# Grade 1 Louisiana Student Standards: Companion Document for Teachers

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8 Operations and Algebraic Thinking (OA) Work with addition and subtraction equations. Mathematically proficient students communicate precisely by engaging in discussion about their reasoning using appropriate mathematical language. The terms students should learn to use with increasing precision with this cluster are equations, equal, the same amount/quantity as, true, false, addition, putting together, adding to, counting on, making ten, subtract taking apart, taking from, and unknown. Louisiana Standard Explanations and Examples 1.OA.D.7. Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false. For example, which of the following equations are true and which are false? 6 = 6, 7 = 8 1, = 2 + 5, = Interchanging the language of equal to and the same as as well as not equal to and not the same as will help students grasp the meaning of the equal sign. Students should understand that equality means the same quantity as. In order for students to avoid the common pitfall that the equal sign means to do something or that the equal sign means the answer is, they need to be able to: Express their understanding of the meaning of the equal sign. Accept sentences other than a + b = c as true (a = a, c = a + b, a = a + 0, a + b = b + a). Know that the equal sign represents a relationship between two equal quantities Compare expressions without calculating. These key skills are hierarchical in nature and need to be developed over time. Experiences determining if equations are true or false help students develop these skills. Initially, students develop an understanding of the meaning of equality using models. However, the goal is for students to reason at a more abstract level. At all times students should justify their answers, make conjectures (e.g., if you add a number and then subtract that same number, you get the original number that you started with), and make estimations. Once students have a solid foundation of the key skills listed above, they can begin to rewrite true/false statements using the symbols < and >. Examples of true and false statements: 7 = = = = = = = = = = = = = = 19 7

10 Number and Operations in Base Ten (NBT) Understand place value. Mathematically proficient students communicate precisely by engaging in discussion about their reasoning using appropriate mathematical language. The terms students should learn to use with increasing precision with this cluster are tens, ones, bundle, left-overs, singles, groups, greater/less than, equal to, compare, digit, number, and numeral. Louisiana Standard Explanations and Examples 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: a. 10 can be thought of as a bundle of ten ones called a ten. First-grade students are introduced to the idea that a bundle of ten ones is called a ten. This is known as unitizing. When first-grade students unitize a group of ten ones as a whole unit ( a ten ), they are able to count groups as though they were individual objects. For example, 4 trains of ten cubes each have a value of 10 and would be counted as 40 rather than as 4. This is a monumental shift in thinking and can often be challenging for young children to consider a group of something as one when all previous experiences have been counting single objects. This is the foundation of the place value system and requires time and rich experiences with concrete manipulatives to develop. A student s ability to conserve number is an important aspect of this standard. It is not obvious to young children that 42 cubes is the same amount as 4 tens and 2 leftovers. It is also not obvious that 42 could also be composed of 2 groups of 10 and 22 leftovers. Therefore, first graders require numerous experiences with grouping proportional objects (e.g., cubes, beans, beads, ten-frames, sticks, straws) to make groups of ten, prior to using pre-grouped materials (e.g., base-ten blocks, pre-made bean sticks) that have to be traded or are nonproportional (e.g., money). (See note in the section for part c of this standard.) Example: 42 cubes can be grouped many different ways and still remain a total of 42 cubes. We want children to construct the idea that all of these are the same and that the sameness is clearly evident by virtue of the groupings of ten. Groupings by tens is not just a rule that is followed but that any grouping by tens, including all or some of the singles, can help tell how many. (Van de Walle & Lovin, p. 124) 9

12 1.NBT.B.2 continued c. 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). First-grade students apply their understanding of groups of ten as stated in 1.NBT.2b to decade numbers (e.g. 10, 20, 30, 40). As they work with groupable objects, first-grade students understand that 10, 20, 30 80, 90 are comprised of a certain amount of groups of tens with none left over. Base-Ten Materials: Groupable and Pre-Grouped Ample experiences with a variety of groupable materials that are proportional (e.g., cubes, links, beans, beads, sticks, straws) and ten frames allow students opportunities to create tens and break apart tens, rather than trade one for another. Since students first learning about place value concepts primarily relies on counting, the physical opportunity to build tens helps them to see that a ten stick has ten items within it. Pre-grouped materials (e.g., base ten blocks, bean sticks) are not introduced or used until a student has a firm understanding of composing and decomposing tens. (Van de Walle & Lovin, 2006) 1.NBT.B.3. Compare two twodigit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <. Students use models that represent two sets of numbers. To compare, students first attend to the number of tens, then, if necessary, to the number of ones. Students may also use pictures, number lines, and spoken or written words to compare two numbers. After numerous experiences verbally comparing two sets of objects using comparison vocabulary (e.g., 42 is more than is less than 52, 61 is the same amount as 61.), first-grade students connect the vocabulary to the symbols: greater than (>), less than (<), equal to (=). Example: Compare these two numbers Student A 42 has 4 tens and 2 ones. 45 has 4 tens and 5 ones. They have the same number of tens, but 45 has more ones than 42. So, 42 is less than < 45 Student B 42 is less than 45. I know this because when I count up I say 42 before I say < 45 This says 42 is less than

14 1.NBT.C.4. continued Example: 24 red apples and 8 green apples are on the table. How many apples are on the table? Student A: I used ten frames. I put 24 chips on 3 ten frames. Then, I counted out 8 more chips. 6 of them filled up the third ten frame. That meant I had 2 left over. 3 tens and 2 left over. That s 32. So, there are 32 apples on the table = = 32 Student B: I used an open number line. I started at 24. I knew that I needed 6 more jumps to get to 30. So, I broke apart 8 into 6 and 2. I took 6 jumps to land on 30 and then 2 more. I landed on 32. So, there are 32 apples on the table = = 32 Student C: I turned 8 into 10 by adding 2 because it s easier to add. So, 24 and ten more is 34. But, since I added 2 extra, I had to take them off again. 34 minus 2 is 32. There are 32 apples on the table = = = 32 Example: 63 apples are in the basket. Mary put 20 more apples in the basket. How many apples are in the basket? Student Response: I used a hundreds chart. I started at 63 and jumped down one row to 73. That means I moved 10 spaces. Then, I jumped down one more row (that s another 10 spaces) and landed on 83. So, there are 83 apples in the basket. 13

15 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. 1.NBT.C.6. Subtract multiples of 10 in the range from multiples of 10 in the range (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. This standard requires students to understand and apply the concept of 10 which leads to future place value concepts. Extensive use of models such as base-ten blocks, number lines, and 100s charts will help facilitate this understanding and will move students beyond simply rote counting by ten. It also helps students see the pattern involved when adding or subtracting 10. However, it is critical for students to mentally find 10 more or 10 less than the number by the end of the year. Examples: 10 more than 43 is 53 because 53 is one more 10 than less than 43 is 33 because 33 is one 10 less than 43 Students may use interactive versions of models (base-ten blocks, 100s charts, number lines, etc.) to develop understanding. This standard is foundational for future work in subtraction with more complex numbers. Students should have multiple experiences representing numbers that are multiples of 10 (e.g. 90) with models or drawings. Then they subtract multiples of 10 (e.g. 20) using these representations or strategies based on place value. These opportunities develop fluency of addition and subtraction facts and reinforce counting up and back by 10s. Examples using Models Example: There are 60 students in the gym. 30 students leave. How many students are still in the gym? Student A I used a number line. I started at 60 and moved back 3 jumps of 10 and landed on 30. There are 30 students left = = = 30 14

16 1.NBT.C.6 continued Student B I used ten frames. I had 6 ten frames that s 60. I removed three ten frames because 30 students left the gym. There are 30 students left in the gym = 30 Examples with explanations and no models: 70 30: Seven 10s take away three 10s is four 10s 80 50: 80, 70 (one 10), 60 (two 10s), 50 (three 10s), 40 (four 10s), 30 (five 10s) 60 40: I know 6 4 is 2, so 6 tens 4 tens equals 2 tens, so the answer is

17 Measurement and Data (MD) Measure lengths indirectly and by iterating length units. Mathematically proficient students communicate precisely by engaging in discussion about their reasoning using appropriate mathematical language. The terms students should learn to use with increasing precision with this cluster are measure, order, length, width, height, more, less, longer than, shorter than, first, second, third, gap, overlap, about, a little less than, a little more than, taller, and higher. Louisiana Standard Explanations and Examples 1.MD.A.1. Order three objects by length; compare the lengths of two objects indirectly by using a third object. In order for students to be able to compare objects, students need to understand that length is measured from one end point to another end point. They determine which of two objects is longer by physically aligning the objects. Typical language of length includes taller, shorter, longer, and higher. When students use bigger or smaller as a comparison, they should explain what they mean by the word. Some objects may have more than one measurement of length, so students identify the length they are measuring. Both the length and the width of an object are measurements of length. Examples for ordering: Order three students by their height Order pencils, crayons, and/or markers by length Build three towers (with cubes) and order them from shortest to tallest Three students each draw one line, then order the lines from longest to shortest Example for comparing indirectly: Two students each make a dough snake. Given a tower of cubes, each student compares his/her snake to the tower. Then students make statements such as My snake is longer than the cube tower and your snake is shorter than the cube tower. So, my snake is longer than your snake. 16

18 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. Limit to contexts where the object being measured is spanned by a whole number of length units with no gaps or overlaps. First-graders use objects to measure items to help students focus on the attribute being measured. Measuring objects in this way also lends itself to future discussions regarding the need for a standard unit. First-grade students use multiple copies of one object (tiles, unifix cubes, paper clips, etc) to measure the length of a larger object. They learn to lay physical units such as centimeter or inch manipulatives end-to-end and count them to measure a length. Through numerous experiences and careful questioning by the teacher, students will recognize the importance of careful measuring so that there are not any gaps or overlaps in order to get an accurate measurement. This concept is a foundational building block for the concept of area in third grade. Note: While objects used to measure a length may include centimeter or inch manipulatives, students are not introduced to those terms or to a ruler in first grade. The focus should be on giving lengths in terms of the number of object used (e.g., tiles, cubes, etc.). Students should not be required to measure in centimeters or inches. Example: How many paper clips long is the pencil? Student Response: The pencil is about 6 paper clips long. 17

19 Measurement and Data (MD) Tell and write time. Mathematically proficient students communicate precisely by engaging in discussion about their reasoning using appropriate mathematical language. The terms students should learn to use with increasing precision with this cluster are time, hour, half-hour, about, o clock, past, six -thirty, analog clock, and digital clock. Louisiana Standard Explanations and Examples 1.MD.B.3. Tell and write time in hours and half-hours using analog and digital clocks. Ideas to support telling time: within a day, the hour hand goes around a clock twice (the hand moves only in one direction) when the hour hand points exactly to a number, the time is exactly on the hour time on the hour is written in the same manner as it appears on a digital clock the hour hand moves as time passes, so when it is half way between two numbers it is at the half hour there are 60 minutes in one hour; so halfway between an hour, 30 minutes have passed half hour is written with 30 after the colon It is 4 o clock It is halfway between 8 o clock and 9 o clock. It is 8:30. The idea of 30 being halfway is difficult for students to grasp. To help students understand this concept, have students write the numbers from 0 through 60, counting by tens, on a sentence strip. Fold the paper in half and determine that halfway between 0 and 60 is 30. A number line may also be used to demonstrate this. 18

21 Measurement and Data (MD) Work with money. Mathematically proficient students recognize that a coin represents a specific value and use number patterns to find the value of a collection of coins of the same type. The terms students should learn to use with increasing precision with this cluster are penny, nickel, dime, quarter, value, and cents. Louisiana Standard Explanations and Examples 1.MD.D.5 Determine the value of a collection of coins up to 50 cents. (Pennies, nickels, dimes, and quarters in isolation; not to include a combination of different coins.) First-grade students extend their knowledge of coin names and values to determine the value of a set of pennies, nickels, dimes or quarters whose total value is no greater than 50 cents. For pennies, nickels, and dimes, students can skip-count to determine the total value. Since the limit is 50 cents, the number of quarters is limited to two. It is important to recognize that first grade students do not have an understanding of decimal place values; therefore, requiring students to use decimals is prohibited. Example: Provide students with a set containing 7 nickels. Students can skip-count by 5s to find that the value is 35 cents Geometry (G) Reason with shapes and their attributes. Mathematically proficient students communicate precisely by engaging in discussion about their reasoning using appropriate mathematical language. The terms students should learn to use with increasing precision with this cluster are shape, closed, open, side, attribute 1, feature 1, two-dimensional, rectangle, square, rhombus, trapezoid, triangle, half-circle, and quarter-circle, three-dimensional, cube, cone, prism, cylinder, partition, equal shares, halves, fourths, quarters, half of, fourth of, and quarter of. 1 Attributes and features are used interchangeably to indicate any characteristic of a shape, including properties, and other defining characteristics (e.g., straight sides) and non-defining characteristics (e.g., right-side up ). Louisiana Standard 1.G.A.1. Distinguish between defining attributes (e.g., triangles are closed and three-sided) versus nondefining attributes (e.g., color, orientation, overall size); build and draw shapes to possess defining attributes. Explanations and Examples First-grade students use their beginning knowledge of defining and non-defining attributes of two-dimensional shapes to identify, name, build and draw shapes (including triangles, squares, rectangles, and trapezoids). They understand that defining attributes are alwayspresent features that classify a particular object (e.g., number of sides, angles, etc.). They also understand that non-defining attributes are features that may be present, but do not identify what the shape is called (e.g., color, size, orientation, etc.). Example: All triangles must be closed figures and have 3 sides. These are defining attributes. Triangles can be different colors, sizes and be turned in different directions. These are non-defining attributes. Student I know that this shape is a triangle because it has 3 sides. It s also closed, not open. Student I used toothpicks to build a square. I know it s a square because it has 4 sides. And, all 4 sides are the same size. 20

22 1.G.A.2. Compose twodimensional shapes (rectangles, squares, trapezoids, triangles, halfcircles, and quarter-circles) and 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. As first graders create composite (a figure made up of two or more geometric shapes) two- and three-dimensional shapes, they begin to see how shapes fit together to create different shapes. They also begin to notice shapes within an already existing shape. They may use such tools as pattern blocks, tangrams, attribute blocks, or virtual shapes to compose different shapes. First-grade students are not required to know formal names for right rectangular prism, right rectangular cones, and right rectangular prisms. They should recognize a tissue box or a cube as a prism, a soup can as a cylinder, and an ice cream cone (pointed end) as a cone. Example: What shapes can you create with triangles? Student A: I made a square. I used 2 triangles. Student B: I made a trapezoid. I used 4 triangles. Student C: I made a tall skinny rectangle. I used 6 triangles. *Students do not need to learn formal names such as right rectangular prism. First graders learn to perceive a combination of shapes as a single new shape (e.g., recognizing that two (isosceles) triangles can be combined to make a rhombus, and simultaneously seeing the rhombus and the two triangles). Note: The term isosceles is not required in grade 1; however, isosceles triangles are found in pattern blocks and students will likely use two such triangles to form a rhombus. Thus, they develop competencies that include: 1. Solving shape puzzles 2. Constructing designs with shapes 3. Creating and maintaining a shape as a unit As students combine shapes, they continue to develop their sophistication in describing geometric attributes and properties and determining how shapes are alike and different, building foundations for measurement and initial understandings of properties such as congruence and symmetry. Students can make three-dimensional shapes with clay or dough, slice into two pieces (not necessarily congruent) and describe the two resulting shapes. For example, slicing a cylinder will result in two smaller cylinders. 21

23 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 Students need experiences with different sized circles and rectangles to recognize that when they cut something into two equal pieces, each piece will equal one-half of its original whole. Students should recognize that there are different ways to find halves of the same figure. Also they should reason that decomposing equal shares into more equal shares results in smaller equal shares. Examples: Student partitions a rectangular candy bar to share equally with one friend and thinks I cut the rectangle into two equal parts. When I put the two parts back together, they equal the whole candy bar. One-half of the candy bar is smaller than the whole candy bar. How can you and a friend share equally (partition) this piece of paper so that you both have the same amount of paper to paint a picture? Student 1 I would match the short sides of the paper and fold down the middle. That gives us 2 halves. I have half of the paper and my friend has the other half of the paper. Student 2 I would split it from corner to corner (diagonally). She gets half of the paper and I get half of the paper. See, if we cut on the line, the parts are the same size. You can have only one slice of pizza. Which pizza should you pick your slice from if you want the biggest piece of pizza? The pizzas are the same size and are each divided into equal pieces. Explain how you know. I would get more pizza if I took a slice from the pizza that is divided into 2 equal parts. The more equal slices there are, the smaller the pieces get. I would not get as much pizza if I only got a fourth of the pizza instead of half of the pizza. 22

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