FIRST GRADE MATH Summer 2011

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1 Standards Summer OA.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. OA.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. OA.3 Apply properties of operations as strategies to add and subtract. Examples: If = 11 is known, then = 11 is also known. (Commutative property of addition.) To add , the second two numbers can be added to make a ten, so = = 12. (Associative property of addition.) OA.4 Understand subtraction as an unknownaddend problem. For example, subtract 10-8 by finding the number that makes 10 when added to 8. Utilize the three most common types of addition and subtraction problems: Result Unknown, Change Unknown, and Start Unknown. See Glossary, Table 1 Can increase the level of difficulty by using Change Unknown or Start Unknown Students need not use formal terms for these properties. Commutative Property of Addition: addends can be added in any without changing the sum Associative Property of Addition: the sum is always the sun regardless of the grouping of the addends Options for students to use to solve: number line ten frame counters drawings hundreds chart Start Unknown: (most difficult of the basic addition problems) There are some students in the cafeteria. 7 more students came. Now there are 18 students in the cafeteria. How many students were in the cafeteria at first? + 7 = 18 Mom filled the fruit bowl with 5 apples, 6 oranges, and 6 pears. How many pieces of fruit are in the bowl? To solve: Students can use a number line, counters, drawings, etc. Students use manipulative such as cubes and counters to apply these properties. A number line may also be used. Students can use two different unfix cubes to show that = Students can also use 3 different colors of counters o prove that (2 + 8) + 5 is equal to 2 + (8 + 5). Student will model and solve 14 5 = Students will demonstrate that the above problem can be expressed as (inverse relationship). Using a hundreds chart, the student starts at five and counts until 14 is reached. Student will show that 9 numbers were counted, so 14 5 = 9.

2 Standards 2 OA.5 Relate counting to addition and subtraction (e.g., by counting on 2 to add 2). OA.6 Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., = = = 14); decomposing a number leading to a ten (e.g., 13-4 = = 10-1 = 9); using the relationship between addition and subtraction (e.g., knowing that = 12, one knows 12-8 = 4); and creating equivalent but easier or known sums (e.g., adding by creating the known equivalent = = 13). OA.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, = OA.8 Determine the unknown number in an addition or subtraction equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 +? = 11, 5 = 3, =. Evaluate Students will use counting all, counting on, and counting back strategies. Fluency is accurate, quick, and effortless to allow for more effort towards problem solving. Characteristics of fluency: - accuracy - efficiency (rate is about 2 seconds per problem) - application of strategies The equal sign means that the left and right side are balanced. It does not mean that the result is next. Students must understand the relationship between the left side and the right side. Expanding on standard OA = Counting back: Student will start at 16 and count back seven times. This may be demonstrated using counters. Student starts will 16 counters and each time a counter is removed the student counts back. See website for fluency activities: 5mathteachingresources.com/1st-gradenumber-activities.html Students show understanding by modeling using cubes, counters, drawings, etc. the various representations in this standard. 4 = 4 14 = = = Five plus three is the same amount as eight 12 9 = = = - 5 Student knows that is = 6 Student shows knowledge and application of addition (inverse operation) to solve subtraction problems.

3 Standards 3 NBT.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. NBT.2 Understand that the two digits of a twodigit 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." Comprehension Counting should show the sequence of numbers is one more than the number before. Extend by discovering patterns place value using hundreds charts (rows, columns) Understanding place value Do you have ones remaining when you create bundles of ten? Students demonstrate counting on strategy with a missing number grid. The word and should not be used when reading/writing whole numbers: one hundred five Students model that a group of ten cubes, straws, etc. means one bundle of ten rather than ten individual items. b. The numbers from 11 to 19 are composed of a ten and one, two, three, four, five, six, seven, eight, or nine ones. Ten frame filling it to make a unit of ten Place value cubes connecting them to make a ten. See website below Students model the understanding of teen numbers. Expanding on standard 2a, students will create a unit of ten by using a ten frame, place value cubes, etc. Students will bundle a group of ten with ones remaining to show the numbers 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). Students discover that there are no left overs zero ones when bundling objects. Using various manipulatives (place value cube, straws, etc.), students will create bundles of ten to show the numbers 10, 20, 30, 40, 50, 60, 70, 80, 90. NBT.3 Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <. Evaluate Check for understanding by asking students to explain why it is less than, greater than, or equal to. See website below for activities.

4 4 Standards NBT.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. NBT.5 Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used. NBT.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. Example question prompt: How do you calculate the sum? difference? Students discover place value patterns using a hundreds chart. ten frames hundreds chart unifx cubes A first grader added His sum was 745. What was his mistake? Here is his work: Students express understanding that the student did not add ones and ones and tens and tens. Result Unknown: There are 25 students on the bus. 10 students got off at the first stop. How many students are left on the bus? = Result Unknown: 40 1 st graders are going on a field trip. 30 students will ride on the first bus. How many students will ride on the second bus? Explain your answer based on place value = MD.1 Order three objects by length; compare the lengths of two objects indirectly by using a third object. transitivity transferring the measurement characteristic of an object to another object in order to make a comparison Students will compare the lengths of two objects in the classroom: the teacher s desk and a bookshelf by cutting a piece of string to the length of the teacher s desk. Then students compare the length of the string to the length of the bookshelf. Students determine whether or not the bookshelf is longer or shorter than the teacher s desk.

5 5 Standards MD.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. MD.3 Tell and write time in hours and half-hours using analog and digital clocks. Comprehension In order to become proficient in measuring space (in terms of length, area, or volume), students need to understand two fundamental concepts: the idea of a unit and the process of iterating a unit to complete a measurement. Iteration applying a unit of measure one or more times to an object being measured (e.g., a yard stick is iterated 100 times along the length of a football field) Students must know that at the half-hour the hour hand is between the numbers. Where is the hour hand at 3:00? Minute hand? Where is the hour hand at 3:30? Minute hand? Students measure the length of a book using paper clips. Students will recognize the importance of getting an accurate measurement by making sure that there are no gaps or overlaps of the paperclips. Students will read an analog clock, write the time, and discuss the placement of the hour and minute hand. The time should read on the hour or half-hour. MD.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. What punctuation mark is use to separate the hour and the minutes? Use question prompts regarding the data. Picture and bar graphs are introduced in 2 nd grade. Students will conduct a survey (e.g., What color do you like best? Red, blue, or green?). Results are organized in a chart or table. Students will discuss the results.

6 6 Standards G.1 Distinguish between defining attributes (e.g., triangles are closed and threesided) versus non-defining attributes (e.g., color, orientation, overall size) for a wide variety of shapes; build and draw shapes to possess defining attributes. Students must know the difference between defining attributes and non-defining attributes. See Comparing 3D Shapes writing template: 5mathteachingresources.com/geometryactivities.html Using a list of defining attributes and nondefining attributes, students will determine which attributes are needed to draw a shape. G.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. Students do not need to learn formal names such as right rectangular prism. Students create their new shapes using two-dimensional shapes or threedimensional shapes. G.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. Analysis This is building the foundation for fractions. How can a sheet of drawing paper be partitioned so that your friend can have an equal piece? Students will demonstrate the ways to divide the paper (horizontally, vertically, diagonally).

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