Mathematics, grade 1
One skill at a time, grade 1, in the order it builds.
11 topics · 41 skills across grade 1 · 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 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 Close
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
- Ask for 8 + 5 and listen for whether they take 2 off the 5 to make 10 first.
- Ask for 13 - 5 and listen for whether they come down to 10 first and take the other 2 after.
Part of the adding and subtracting topic
- Grade 1 1.3.E Explain add and subtract strategies to 20 Close
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
- After they answer 7 + 8, ask them to say out loud how they got there.
- Ask them to show that same 7 + 8 with counters, then write it as a number sentence.
Part of the adding and subtracting topic
- Grade 1 1.3.F Generate, solve stories for number sentences Close
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
- Write 12 - 5 = 7 and ask them to invent a story the sentence answers.
- Write 6 + 9 = 15 and ask for a story where the 9 is something arriving, not something already there.
Part of the adding and subtracting topic
- Grade 1 1.5.D Model addition and subtraction problems to 20 Close
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
- Tell them 7 birds were on a wire and 5 more landed. Ask for the drawing and the number sentence first.
- Put 15 stones out, say 6 got carried off, and ask for the model and the number sentence before the answer.
Part of the adding and subtracting topic
- Grade 1 1.5.F Determine the unknown in any term Close
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
- Write 8 + [ ] = 15 and ask for the missing number.
- Write [ ] - 4 = 9, where the unknown starts the sentence instead of ending it.
- Write 5 + 3 = [ ] + 6 and ask for the missing number in the one with four terms.
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
- Ask for 7 + 4, then 4 + 7, and ask why the answer did not move.
- Ask for 8 + 2 + 5 and watch whether they take the 8 and the 2 first.
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 Close
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
- Slide 8 pennies across the table and ask them to count by twos to the total.
- Put out 6 nickels and ask them to count by fives.
- Put out 4 dimes and 3 pennies and ask them to count the dimes by tens before picking up the pennies.
Part of the counting topic
- Grade 1 1.5.B Skip count twos, fives, tens to 120 Close
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
- Pour out a jar of buttons, ask them to push the buttons into groups of 10, and count by tens to the total.
- Lay out 30 pennies in pairs and ask for the total by twos.
- Ask them to count a page of tally marks by fives.
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 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
- Hand over a tortilla and ask them to split it into two fair shares, then name one piece out loud.
- Fold a square of paper into four equal parts and ask what one part is called.
Part of the fractions topic
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 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
- Ask them to show 7 + 6 two ways: as a drawing, and as a number sentence.
- Ask them to tell you in one sentence what a bar graph on a visitor-center wall is saying.
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
- On a drive, ask them to keep tally marks for three things: cars, trucks, and motorcycles.
- Ask them to set the T-chart up before the counting starts, with a heading written over each column.
Part of the graphs and data topic
- Grade 1 1.8.B Make picture and bar-type graphs from data Close
1.8.B · Grade 1
Make picture and bar-type graphs from data
use data to create picture and bar-type graphs
Example
- Turn the tally into a picture graph, one small drawing per vehicle.
- Ask them to redraw the same counts as bars, one square per vehicle.
Part of the graphs and data topic
- Grade 1 1.8.C Ask, answer, and conclude from graphs Close
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
- Ask which bar is tallest, and how many more it holds than the shortest one.
- Ask them to make up a question their own graph can answer, then answer it.
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 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
- Hand over a tape measure and ask for the length of the picnic table, then the bench beside it.
- Watch whether they line the end of the object up with the zero on the tape rather than with the first number they see.
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
- Ask them to measure a book with color tiles laid end to end, and watch for gaps and overlaps.
- Slide one tile out of the middle of the finished row and ask what the measurement says now.
Part of the measurement topic
- Grade 1 1.7.C Measure with two unit sizes, explain why Close
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
- 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.
Part of the measurement topic
- Grade 1 1.7.D Describe length using number and whole unit Close
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
- After they measure a leaf, ask for the answer as a number and a unit, not a number on its own.
- When the end of the object lands between two marks, ask which whole one is nearer.
Part of the measurement topic
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 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
- Lay out a penny, a nickel, a dime, and a quarter, and ask them to name each one and say what it is worth.
- Ask how many pennies make a nickel, how many nickels make a dime, and how many nickels make a quarter.
Part of the money topic
- 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 Close
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
- At a gas stop, ask which things on the shelf are wants and which are needs.
- Ask how the money someone earns turns into a loaf of bread and a haircut, and which of the two is a service.
Part of the money topic
- Grade 1 1.9.C Spending versus saving
Earning, spending, saving and sharing — then taxes, credit and what borrowing costs, and making the budget balance.
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 Close
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
- Put 89 and 98 side by side and ask which is greater, and how the tens told them.
- Ask them to finish "45 is ___ 54" out loud rather than writing anything.
Part of the place value topic
- Grade 1 1.2.F Order whole numbers to 120 Close
1.2.F · Grade 1
Order whole numbers to 120
order whole numbers up to 120 using place value and open number lines
Example
- Write 31, 13, and 103 on three cards and ask them to lay them out smallest first.
- Draw a line with no marks on it at all and ask them to place 20, 65, and 90 along it in order.
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 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
- Read out a story problem and stop before any arithmetic. Ask what they already know and what the question is asking for.
- After an answer, ask how they know it is right, and whether that number makes sense for the story.
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
- Put counters, paper, and a pencil on the table, ask for 8 + 5, and watch which one they reach for.
- 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.
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
- Put 9 stones in one pile and 6 in another and ask how many altogether.
- They have 8 pinecones and want 14 — ask how many more, with the pinecones on the table to move.
- Say they ended with 5 pinecones after giving 3 away, pinecones on the table, and ask how many they started with.
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
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 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
- 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.
- Ask them to pull out every shape with three corners, crooked ones included.
Part of the shapes and geometry topic
- Grade 1 1.6.B Defining versus non-defining attributes Close
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
- Draw a large red triangle and a small blue one tipped onto its point, and ask what makes both of them triangles.
- Ask whether a square standing on a corner is still a square, and why the turning did not change it.
- Put a tall can and a short one side by side and ask what makes both of them cylinders.
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
- Hand over a pencil and ask them to draw each one: a circle, a triangle, a rectangle, a square, a rhombus, and a hexagon.
- Ask them to build the same shapes out of straws, then ask what the circle would take instead.
Part of the shapes and geometry topic
- Grade 1 1.6.D Name 2D shapes and their attributes formally Close
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
- 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.
- Ask what makes a square a special kind of rectangle.
Part of the shapes and geometry topic
- 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
- 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.
- Ask how many faces the shoebox has, then how many vertices.
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
- Ask them to make a hexagon out of pattern blocks, then to make the same hexagon a different way.
- Ask for a rectangle built from four blocks, then for the same rectangle built from two.
Part of the shapes and geometry topic
- Grade 1 1.6.G Partition into two and four equal parts
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 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
- Point at an analog clock at 3:00 and ask for the time, then move the hands to 3:30 and ask again.
- Ask them to read those same two times off a digital clock, and to say what the 30 is counting.
Part of the telling time topic