Grade 1 Math: build number sense by talking it through

A taste of a lesson on Making Ten and Decomposing to Add and Subtract within 20

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The 22 topics in Grade 1 Math

Each topic builds on the ones before it. The tutor checks what you already know and starts there.

1. Counting and Reading Numerals to 120

   Count forward to 120 starting from any number below 120, including across decade boundaries (e.g., 39 to 41, 99 to 101). Read and write numerals up to 120 and represent a given number of objects with the correct written numeral. Recognize common errors such as writing 'forty-three' as 43 reversed or skipping 'teens' sequences.

2. Addition and Subtraction Situations and Word Problems within 20

   Model the situations of adding to, taking from, putting together, taking apart, and comparing with objects and drawings, then write equations. Teach that unknowns can be in any position (start, change, or result unknown; both addends unknown; difference unknown). Students solve one-step word problems within 20 and explain their representation.

   Builds on Counting and Reading Numerals to 120

3. Counting On and Relating Counting to Addition and Subtraction

   Use counting on from the larger addend (e.g., 5 + 2 by counting 6, 7) and counting back for subtraction. Show that adding 2 is the same as counting on 2, and that subtraction can be counted back or counted up. Students connect number-line movements and counting sequences to equations.

   Builds on Counting and Reading Numerals to 120

4. Addition Fluency within 10 and Properties of Operations

   Build fluency with addition and subtraction facts within 10 through strategies: commutativity (5 + 3 = 3 + 5), associativity for adding three numbers (e.g., 3 + 4 + 6 by making ten or grouping), and the relationship between addition and subtraction (if 8 + 4 = 12 then 12 - 4 = 8). Students explain why these properties let them solve problems more easily.

   Builds on Addition and Subtraction Situations and Word Problems within 20, Counting On and Relating Counting to Addition and Subtraction

5. Three-Addend Addition Word Problems

   Solve word problems requiring addition of three whole numbers whose sum is 20 or less. Students group addends strategically (adding two that make ten, or doubles), represent the problem with objects, drawings, or an equation with a symbol for the unknown, and check the answer for reasonableness.

   Builds on Addition Fluency within 10 and Properties of Operations

6. Making Ten and Decomposing to Add and Subtract within 20

   Add and subtract within 20 with fluency using making ten (8 + 6 = 8 + 2 + 4 = 10 + 4 = 14) and decomposing a number leading to a ten (13 - 4 = 13 - 3 - 1 = 10 - 1 = 9). Students use ten-frames and explain each step. Fluency means answering these facts quickly and accurately with explained strategies.

   Builds on Addition Fluency within 10 and Properties of Operations

7. Subtraction as an Unknown-Addend Problem

   Understand subtraction as finding the missing addend: 10 - 8 is the number that makes 10 when added to 8. Students rewrite subtraction problems as addition with a missing addend and use this to subtract within 20.

   Builds on Making Ten and Decomposing to Add and Subtract within 20

8. Meaning of the Equal Sign and True or False Equations

   Understand that the equal sign means the two sides have the same value, not 'the answer comes next.' Determine whether equations such as 6 = 6, 7 = 8 - 1, 5 + 2 = 2 + 5, and 4 + 1 = 5 + 2 are true or false, and rewrite equations with the equal sign in different positions (e.g., 8 = 3 + 5).

   Builds on Subtraction as an Unknown-Addend Problem

9. Finding Unknowns in Addition and Subtraction Equations

   Determine the unknown whole number in equations relating three whole numbers in any position, such as 8 + ? = 11, 5 = ? - 3, and 6 + 6 = ?. Students use related facts, the meaning of the equal sign, and the unknown-position situations from word problems to solve and check.

   Builds on Addition and Subtraction Situations and Word Problems within 20, Meaning of the Equal Sign and True or False Equations

10. Tens and Ones in Two-Digit Numbers

    Understand that the two digits of a two-digit number represent tens and ones. Teach that 10 is a bundle of ten ones called a 'ten'; that the numbers 11 to 19 are one ten and 1 to 9 ones; and that 10, 20, ..., 90 are 1 to 9 tens and zero ones. Students build numbers with base-ten blocks or ten-frames and write them in expanded form.

    Builds on Counting and Reading Numerals to 120

11. Comparing Two-Digit Numbers

    Compare two two-digit numbers by first comparing tens digits, then ones digits, and record results with >, =, and <. Students explain comparisons using base-ten models, such as why 47 is greater than 38 without counting.

    Builds on Tens and Ones in Two-Digit Numbers

12. Mentally Finding 10 More and 10 Less

    Given a two-digit number, mentally find 10 more or 10 less without counting one by one, and explain the reasoning (the tens digit changes, the ones digit stays the same). Works across the decade boundary as well, e.g., 10 more than 47 is 57.

    Builds on Tens and Ones in Two-Digit Numbers

13. Adding a Two-Digit Number and a One-Digit or Multiple of Ten

    Add within 100 by adding a two-digit number and a one-digit number, and a two-digit number and a multiple of 10, using base-ten models, drawings, and place-value strategies (e.g., 34 + 5 = 39; 34 + 20 = 54). Students explain that tens are added to tens and ones to ones, and handle making a ten when needed.

    Builds on Making Ten and Decomposing to Add and Subtract within 20, Tens and Ones in Two-Digit Numbers, Mentally Finding 10 More and 10 Less

14. Subtracting Multiples of Ten

    Subtract multiples of 10 in the range 10 to 90 from multiples of 10 in the range 10 to 90 (non-negative results), using base-ten rods, drawings, and place-value reasoning (e.g., 70 - 30 = 40 because 7 tens minus 3 tens is 4 tens).

    Builds on Tens and Ones in Two-Digit Numbers, Mentally Finding 10 More and 10 Less

15. Ordering Objects by Length and Indirect Comparison

    Order three objects by length and compare two objects indirectly by using a third object as a measuring tie (e.g., the pencil is longer than the crayon, and the crayon is longer than the eraser, so the pencil is longer than the eraser). Students align endpoints and explain why direct comparison is needed.

    Builds on Counting and Reading Numerals to 120

16. Measuring Length with Non-Standard Units

    Express the length of an object as a whole number of length units by laying identical shorter objects (length units) end to end with no gaps or overlaps. Understand that the measurement is the count of same-size units, and that using a longer unit gives a smaller number.

    Builds on Addition and Subtraction Situations and Word Problems within 20, Ordering Objects by Length and Indirect Comparison

17. Telling and Writing Time to the Half Hour

    Read and write time in hours and half-hours on analog and digital clocks. Teach that the short hand shows the hour, the long hand shows minutes, the long hand at 6 means half past, and digital times like 3:30 are read as 'three thirty'. Students set clock faces to given times.

    Builds on Counting and Reading Numerals to 120

18. Organizing and Interpreting Data with Up to Three Categories

    Sort objects into up to three categories, represent the data with a table, tally chart, or picture or bar graph, and ask and answer questions: how many total data points, how many in each category, and how many more or fewer are in one category than another. Students use subtraction within 20 to compare categories.

    Builds on Addition and Subtraction Situations and Word Problems within 20, Addition Fluency within 10 and Properties of Operations

19. Defining and Non-Defining Attributes of Shapes

    Distinguish defining attributes (e.g., a triangle is closed and has three straight sides; a rectangle has four sides and four right angles) from non-defining attributes (color, orientation, overall size). Students build and draw shapes that possess the required defining attributes, and recognize a shape in varied orientations and sizes.

    Builds on Counting and Reading Numerals to 120

20. Composing Two- and Three-Dimensional Shapes

    Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, quarter-circles) and three-dimensional shapes (cubes, right rectangular prisms, right circular cones, right circular cylinders) to make larger composite shapes. Students fit pieces together, name the new shape, and describe which shapes were used.

    Builds on Defining and Non-Defining Attributes of Shapes

21. Equal Shares: Halves and Fourths

    Partition circles and rectangles into two or four equal shares, and describe the shares with the words halves, fourths, and quarters. Use the phrases 'half of', 'fourth of', and 'quarter of'. Explain that the whole can be described as two halves or four fourths, and that shares must be equal in size, not just in count.

    Builds on Defining and Non-Defining Attributes of Shapes

22. Fact Fluency Checkpoint: Sums and Differences within 20

    A cumulative checkpoint in which the student answers addition and subtraction facts within 20 quickly and accurately, explaining the strategy used for each (counting on, making ten, decomposing, or related facts). Covers doubles, make-ten sums, and subtraction through related addition facts. Serves as the end-of-grade fluency benchmark for OA.C.6.

    Builds on Making Ten and Decomposing to Add and Subtract within 20, Subtraction as an Unknown-Addend Problem, Finding Unknowns in Addition and Subtraction Equations

Practice questions in Grade 1 Math

A few of the kinds of questions you will work through, with answers.