joining equivalent sets
  Close

  Prerequisites

  1. 1.5.B · Grade 1Skip count twos, fives, tens to 120

  2.6.A · Grade 2

  Multiplication as joining equivalent sets

  model, create, and describe contextual multiplication situations in which equivalent sets of concrete objects are joined

  Example

  1. Set out four cups with three stones in each and ask them to say what they see, then how many stones altogether.

  19 TAC §111.4

  Part of the multiplication and division topic

• Grade 2 2.6.B Division as separating into equivalent sets
  Close

  Prerequisites

  1. 1.6.G · Grade 1Partition into two and four equal parts
  2. 2.6.A · Grade 2Multiplication as joining equivalent sets

  2.6.B · Grade 2

  Division as separating into equivalent sets

  model, create, and describe contextual division situations in which a set of concrete objects is separated into equivalent sets

  Example

  1. Hand over twelve stones and ask them to share the stones fairly among three people, then say how they did it.

  19 TAC §111.4

  Part of the multiplication and division topic

• Grade 3 3.4.E Represent multiplication facts several ways
• Grade 3 3.4.F Recall multiplication and division facts to 10
  Close

  Prerequisites

  1. 3.4.D · Grade 3Total objects in equal groups or arrays

  3.4.F · Grade 3

  Recall multiplication and division facts to 10

  recall facts to multiply up to 10 by 10 with automaticity and recall the corresponding division facts

  Example

  1. Ask 7 x 8 and 6 x 9 in the car with no paper. Listen for an answer in a couple of seconds, not a count.
  2. Right after 7 x 8, ask for 56 divided by 8.

  19 TAC §111.5

  Part of the multiplication and division topic

• Grade 3 3.4.G Multiply two-digit by one-digit numbers
  Close

  Prerequisites

  1. 3.2.A · Grade 3Compose and decompose numbers to 100,000
  2. 3.4.F · Grade 3Recall multiplication and division facts to 10

  3.4.G · Grade 3

  Multiply two-digit by one-digit numbers

  use strategies and algorithms, including the standard algorithm, to multiply a two-digit number by a one-digit number. Strategies may include mental math, partial products, and the commutative, associative, and distributive properties

  Example

  1. Ask for 34 x 6, then ask them to do it a second way with partial products.
  2. Ask for 48 x 5 and listen for whether they break the 48 apart or go straight to the standard algorithm.

  19 TAC §111.5

  Part of the multiplication and division topic

• Grade 3 3.4.J Use multiplication to determine a quotient
  Close

  Prerequisites

  1. 3.4.F · Grade 3Recall multiplication and division facts to 10

  3.4.J · Grade 3

  Use multiplication to determine a quotient

  determine a quotient using the relationship between multiplication and division

  Example

  1. Ask for 63 divided by 9, then ask which multiplication fact they used to get there.
  2. Write 8 x ? = 48 and ask them to say the division fact that answers it.

  19 TAC §111.5

  Part of the multiplication and division topic

• Grade 3 3.4.K Solve division and multiplication within 100
  Close

  Prerequisites

  1. 3.4.F · Grade 3Recall multiplication and division facts to 10
  2. 3.4.H · Grade 3Find how many are in each group

  3.4.K · Grade 3

  Solve division and multiplication within 100

  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

  Example

  1. Nine campsites hold four tents each. Ask how many tents that is, then how many are still to go up if 30 are already standing.
  2. Ask how many packs of six water bottles it takes to fill a cooler that holds 42.

  19 TAC §111.5

  Part of the multiplication and division topic

• Grade 3 3.5.B Model and solve multiplication and division
  Close

  Prerequisites

  1. 3.4.E · Grade 3Represent multiplication facts several ways

  3.5.B · Grade 3

  Model and solve multiplication and division

  represent and solve one- and two-step multiplication and division problems within 100 using arrays, strip diagrams, and equations

  Example

  1. Tell a story about 5 rows of 8 camp chairs and ask them to draw the array and write the equation.
  2. Ask them to draw a strip diagram for 48 crackers split among 6 people before they say the answer.

  19 TAC §111.5

  Part of the multiplication and division topic

• Grade 3 3.5.C Describe multiplication as a comparison
  Close

  Prerequisites

  1. 3.4.E · Grade 3Represent multiplication facts several ways

  3.5.C · Grade 3

  Describe multiplication as a comparison

  describe a multiplication expression as a comparison such as 3 x 24 represents 3 times as much as 24

  Example

  1. Write 4 x 15 and ask them to say it out loud as a comparison, not as a total.
  2. Say one tent sleeps 3 people and the group is 5 times that, and ask for the expression.

  19 TAC §111.5

  Part of the multiplication and division topic

• Grade 3 3.5.D Find the unknown factor or product
  Close

  Prerequisites

  1. 2.7.C · Grade 2Represent and solve problems with any unknown
  2. 3.4.J · Grade 3Use multiplication to determine a quotient

  3.5.D · Grade 3

  Find the unknown factor or product

  determine the unknown whole number in a multiplication or division equation relating three whole numbers when the unknown is either a missing factor or product

  Example

  1. Write 6 x ? = 42 and ask for the missing number, then ask how they found it.
  2. Write 56 divided by 7 = ? and ask which multiplication fact gives the answer.

  19 TAC §111.5

  Part of the multiplication and division topic

• Grade 3 3.6.C Determine rectangle area using multiplication
  Close

  Prerequisites

  1. 2.9.F · Grade 2Find rectangle area with square unit models
  2. 3.4.D · Grade 3Total objects in equal groups or arrays

  3.6.C · Grade 3

  Determine rectangle area using multiplication

  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

  Example

  1. Draw a rectangle five squares across and four squares down, ask for the area, and listen for a multiplication rather than a count.
  2. Ask how many square feet of tarp covers a floor 7 feet by 6 feet, and listen for whether the answer carries a unit.

  19 TAC §111.5

  Part of the multiplication and division topic

Earlier grades (3)(6)

• Grade 1 1.9.A Money earned is income
• Grade 1 1.9.B Income buys goods, services; wants or needs
• Grade 1 1.9.C Spending versus saving
• Grade 2 2.11.B Saving instead of spending
• Grade 2 2.11.D Examples of borrowing, responsible or not
  Close

  2.11.D · Grade 2

  Examples of borrowing, responsible or not

  identify examples of borrowing and distinguish between responsible and irresponsible borrowing

  Example

  1. Ask for an example of borrowing something, and what would make the borrowing irresponsible.

  19 TAC §111.4

  Part of the personal finance topic

• Grade 2 2.11.E Lending examples; weigh benefits and costs
  Close

  Prerequisites

  1. 2.11.D · Grade 2Examples of borrowing, responsible or not

  2.11.E · Grade 2

  Lending examples; weigh benefits and costs

  identify examples of lending and use concepts of benefits and costs to evaluate lending decisions

  Example

  1. Ask what a person lending a bike gives up, and what they get out of it.

  19 TAC §111.4

  Part of the personal finance topic

• Grade 3 3.9.A Explain how human capital earns income
• Grade 3 3.9.D Explain credit and repayment with interest
  Close

  Prerequisites

  1. 2.11.D · Grade 2Examples of borrowing, responsible or not

  3.9.D · Grade 3

  Explain credit and repayment with interest

  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

  Example

  1. Ask why a person hands over a card when the thing they want costs more than the cash in their pocket, and who pays the store that day.
  2. Ask what a person owes back on a $20 loan, and why it comes to more than $20.

  19 TAC §111.5

  Part of the personal finance topic

• Grade 3 3.9.F Identify decisions about money and giving

Earlier grades (2)(7)

• Grade 1 1.2.E Compare whole numbers to 120 in words
  Close

  Prerequisites

  1. 1.2.B · Grade 1Compose and decompose numbers to 120

  1.2.E · Grade 1

  Compare whole numbers to 120 in words

  use place value to compare whole numbers up to 120 using comparative language

  Example

  1. Put 89 and 98 side by side and ask which is greater, and how the tens told them.
  2. Ask them to finish "45 is ___ 54" out loud rather than writing anything.

  19 TAC §111.3

  Part of the place value topic

• Grade 1 1.2.F Order whole numbers to 120
  Close

  Prerequisites

  1. 1.2.E · Grade 1Compare whole numbers to 120 in words

  1.2.F · Grade 1

  Order whole numbers to 120

  order whole numbers up to 120 using place value and open number lines

  Example

  1. Write 31, 13, and 103 on three cards and ask them to lay them out smallest first.
  2. Draw a line with no marks on it at all and ask them to place 20, 65, and 90 along it in order.

  19 TAC §111.3

  Part of the place value topic

• Grade 2 2.2.B Numbers to 1,200: standard, word, expanded
  Close

  Prerequisites

  1. 1.2.C · Grade 1Show numbers to 120 several ways

  2.2.B · Grade 2

  Numbers to 1,200: standard, word, expanded

  use standard, word, and expanded forms to represent numbers up to 1,200

  Example

  1. Write 1,062 and ask them to say it and then write it as 1,000 + 60 + 2.
  2. Say "nine hundred four" and ask them to write the numeral. Watch for a four-digit answer.

  19 TAC §111.4

  Part of the place value topic

• Grade 2 2.2.D Compare and order numbers to 1,200
  Close

  Prerequisites

  1. 1.2.F · Grade 1Order whole numbers to 120
  2. 1.2.G · Grade 1Represent comparisons to 100 with symbols

  2.2.D · Grade 2

  Compare and order numbers to 1,200

  use place value to compare and order whole numbers up to 1,200 using comparative language, numbers, and symbols (>, <, or =)

  Example

  1. Put 1,110 and 1,101 side by side and ask which is greater, and how they know.
  2. Ask them to write the symbol between 476 and 467 rather than saying the word.

  19 TAC §111.4

  Part of the place value topic

• Grade 2 2.4.B Up to four two-digit addends, and subtraction
• Grade 2 2.4.C One- and multi-step word problems within 1,000
• Grade 2 2.7.B 10 or 100 more/less to 1,200
  Close

  Prerequisites

  1. 1.5.C · Grade 1Find 10 more, 10 less, to 120
  2. 2.2.A · Grade 2Compose and decompose numbers to 1,200

  2.7.B · Grade 2

  10 or 100 more/less to 1,200

  use an understanding of place value to determine the number that is 10 or 100 more or less than a given number up to 1,200

  Example

  1. Say 1,140 and ask for 10 more, then 100 less.
  2. Say 995 and ask for 10 more. The crossing is the part worth watching.

  19 TAC §111.4

  Part of the place value topic

• Grade 3 3.2.A Compose and decompose numbers to 100,000
  Close

  Prerequisites

  1. 2.2.A · Grade 2Compose and decompose numbers to 1,200

  3.2.A · Grade 3

  Compose and decompose numbers to 100,000

  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

  Example

  1. Write 34,208 and ask how many ten thousands, thousands, hundreds, tens, and ones it holds, then ask them to write it as 30,000 + 4,000 + 200 + 8.
  2. Ask how many hundreds are in 4,300, then how many tens are in the same number.

  19 TAC §111.5

  Part of the place value topic

• Grade 3 3.2.B Describe place value to hundred thousands
  Close

  Prerequisites

  1. 3.2.A · Grade 3Compose and decompose numbers to 100,000

  3.2.B · Grade 3

  Describe place value to hundred thousands

  describe the mathematical relationships found in the base-10 place value system through the hundred thousands place

  Example

  1. Point at the two 4s in 44,000 and ask what makes the left one worth ten times the other.
  2. Ask how many hundreds it takes to make one thousand, then how many thousands make one hundred thousand.

  19 TAC §111.5

  Part of the place value topic

• Grade 3 3.4.A Add and subtract fluently within 1,000

Earlier grades (6)(12)

• Grade 1 1.1.B Analyze, plan, solve, justify, evaluate
  Close

  1.1.B · Grade 1

  Analyze, plan, solve, justify, evaluate

  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

  Example

  1. Read out a story problem and stop before any arithmetic. Ask what they already know and what the question is asking for.
  2. After an answer, ask how they know it is right, and whether that number makes sense for the story.

  19 TAC §111.3

  Part of the problem solving topic

• Grade 1 1.1.C Select tools and techniques for problems
  Close

  1.1.C · Grade 1

  Select tools and techniques for problems

  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 problems

  Example

  1. Put counters, paper, and a pencil on the table, ask for 8 + 5, and watch which one they reach for.
  2. Ask for 10 + 3 and see whether they still count objects out. Doing it in their head at this size is the thing worth noticing.

  19 TAC §111.3

  Part of the problem solving topic

• Grade 1 1.3.B Solve join, separate, compare problems to 20
  Close

  1.3.B · Grade 1

  Solve join, separate, compare problems to 20

  use objects and pictorial models to solve word problems involving joining, separating, and comparing sets within 20 and unknowns as any one of the terms in the problem such as 2 + 4 = [ ]; 3 + [ ] = 7; and 5 = [ ] - 3

  Example

  1. Put 9 stones in one pile and 6 in another and ask how many altogether.
  2. They have 8 pinecones and want 14 — ask how many more, with the pinecones on the table to move.
  3. Say they ended with 5 pinecones after giving 3 away, pinecones on the table, and ask how many they started with.

  19 TAC §111.3

  Part of the problem solving topic

• Grade 1 1.3.E Explain add and subtract strategies to 20
• Grade 1 1.3.F Generate, solve stories for number sentences
• Grade 1 1.5.D Model addition and subtraction problems to 20
• Grade 2 2.1.B Use a problem-solving model
  Close

  2.1.B · Grade 2

  Use a problem-solving model

  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

  Example

  1. Give a problem with a number missing and ask what they would do first, before any arithmetic happens.
  2. After an answer, ask "does that seem about right?" and listen for a reason rather than a re-check.

  19 TAC §111.4

  Part of the problem solving topic

• Grade 2 2.1.C Select tools and techniques to solve problems
  Close

  2.1.C · Grade 2

  Select tools and techniques to solve problems

  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 problems

  Example

  1. Ask for 30 + 40 and watch whether they reach for paper. Reaching for it at this size is the thing worth noticing.
  2. Ask which is easier for 402 - 178, mental math or writing it down, and why.

  19 TAC §111.4

  Part of the problem solving topic

• Grade 2 2.4.C One- and multi-step word problems within 1,000
• Grade 2 2.4.D Write and solve problems from number sentences
• Grade 2 2.7.C Represent and solve problems with any unknown
• Grade 2 2.10.C Write and solve one-step graph problems
• Grade 3 3.1.B Use a problem-solving model
  Close

  3.1.B · Grade 3

  Use a problem-solving model

  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

  Example

  1. Give a two-step problem and ask what they would do first, before any arithmetic happens.
  2. After an answer, ask why it is reasonable. Listen for a reason rather than a re-check of the steps.

  19 TAC §111.5

  Part of the problem solving topic

• Grade 3 3.1.C Select tools and techniques for problems
  Close

  3.1.C · Grade 3

  Select tools and techniques for problems

  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 problems

  Example

  1. Ask for 5 x 60 and watch whether they reach for paper. Reaching for it at this size is the thing worth noticing.
  2. Ask which is easier for 47 x 6, mental math or writing it down, and why.

  19 TAC §111.5

  Part of the problem solving topic

• Grade 3 3.3.E Partition objects into fractional shares
• Grade 3 3.4.A Add and subtract fluently within 1,000
• Grade 3 3.4.K Solve division and multiplication within 100
• Grade 3 3.5.B Model and solve multiplication and division
• Grade 3 3.8.B Solve problems from categorical data displays

Earlier grades (7)(13)

• Grade 1 1.6.A Classify and sort 2D shapes by attributes
  Close

  1.6.A · Grade 1

  Classify and sort 2D shapes by attributes

  classify and sort regular and irregular two-dimensional shapes based on attributes using informal geometric language

  Example

  1. Cut out a dozen paper shapes, some neat and some lopsided, and ask them to sort the pile and say what each group has in common.
  2. Ask them to pull out every shape with three corners, crooked ones included.

  19 TAC §111.3

  Part of the shapes and geometry topic

• Grade 1 1.6.B Defining versus non-defining attributes
  Close

  Prerequisites

  1. 1.6.A · Grade 1Classify and sort 2D shapes by attributes

  1.6.B · Grade 1

  Defining versus non-defining attributes

  distinguish between attributes that define a two-dimensional or three-dimensional figure and attributes that do not define the shape

  Example

  1. Draw a large red triangle and a small blue one tipped onto its point, and ask what makes both of them triangles.
  2. Ask whether a square standing on a corner is still a square, and why the turning did not change it.
  3. Put a tall can and a short one side by side and ask what makes both of them cylinders.

  19 TAC §111.3

  Part of the shapes and geometry topic

• Grade 1 1.6.C Create two-dimensional figures
  Close

  1.6.C · Grade 1

  Create two-dimensional figures

  create two-dimensional figures, including circles, triangles, rectangles, and squares, as special rectangles, rhombuses, and hexagons

  Example

  1. Hand over a pencil and ask them to draw each one: a circle, a triangle, a rectangle, a square, a rhombus, and a hexagon.
  2. Ask them to build the same shapes out of straws, then ask what the circle would take instead.

  19 TAC §111.3

  Part of the shapes and geometry topic

• Grade 1 1.6.D Name 2D shapes and their attributes formally
  Close

  Prerequisites

  1. 1.6.B · Grade 1Defining versus non-defining attributes

  1.6.D · Grade 1

  Name 2D shapes and their attributes formally

  identify two-dimensional shapes, including circles, triangles, rectangles, and squares, as special rectangles, rhombuses, and hexagons and describe their attributes using formal geometric language

  Example

  1. Lay out a circle, a triangle, a rectangle, a square, a rhombus, and a hexagon, and ask them to name each and say how many sides and vertices it has.
  2. Ask what makes a square a special kind of rectangle.

  19 TAC §111.3

  Part of the shapes and geometry topic

  what we did

• Grade 1 1.6.E Identify 3D solids and describe attributes
  Close

  1.6.E · Grade 1

  Identify 3D solids and describe attributes

  identify three-dimensional solids, including spheres, cones, cylinders, rectangular prisms (including cubes), and triangular prisms, and describe their attributes using formal geometric language

  Example

  1. Put out a ball, a party hat, a soup can, a shoebox, a die, and a wedge-shaped box, and ask them to name each: sphere, cone, cylinder, rectangular prism, cube, triangular prism.
  2. Ask how many faces the shoebox has, then how many vertices.

  19 TAC §111.3

  Part of the shapes and geometry topic

• Grade 1 1.6.F Join figures into a target shape
  Close

  1.6.F · Grade 1

  Join figures into a target shape

  compose two-dimensional shapes by joining two, three, or four figures to produce a target shape in more than one way if possible

  Example

  1. Ask them to make a hexagon out of pattern blocks, then to make the same hexagon a different way.
  2. Ask for a rectangle built from four blocks, then for the same rectangle built from two.

  19 TAC §111.3

  Part of the shapes and geometry topic

• Grade 1 1.6.G Partition into two and four equal parts
• Grade 2 2.8.A Create 2D shapes from sides and vertices
  Close

  Prerequisites

  1. 1.6.C · Grade 1Create two-dimensional figures

  2.8.A · Grade 2

  Create 2D shapes from sides and vertices

  create two-dimensional shapes based on given attributes, including number of sides and vertices

  Example

  1. Ask them to draw a shape with five sides and five vertices.

  19 TAC §111.4

  Part of the shapes and geometry topic

• Grade 2 2.8.B Classify and sort 3D solids by attributes
  Close

  Prerequisites

  1. 1.6.E · Grade 1Identify 3D solids and describe attributes

  2.8.B · Grade 2

  Classify and sort 3D solids by attributes

  classify and sort three-dimensional solids, including spheres, cones, cylinders, rectangular prisms (including cubes as special rectangular prisms), and triangular prisms, based on attributes using formal geometric language

  Example

  1. Put out two of each: soup cans, balls, party hats, shoeboxes, dice, and a wedge-shaped box. Ask them to sort the pile and name each group: cylinder, sphere, cone, rectangular prism, cube, triangular prism.

  19 TAC §111.4

  Part of the shapes and geometry topic

• Grade 2 2.8.C Sort and classify polygons to 12 sides
  Close

  Prerequisites

  1. 1.6.D · Grade 1Name 2D shapes and their attributes formally

  2.8.C · Grade 2

  Sort and classify polygons to 12 sides

  classify and sort polygons with 12 or fewer sides according to attributes, including identifying the number of sides and number of vertices

  Example

  1. Draw several polygons, none with more than 12 sides, and ask them to group the ones with the same number of sides, then count the vertices in each group.

  19 TAC §111.4

  Part of the shapes and geometry topic

• Grade 2 2.8.D Compose shapes and solids from attributes
  Close

  Prerequisites

  1. 1.6.F · Grade 1Join figures into a target shape

  2.8.D · Grade 2

  Compose shapes and solids from attributes

  compose two-dimensional shapes and three-dimensional solids with given properties or attributes

  Example

  1. Ask them to make a hexagon out of pattern blocks in two different ways.

  19 TAC §111.4

  Part of the shapes and geometry topic

• Grade 2 2.8.E Decompose 2D shapes and identify the parts
  Close

  Prerequisites

  1. 2.8.D · Grade 2Compose shapes and solids from attributes

  2.8.E · Grade 2

  Decompose 2D shapes and identify the parts

  decompose two-dimensional shapes such as cutting out a square from a rectangle, dividing a shape in half, or partitioning a rectangle into identical triangles and identify the resulting geometric parts

  Example

  1. Ask them to cut a square out of a rectangle and name both pieces that result.
  2. Ask them to divide a rectangle into two identical triangles.

  19 TAC §111.4

  Part of the shapes and geometry topic

• Grade 2 2.9.F Find rectangle area with square unit models
• Grade 3 3.6.A Classify and sort 2D and 3D figures
  Close

  Prerequisites

  1. 2.8.B · Grade 2Classify and sort 3D solids by attributes
  2. 2.8.C · Grade 2Sort and classify polygons to 12 sides

  3.6.A · Grade 3

  Classify and sort 2D and 3D figures

  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

  Example

  1. Put out a party hat, a soup can, a ball, a wedge-shaped block, a shoebox, and a die. Ask them to sort the pile and name each group: cone, cylinder, sphere, triangular prism, rectangular prism, cube.
  2. Draw a triangle, a square, a pentagon, and a hexagon, and ask them to sort those by number of sides and name each one.
  3. Ask what makes a cube a rectangular prism as well, using the words faces, edges, and vertices.

  19 TAC §111.5

  Part of the shapes and geometry topic

• Grade 3 3.6.B Recognize quadrilateral types and draw others
  Close

  Prerequisites

  1. 3.6.A · Grade 3Classify and sort 2D and 3D figures

  3.6.B · Grade 3

  Recognize quadrilateral types and draw others

  use attributes to recognize rhombuses, parallelograms, trapezoids, rectangles, and squares as examples of quadrilaterals and draw examples of quadrilaterals that do not belong to any of these subcategories

  Example

  1. Draw a rhombus, a parallelogram, a trapezoid, a rectangle, and a square. Ask them to name each and say what makes all five quadrilaterals.
  2. Ask them to draw a four-sided figure that is none of those five, and explain why it still counts as a quadrilateral.

  19 TAC §111.5

  Part of the shapes and geometry topic

• Grade 3 3.6.C Determine rectangle area using multiplication
• Grade 3 3.6.D Find area by decomposing composite figures
  Close

  Prerequisites

  1. 2.8.E · Grade 2Decompose 2D shapes and identify the parts
  2. 3.6.C · Grade 3Determine rectangle area using multiplication

  3.6.D · Grade 3

  Find area by decomposing composite figures

  decompose composite figures formed by rectangles into non-overlapping rectangles to determine the area of the original figure using the additive property of area

  Example

  1. Draw an L-shaped room, ask them to cut it into two rectangles with one line, find the area of each, then the whole.
  2. Ask whether the two rectangles overlap anywhere, and why that matters to the total.

  19 TAC §111.5

  Part of the shapes and geometry topic

• Grade 3 3.6.E Decompose figures into unit-fraction parts

Earlier grades (1)

• Grade 1 1.7.E Tell time to hour and half hour
  Close

  1.7.E · Grade 1

  Tell time to hour and half hour

  tell time to the hour and half hour using analog and digital clocks

  Example

  1. Point at an analog clock at 3:00 and ask for the time, then move the hands to 3:30 and ask again.
  2. Ask them to read those same two times off a digital clock, and to say what the 30 is counting.

  19 TAC §111.3

  Part of the telling time topic

  what we did

• Grade 2 2.9.G Time to the minute, am or pm
  Close

  Prerequisites

  1. 1.7.E · Grade 1Tell time to hour and half hour

  2.9.G · Grade 2

  Time to the minute, am or pm

  read and write time to the nearest one-minute increment using analog and digital clocks and distinguish between a.m. and p.m

  Example

  1. Point at an analog clock at 3:47 and ask for the time to the minute.
  2. Ask whether breakfast is a.m. or p.m., then ask which one 7:00 in the evening is.

  19 TAC §111.4

  Part of the telling time topic