(And the Educational Razzie Mummified Banana Statuette goes to….)

A post to start the New Year:

Here’s the thing: You can’t just grab any kid off the desert sands, throw him in the pod racer, and say, “Fly!!”

You can feed a third-grader nuclear physics all day long. You can throw in a dose of calculus for engineers. Perhaps a soupçon de Mandarin Chinese? Whatever. I return to a favorite saying: There is no teaching without learning.

From  http://www.corestandards.org/Math/Content/1/introduction/, I offer the Common Core math standards for the first grade. Feel free to mostly skim these. I recommend looking at mathematical practices, though.

Grade 1 » Introduction

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In Grade 1, instructional time should focus on four critical areas: (1) developing understanding of addition, subtraction, and strategies for addition and subtraction within 20; (2) developing understanding of whole number relationships and place value, including grouping in tens and ones; (3) developing understanding of linear measurement and measuring lengths as iterating length units; and (4) reasoning about attributes of, and composing and decomposing geometric shapes.

1. Students develop strategies for adding and subtracting whole numbers based on their prior work with small numbers. They use a variety of models, including discrete objects and length-based models (e.g., cubes connected to form lengths), to model add-to, take-from, put-together, take-apart, and compare situations to develop meaning for the operations of addition and subtraction, and to develop strategies to solve arithmetic problems with these operations. Students understand connections between counting and addition and subtraction (e.g., adding two is the same as counting on two). They use properties of addition to add whole numbers and to create and use increasingly sophisticated strategies based on these properties (e.g., “making tens”) to solve addition and subtraction problems within 20. By comparing a variety of solution strategies, children build their understanding of the relationship between addition and subtraction.
2. Students develop, discuss, and use efficient, accurate, and generalizable methods to add within 100 and subtract multiples of 10. They compare whole numbers (at least to 100) to develop understanding of and solve problems involving their relative sizes. They think of whole numbers between 10 and 100 in terms of tens and ones (especially recognizing the numbers 11 to 19 as composed of a ten and some ones). Through activities that build number sense, they understand the order of the counting numbers and their relative magnitudes.
3. Students develop an understanding of the meaning and processes of measurement, including underlying concepts such as iterating (the mental activity of building up the length of an object with equal-sized units) and the transitivity principle for indirect measurement.¹
4. 4. Students compose and decompose plane or solid figures (e.g., put two triangles together to make a quadrilateral) and build understanding of part-whole relationships as well as the properties of the original and composite shapes. As they combine shapes, they recognize them from different perspectives and orientations, describe their geometric attributes, and determine how they are alike and different, to develop the background for measurement and for initial understandings of properties such as congruence and symmetry.

Grade 1 Overview

Operations and Algebraic Thinking

• Represent and solve problems involving addition and subtraction.
• Understand and apply properties of operations and the relationship between addition and subtraction.
• Add and subtract within 20.
• Work with addition and subtraction equations.

Number and Operations in Base Ten

• Extend the counting sequence.
• Understand place value.
• Use place value understanding and properties of operations to add and subtract.

Measurement and Data

• Measure lengths indirectly and by iterating length units.
• Tell and write time.
• Represent and interpret data.

Geometry

• Reason with shapes and their attributes.

Mathematical Practices

1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning

The site https://www.ixl.com/standards/common-core/math/grade-1 expands on these expectations. This is an example of the curriculum expected to proceed from the Common Core standards — a mostly rational curriculum that I also recommend skimming, keeping in mind that this is for a six-year-old in 180 days of school. You might pause and read place value, data interpretation and geometry more slowly.

1.OA Operations and Algebraic Thinking

• 1.OA.A Represent and solve problems involving addition and subtraction.

  • 1.OA.A.1 Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.

    • Add with pictures – sums up to 10 (1-B.1)
    • Addition sentences – sums up to 10 (1-B.2)
    • Complete the addition sentence – sums up to 10 (1-D.3)
    • Addition word problems – sums up to 10 (1-D.5)
    • Addition sentences for word problems – sums up to 10 (1-D.6)
    • Addition word problems – sums up to 18 (1-D.9)
    • Addition sentences for word problems – sums up to 18 (1-D.10)
    • Addition sentences for word problems – sums up to 20 (1-D.13)
    • Subtract with pictures – numbers up to 10 (1-F.1)
    • Subtraction sentences – numbers up to 10 (1-F.2)
    • Complete the subtraction sentence (1-H.5)
    • Subtraction word problems – numbers up to 10 (1-H.6)
    • Subtraction sentences for word problems – numbers up to 10 (1-H.7)
    • Subtraction word problems – numbers up to 18 (1-H.10)
    • Subtraction sentences for word problems – numbers up to 18 (1-H.11)
    • Addition and subtraction word problems (1-J.6)
    • Comparison word problems (1-K.4)
    • Customary units of length: word problems (1-P.6)
    • Metric units of length: word problems (1-P.11)

  • 1.OA.A.2 Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.

    • Add three numbers – use doubles (1-E.6)
    • Add three numbers – make ten (1-E.8)
    • Add three numbers (1-E.11)
    • Add three numbers – word problems (1-E.12)

• 1.OA.B Understand and apply properties of operations and the relationship between addition and subtraction.

  • 1.OA.B.3 Apply properties of operations as strategies to add and subtract.

    • Related addition facts (1-D.14)
    • Add three numbers (1-E.11)
    • Add three numbers – word problems (1-E.12)
    • Related subtraction facts (1-H.13)
    • Fact families (1-J.3)

  • 1.OA.B.4 Understand subtraction as an unknown-addend problem.

    • Complete the addition sentence – sums up to 10 (1-D.3)
    • Fact families (1-J.3)

• 1.OA.C Add and subtract within 20.

  • 1.OA.C.5 Relate counting to addition and subtraction (e.g., by counting on 2 to add 2).

    • Counting forward and backward (1-A.11)
    • Skip-counting patterns – with tables (1-A.19)
    • Sequences – count up and down by 1, 2, 3, 5, and 10 (1-A.20)
    • Addition sentences using number lines – sums up to 10 (1-B.3)
    • Subtraction sentences using number lines – numbers up to 10 (1-F.3)

  • 1.OA.C.6 Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 – 4 = 13 – 3 – 1 = 10 – 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 – 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13).

    • Adding zero (1-B.4)
    • Adding 1 (1-C.1)
    • Adding 2 (1-C.2)
    • Adding 3 (1-C.3)
    • Adding 4 (1-C.4)
    • Adding 5 (1-C.5)
    • Adding 6 (1-C.6)
    • Adding 7 (1-C.7)
    • Adding 8 (1-C.8)
    • Adding 9 (1-C.9)
    • Adding 0 (1-C.10)
    • Addition facts – sums up to 10 (1-D.1)
    • Make a number using addition – sums up to 10 (1-D.2)
    • Ways to make a number – addition sentences (1-D.4)
    • Addition sentences using number lines – sums up to 18 (1-D.7)
    • Addition facts – sums up to 18 (1-D.8)
    • Addition facts – sums up to 20 (1-D.11)
    • Make a number using addition – sums up to 20 (1-D.12)
    • Add doubles (1-E.2)
    • Add using doubles plus one (1-E.4)
    • Add using doubles minus one (1-E.5)
    • Complete the addition sentence – make ten (1-E.7)
    • Subtract zero and all (1-F.4)
    • Subtracting 1 (1-G.1)
    • Subtracting 2 (1-G.2)
    • Subtracting 3 (1-G.3)
    • Subtracting 4 (1-G.4)
    • Subtracting 5 (1-G.5)
    • Subtracting 6 (1-G.6)
    • Subtracting 7 (1-G.7)
    • Subtracting 8 (1-G.8)
    • Subtracting 9 (1-G.9)
    • Subtracting 0 (1-G.10)
    • Subtraction facts – numbers up to 10 (1-H.1)
    • Make a number using subtraction – numbers up to 10 (1-H.2)
    • Ways to make a number – subtraction sentences (1-H.3)
    • Ways to subtract from a number – subtraction sentences (1-H.4)
    • Subtraction sentences using number lines – numbers up to 18 (1-H.8)
    • Subtraction facts – numbers up to 18 (1-H.9)
    • Make a number using subtraction – numbers up to 20 (1-H.12)
    • Subtract one-digit numbers from two-digit numbers (1-H.15)
    • Relate addition and subtraction sentences (1-I.1)
    • Subtract doubles (1-I.2)
    • Addition and subtraction – ways to make a number (1-J.1)
    • Addition and subtraction facts – numbers up to 10 (1-J.4)
    • Addition and subtraction facts – numbers up to 18 (1-J.5)

• 1.OA.D Work with addition and subtraction equations.

  • 1.OA.D.7 Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false.

    • Addition sentences: true or false? (1-D.15)
    • Subtraction sentences: true or false? (1-H.14)
    • Which sign makes the number sentence true? (1-J.2)
    • Addition and subtraction sentences: true or false? (1-J.7)

  • 1.OA.D.8 Determine the unknown whole number in an addition or subtraction equation relating three whole numbers.

    • Complete the addition sentence – sums up to 10 (1-D.3)
    • Complete the subtraction sentence (1-H.5)

1.NBT Number and Operations in Base Ten

• 1.NBT.A Extend the counting sequence.

  • 1.NBT.A.1 Count to 120, starting at any number less than 120. In this range, read and write numerals and represent a number of objects with a written numeral.

    • Counting review – up to 10 (1-A.1)
    • Counting review – up to 20 (1-A.3)
    • Counting – up to 30 (1-A.5)
    • Counting – up to 100 (1-A.7)
    • Counting on the hundred chart (1-A.13)
    • Writing numbers in words (1-A.22)

• 1.NBT.B Understand place value.

  • 1.NBT.B.2 Understand that the two digits of a two-digit number represent amounts of tens and ones. Understand the following as special cases:

    • Counting tens and ones – up to 99 (1-A.8)
    • Hundred chart (1-A.14)

    • 1.NBT.B.2a 10 can be thought of as a bundle of ten ones – called a “ten.”

      • Counting tens and ones – up to 20 (1-A.4)
      • Convert between tens and ones (1-M.4)

    • 1.NBT.B.2b The numbers from 11 to 19 are composed of a ten and one, two, three, four, five, six, seven, eight, or nine ones.

      • Counting review – up to 20 (1-A.3)
      • Counting tens and ones – up to 20 (1-A.4)
      • Place value models up to 20 (1-M.1)
      • Write numbers as tens and ones up to 20 (1-M.2)

    • 1.NBT.B.2c The numbers 10, 20, 30, 40, 50, 60, 70, 80, 90 refer to one, two, three, four, five, six, seven, eight, or nine tens (and 0 ones).

      • Counting by tens – up to 100 (1-A.6)

  • 1.NBT.B.3 Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <.

    • Comparing numbers up to 100 (1-K.3)
    • Put numbers in order (1-T.3)

• 1.NBT.C Use place value understanding and properties of operations to add and subtract.

  • 1.NBT.C.4 Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Understand that in adding two-digit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten.

    • Add a one-digit number to a two-digit number – without regrouping (1-D.16)
    • Regroup tens and ones – ways to make a number (1-D.17)
    • Regroup tens and ones (1-D.18)
    • Add a one-digit number to a two-digit number – with regrouping (1-D.19)
    • Add two multiples of ten (1-E.9)
    • Add a multiple of ten (1-E.10)
    • Add and subtract tens (1-J.9)

  • 1.NBT.C.5 Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used.

    • Ten more or less (1-J.8)

  • 1.NBT.C.6 Subtract multiples of 10 in the range 10-90 from multiples of 10 in the range 10-90 (positive or zero differences), using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.

    • Subtract multiples of 10 (1-I.3)
    • Add and subtract tens (1-J.9)

1.MD Measurement and Data

• 1.MD.A Measure lengths indirectly and by iterating length units.

  • 1.MD.A.1 Order three objects by length; compare the lengths of two objects indirectly by using a third object.

    • Compare objects: length and height (1-P.2)
    • Customary units of length: word problems (1-P.6)
    • Metric units of length: word problems (1-P.11)

  • 1.MD.A.2 Express the length of an object as a whole number of length units, by laying multiple copies of a shorter object (the length unit) end to end; understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps.

    • Measure using objects (1-P.3)

• 1.MD.B Tell and write time.

  • 1.MD.B.3 Tell and write time in hours and half-hours using analog and digital clocks.

    • Match digital clocks and times (1-U.1)
    • Match analog clocks and times (1-U.2)
    • Match analog and digital clocks (1-U.3)
    • Read clocks and write times (1-U.4)
    • A.M. or P.M. (1-U.5)
    • Compare clocks (1-U.7)

• 1.MD.C Represent and interpret data.

  • 1.MD.C.4 Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another.

    • Comparing – review (1-K.1)
    • Record data with tally charts, picture graphs, tables (1-O.1)
    • Interpret data in tally charts, picture graphs, tables (1-O.2)
    • Interpret bar graphs (1-O.3)
    • Which bar graph is correct? (1-O.4)
    • Count shapes in a Venn diagram (1-T.1)
    • Sort shapes into a Venn diagram (1-T.2)

1.G Geometry

• 1.G.A Reason with shapes and their attributes.

  • 1.G.A.1 Distinguish between defining attributes (e.g., triangles are closed and three-sided) versus non-defining attributes (e.g., color, orientation, overall size); build and draw shapes to possess defining attributes.

    • Name the two-dimensional shape (1-V.1)
    • Select two-dimensional shapes (1-V.2)
    • Count sides and vertices (1-V.3)
    • Compare sides and vertices (1-V.4)
    • Open and closed shapes (1-V.5)
    • Two-dimensional and three-dimensional shapes (1-W.1)
    • Cubes and rectangular prisms (1-W.3)
    • Select three-dimensional shapes (1-W.4)
    • Count vertices, edges, and faces (1-W.5)
    • Compare vertices, edges, and faces (1-W.6)
    • Identify faces of three-dimensional shapes (1-W.8)

  • 1.G.A.2 Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, and quarter-circles) or three-dimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) to create a composite shape, and compose new shapes from the composite shape.

  • 1.G.A.3 Partition circles and rectangles into two and four equal shares, describe the shares using the words halves, fourths, and quarters, and use the phrases half of, fourth of, and quarter of. Describe the whole as two of, or four of the shares. Understand for these examples that decomposing into more equal shares creates smaller shares.

    • Equal parts (1-X.1)
    • Halves, thirds, and fourths (1-X.2)
    • Simple fractions: what fraction does the shape show? (1-X.3)
    • Simple fractions: which shape matches the fraction? (1-X.4)
    • Compare fractions (1-X.7)
    • Fraction models equivalent to whole numbers (1-X.8)

For kids with a stratospheric or even strong mathematical midichlorian count, these standards may make perfect sense. But the Common Core demands here represent no small mountain for an average six-year-old to climb. If the Force is strong in some kids, by implication that Force must be weaker in others.

If you grab random kids off the desert sands, throw them into pod racers, and yell, “Fly!!”, you will end up standing by a field littered with dead kids and wrecked pod racers.

If you force every child in school to tackle all these standards during their first formal school year, you will see a similar effect.

Eduhonesty and my take on these standards: Even when well-administered, I expect the above standards will lead many young children to decide they are “bad” at math. These kids won’t be clamoring to enter the pod race later. They will be trying to stay as far away from math as possible. Mostly, they will be trying to remain unnoticed as the teacher scans the room in search of raised hands that want to answer critical thinking questions. Some of these kids may be done with math — at six years of age. The right teacher may be able to pull these kids back into the game — but what if they never get that teacher? Children vary in their flexibility and malleability. Some kids decide at three years of age that they hate ketchup and never, ever change their mind.

I HATE MATH can become a mantra of sorts. When that mantra has been repeated too many times, I HATE MATH becomes a force in itself, a barrier a kid puts up for self-protection that teachers will be struggling to break through year by year, possibly for that kid’s entire school career.

If we had an educational Razzie awards category for “So Damn Dumb I Almost Can’t Believe It,” I would enter the early elementary Common Core math standards.