Mathematics, grade 2
50 things Texas expects by the end of grade 2, in the state's own words and ours.
How to go at a problem, rather than which problems. These run underneath all the rest.
- 2.1.A Apply math in life, society, and work Close
2.1.A · Grade 2
Apply math in life, society, and work
apply mathematics to problems arising in everyday life, society, and the workplace
Example
- Hand over the receipt at a grocery stop and ask whether the change was right.
- Ask how many days a 900-mile drive takes at 300 miles a day.
- 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
- Give a problem with a number missing and ask what they would do first, before any arithmetic happens.
- After an answer, ask "does that seem about right?" and listen for a reason rather than a re-check.
Part of the problem solving topic
- 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
- Ask for 30 + 40 and watch whether they reach for paper. Reaching for it at this size is the thing worth noticing.
- Ask which is easier for 402 - 178, mental math or writing it down, and why.
Part of the problem solving topic
- 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
- Ask them to show 24 + 18 two ways: with a drawing, and with numbers.
- Ask them to explain a subtraction out loud, without pointing at the page.
Part of the graphs and data topic
- 2.1.E Create and use representations for ideas Close
2.1.E · Grade 2
Create and use representations for ideas
create and use representations to organize, record, and communicate mathematical ideas
Example
- Ask them to keep a tally of something on a drive and turn it into a picture at the end.
- 2.1.F Analyze relationships, connect and communicate Close
2.1.F · Grade 2
Analyze relationships, connect and communicate
analyze mathematical relationships to connect and communicate mathematical ideas
Example
- Ask what 8 + 7 has to do with 80 + 70.
- Ask why knowing 6 + 6 helps with 6 + 7.
- 2.1.G Display, explain, and justify with precision Close
2.1.G · Grade 2
Display, explain, and justify with precision
display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication
Example
- Ask them to convince you that 213 is greater than 199 using the word "hundreds". Listen for whether they get pulled into counting tens, where 199 has more.
19 TAC §111.4 · the rule text · archived · verified 2026-08-05
What numbers are, how big they are, and how they come apart and go back together.
- 2.2.A Compose and decompose numbers to 1,200 Close
2.2.A · Grade 2
Compose and decompose numbers to 1,200
use concrete and pictorial models to compose and decompose numbers up to 1,200 in more than one way as a sum of so many thousands, hundreds, tens, and ones
Example
- Ask them to build 1,145 with base-ten blocks, then build it again a different way.
- Ask for 340 as a sum of hundreds and tens, then ask separately how many tens are in 340.
- 2.2.B Numbers to 1,200: standard, word, expanded Close
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
- Write 1,062 and ask them to say it and then write it as 1,000 + 60 + 2.
- Say "nine hundred four" and ask them to write the numeral. Watch for a four-digit answer.
Part of the place value topic
- 2.2.C Generate greater or lesser numbers to 1,200 Close
2.2.C · Grade 2
Generate greater or lesser numbers to 1,200
generate a number that is greater than or less than a given whole number up to 1,200
Example
- Say 780 and ask for a bigger number that is still under 1,200. Then ask for one smaller than 780 but bigger than 700.
- 2.2.D Compare and order numbers to 1,200 Close
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
- Put 1,110 and 1,101 side by side and ask which is greater, and how they know.
- Ask them to write the symbol between 476 and 467 rather than saying the word.
Part of the place value topic
- 2.2.E Locate a number on an open line Close
2.2.E · Grade 2
Locate a number on an open line
locate the position of a given whole number on an open number line
Example
- Draw a line marked only 0 and 1,000 and ask them to mark roughly where 250 goes.
- 2.2.F Name the whole number at a point Close
2.2.F · Grade 2
Name the whole number at a point
name the whole number that corresponds to a specific point on a number line
Example
- Mark a point between two labeled ticks on a number line and ask what number sits there.
- 2.3.A Partition and name halves, fourths, eighths Close
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
- Hand them a sandwich and ask for fourths, then ask them to name one piece in words.
- Fold a sheet of paper into eighths and ask what one part is called.
Part of the fractions topic
- 2.3.B More parts, smaller parts; fewer, larger Close
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
- Ask which is bigger, a half of a cracker or an eighth of the same cracker, and why.
Part of the fractions topic
- 2.3.C Count parts to and beyond one whole Close
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
- 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.
- Ask how many eighths it takes to make one whole.
Part of the counting topic
- 2.3.D Halves, fourths, eighths: example or not Close
2.3.D · Grade 2
Halves, fourths, eighths: example or not
identify examples and non-examples of halves, fourths, and eighths
Example
- Cut a shape into two uneven pieces and ask whether those are halves. The answer is no, and the reason is the point.
- 2.4.A Automatic addition and subtraction within 20 Close
2.4.A · Grade 2
Automatic addition and subtraction within 20
recall basic facts to add and subtract within 20 with automaticity
Example
- Ask 9 + 6 and 14 - 8 with no paper. Listen for an answer in a couple of seconds, not a count.
Part of the adding and subtracting topic
- 2.4.B Up to four two-digit addends, and subtraction Close
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
- Ask for 23 + 41 + 12 + 30 in one go, all four at once.
- Ask for 62 - 47 and listen for whether they can explain the borrowing, not just do it.
Part of the adding and subtracting topic
- 2.4.C One- and multi-step word problems within 1,000 Close
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
- Two legs of a drive run 235 miles and 148 miles. Ask how far that is altogether, then how much farther to 500.
- A jar holds 412 beads and 175 come out. Ask how many are left, then ask them to check it a different way.
Part of the adding and subtracting topic
- 2.4.D Write and solve problems from number sentences Close
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
- Write 300 - 125 = 175 and ask them to invent a story that the sentence answers.
Part of the adding and subtracting topic
- 2.5.A Coin collection value up to one dollar Close
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
- Hand over three quarters, two dimes, and a nickel and ask for the total. It is one dollar.
- Lay out two quarters, a dime, and a nickel and ask what it comes to. It is 65 cents.
Part of the money topic
- 2.5.B Name coin values with money symbols Close
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
- 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.
Part of the money topic
- 2.6.A Multiplication as joining equivalent sets Close
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
- Set out four cups with three stones in each and ask them to say what they see, then how many stones altogether.
Part of the multiplication and division topic
- 2.6.B Division as separating into equivalent sets Close
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
- Hand over twelve stones and ask them to share the stones fairly among three people, then say how they did it.
Part of the multiplication and division topic
19 TAC §111.4 · the rule text · archived · verified 2026-08-05
Finding the pattern, and finding the missing number.
- 2.7.A Even or odd for numbers to 40 Close
2.7.A · Grade 2
Even or odd for numbers to 40
determine whether a number up to 40 is even or odd using pairings of objects to represent the number
Example
- Ask whether 27 is even or odd, and ask them to prove it by pairing rather than by reciting a rule.
- 2.7.B 10 or 100 more/less to 1,200 Close
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
- Say 1,140 and ask for 10 more, then 100 less.
- Say 995 and ask for 10 more. The crossing is the part worth watching.
Part of the place value topic
- 2.7.C Represent and solve problems with any unknown Close
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
- Say "the drive was some number of miles, then 40 more, and ended at 130," and ask for the first number.
- 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.
Part of the adding and subtracting topic
19 TAC §111.4 · the rule text · archived · verified 2026-08-05
Shapes, and how you measure them: how long, how far, how much time.
- 2.8.A Create 2D shapes from sides and vertices Close
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
- Ask them to draw a shape with five sides and five vertices.
Part of the shapes and geometry topic
- 2.8.B Classify and sort 3D solids by attributes Close
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
- 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.
Part of the shapes and geometry topic
- 2.8.C Sort and classify polygons to 12 sides Close
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
- 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.
Part of the shapes and geometry topic
- 2.8.D Compose shapes and solids from attributes Close
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
- Ask them to make a hexagon out of pattern blocks in two different ways.
Part of the shapes and geometry topic
- 2.8.E Decompose 2D shapes and identify the parts Close
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
- Ask them to cut a square out of a rectangle and name both pieces that result.
- Ask them to divide a rectangle into two identical triangles.
Part of the shapes and geometry topic
- 2.9.A Find length with models of standard units Close
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
- Ask them to measure the picnic table with inch tiles laid end to end, no gaps.
Part of the measurement topic
- 2.9.B Bigger units, fewer units needed Close
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
- Measure the same table in paper clips and then in shoes, and ask why the bigger unit gave the smaller number.
Part of the measurement topic
- 2.9.C A number as distance from any location Close
2.9.C · Grade 2
A number as distance from any location
represent whole numbers as distances from any given location on a number line
Example
- Mark 4 on a number line, not 0, and ask them to show a distance of 6 from it.
- 2.9.D Use measuring tools to the nearest mark Close
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
- Hand over a ruler and ask for the length of a leaf to the nearest marked unit.
- Watch whether they line the object up with zero rather than with the end of the ruler.
Part of the measurement topic
- 2.9.E Solve length problems, including estimates Close
2.9.E · Grade 2
Solve length problems, including estimates
determine a solution to a problem involving length, including estimating lengths
Example
- Ask them to guess the length of the trail sign before measuring, then measure it.
- Ask which of two trails is longer, and by roughly how much, without working it out exactly.
Part of the measurement topic
- 2.9.F Find rectangle area with square unit models Close
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
- 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.
Part of the counting topic
- 2.9.G Time to the minute, am or pm Close
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
- Point at an analog clock at 3:47 and ask for the time to the minute.
- Ask whether breakfast is a.m. or p.m., then ask which one 7:00 in the evening is.
Part of the telling time topic
19 TAC §111.4 · the rule text · archived · verified 2026-08-05
Collecting what you counted, and getting it to say something.
- 2.10.A Bars and pictures stand for data points Close
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
- Show a bar graph and ask what the height of one bar means.
Part of the graphs and data topic
- 2.10.B Four categories in pictographs and bar graphs Close
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
- Ask them to count four kinds of vehicle at a rest stop, then build a bar graph with an interval of two.
Part of the graphs and data topic
- 2.10.C Write and solve one-step graph problems Close
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
- 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.
Part of the adding and subtracting topic
- 2.10.D Draw conclusions and predictions from graphs Close
2.10.D · Grade 2
Draw conclusions and predictions from graphs
draw conclusions and make predictions from information in a graph
Example
- Ask what the graph suggests would happen if you counted again tomorrow, and why.
Part of the graphs and data topic
19 TAC §111.4 · the rule text · archived · verified 2026-08-05
Money: earning it, saving it, and choosing between two things.
- 2.11.A Calculate how savings grow over time
- 2.11.B Saving instead of spending
- 2.11.C Deposits versus withdrawals Close
2.11.C · Grade 2
Deposits versus withdrawals
distinguish between a deposit and a withdrawal
Example
- Ask which one takes money out of an account, a deposit or a withdrawal.
- 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
- Ask for an example of borrowing something, and what would make the borrowing irresponsible.
Part of the personal finance topic
- 2.11.E Lending examples; weigh benefits and costs Close
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
- Ask what a person lending a bike gives up, and what they get out of it.
Part of the personal finance topic
- 2.11.F Producers, consumers, and cost to produce Close
2.11.F · Grade 2
Producers, consumers, and cost to produce
differentiate between producers and consumers and calculate the cost to produce a simple item
Example
- Point at a loaf of bread and ask who made it and who eats it, then work out what the ingredients cost.
19 TAC §111.4 · the rule text · archived · verified 2026-08-05