Mathematics, grade 2
One skill at a time, grades 1-2, in the order it builds.
12 topics · 90 skills across grades 1-2 · 19 TAC chapter 111 the rule text (PDF)
Grouped by what you would call the thing, rather than by where Texas files it. A skill can sit under more than one topic, because most of them do.
This sheet is grade 2. Grade 1 is named here by title only; the wording in full is on its own sheet: grade 1. There are no earlier grades below this window.
Putting together and taking away whole numbers, fractions and decimals — then positive and negative numbers too, first with models, later fluently.
also called sums, take away
- Grade 1 1.3.D Apply fact strategies within 20
- 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 1 1.5.F Determine the unknown in any term
- Grade 1 1.5.G Add and subtract using operation properties
- Grade 2 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
- Grade 2 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
- Grade 2 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
- Grade 2 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
- Grade 2 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
- Grade 2 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
Counting in twos, fives and tens, and using it to total up a pile of coins or a grid of square tiles.
- Grade 1 1.4.C Count pennies, nickels, dimes to find value
- Grade 1 1.5.B Skip count twos, fives, tens to 120
- Grade 2 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
- Grade 2 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
Fair shares of a whole — then ratios and percents too: named, compared, computed, and converted between forms.
- Grade 1 1.6.G Partition into two and four equal parts
- Grade 2 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
- Grade 2 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
- Grade 2 2.3.C Count parts to and beyond one whole
Drawing up data as dot plots, histograms, box plots and scatterplots — and graphing relationships on the coordinate plane to predict what comes next.
also called charts, bar graphs
- Grade 1 1.1.D Communicate ideas, reasoning, implications
- Grade 1 1.8.A Collect, sort, organize up to three categories
- Grade 1 1.8.B Make picture and bar-type graphs from data
- Grade 1 1.8.C Ask, answer, and conclude from graphs
- 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
- 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
- Grade 2 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
- Grade 2 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
- Grade 2 2.10.C Write and solve one-step graph problems
- Grade 2 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
How long, how heavy, how much it holds — and how wide an angle opens, measured in degrees.
also called rulers, how long
- Grade 1 1.7.A Use tools to measure object length
- Grade 1 1.7.B Length is same-size units, end to end
- Grade 1 1.7.C Measure with two unit sizes, explain why
- Grade 1 1.7.D Describe length using number and whole unit
- Grade 2 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
- Grade 2 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
- Grade 2 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
- Grade 2 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
- Grade 2 2.9.F Find rectangle area with square unit models
- Grade 2 2.10.A Bars and pictures stand for data points
Dollars and cents first — naming them, counting them — then earning, spending, saving and investing.
also called coins, allowance
- Grade 1 1.4.A Identify coins by value, relate them
- Grade 1 1.4.B Write coin values with the cent symbol
- 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 2.5.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
- Grade 2 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
- Grade 2 2.11.A Calculate how savings grow over time
- Grade 2 2.11.B Saving instead of spending
Equal groups and fair shares: acted out with objects first, then facts by heart, then multi-digit, decimal and fraction problems on paper.
also called times tables
- Grade 2 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
- Grade 2 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
Earning, spending, saving and sharing — then taxes, credit and what borrowing costs, and making the budget balance.
- 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
- Ask for an example of borrowing something, and what would make the borrowing irresponsible.
Part of the personal finance topic
- Grade 2 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
What each digit is worth, from billions down to thousandths — which is what makes big numbers and small decimals manageable.
- Grade 1 1.2.E Compare whole numbers to 120 in words
- Grade 1 1.2.F Order whole numbers to 120
- Grade 2 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
- Grade 2 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
- 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
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
Word problems, and the habit underneath them: pick a tool, try it, and check whether the answer is sensible.
- Grade 1 1.1.B Analyze, plan, solve, justify, evaluate
- Grade 1 1.1.C Select tools and techniques for problems
- Grade 1 1.3.B Solve join, separate, compare problems to 20
- 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
- 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
- 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
- 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
- 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
Naming shapes and solids, sorting them by sides and angles, moving and resizing them — and measuring around, across and inside them.
- Grade 1 1.6.A Classify and sort 2D shapes by attributes
- Grade 1 1.6.B Defining versus non-defining attributes
- Grade 1 1.6.C Create two-dimensional figures
- Grade 1 1.6.D Name 2D shapes and their attributes formally
- Grade 1 1.6.E Identify 3D solids and describe attributes
- Grade 1 1.6.F Join figures into a target shape
- 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
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
- Grade 2 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
- Grade 2 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
- Grade 2 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
- Grade 2 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
- Grade 2 2.9.F Find rectangle area with square unit models
Reading a clock, analog or digital — to the hour and half hour first, then to the minute.
also called clocks
- Grade 1 1.7.E Tell time to hour and half hour
- Grade 2 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