FIRST GRADE MATH Summer 2011

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FIRST GRADE

MATH

Summer 2011

Standards

Bloom’s

Taxonomy

Specific Instructions

Pacing

Guide

Performance Tasks

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.

Application Utilize the three most common types of addition and subtraction problems:

Result Unknown, Change Unknown, and Start Unknown.

See Glossary, Table 1

Term 1: Term 2: Term 3: Term 4:

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 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.

Application Can increase the level of difficulty by using Change Unknown or Start Unknown

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.

OA.3

Apply properties of operations as strategies to add and subtract. Examples: If 8 + 3 = 11 is known, then 3 + 8 = 11 is also known. (Commutative property of addition.) To add 2 + 6 + 4, the second two numbers can be added to make a ten, so 2 + 6 + 4 = 2 + 10 = 12. (Associative property of addition.)

Application 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

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 3 + 5 = 5 + 3

Students can also use 3 different colors of counters o prove that (2 + 8) + 5 is equal to 2 + (8 + 5).

OA.4

Understand subtraction as an unknown-addend problem. For example, subtract 10 - 8 by finding the number that makes 10 when added to 8.

Application Options for students to use to solve:

number line ten frame counters drawings hundreds chart

Student will model and solve

14 – 5 =



Students will demonstrate that the above problem can be expressed as 5 + 9 (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.

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FIRST GRADE

MATH

Standards

Bloom’s

Taxonomy

Specific Instructions

Pacing

Guide

Performance Tasks

OA.5

Relate counting to addition and subtraction (e.g., by counting on 2 to add 2).

Application Students will use counting all, counting on, and

counting back strategies.

16 – 7 = 

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.

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., 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).

Application 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

See website for fluency activities:

http://www.k- 5mathteachingresources.com/1st-grade-number-activities.html

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, 5 + 2 = 2 + 5, 4 + 1 = 5 + 2.

Application 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.

Students show understanding by modeling using cubes, counters, drawings, etc. the various representations in this standard. 4 = 4

14 = 6 + 8 5 + 7 = 12 3 + 7 = 4 + 6

Five plus three is the same amount as eight 12 – 9 = 3

9 + 5 = 14 + 0 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, 6 + 6 = •.

Evaluate Expanding on standard

OA. 4 Term 1:

Term 2: Term 3: Term 4:

6 = - 5

Student knows that 5 + 6 is 11. 11 – 5 = 6

Student shows knowledge and application of addition (inverse operation) to solve

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FIRST GRADE

MATH

Standards

Bloom’s

Taxonomy

Specific Instructions

Pacing

Guide

Performance Tasks

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.

Application 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)

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

NBT.2

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

Understanding place value

a. 10 can be thought of as a bundle of ten ones - called a "ten."

Comprehension Do you have ones remaining when you create bundles of ten?

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.

Synthesis 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 11 – 19.

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).

Synthesis 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.

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FIRST GRADE

MATH

Standards

Bloom’s

Taxonomy

Specific Instructions

Pacing

Guide

Performance Tasks

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.

Application

A first grader added 73 + 15. His sum was 745. What was his mistake?

Here is his work: 73 + 15 7 4 5

Students express understanding that the student did not add ones and ones and tens and tens.

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.

Application Example question prompt: How do you calculate the sum? difference?

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?

25 – 10 =  NBT.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.

Application Students discover place

value patterns using a hundreds chart.

ten frames hundreds chart unifx cubes

Result Unknown:

40 1st 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.

40 – 30 = 

MD.1

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

Application 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.

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FIRST GRADE

MATH

Standards

Bloom’s

Taxonomy

Specific Instructions

Pacing

Guide

Performance Tasks

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.

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 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.

MD.3

Tell and write time in hours and half-hours using analog and digital clocks.

Application 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? What punctuation mark is use to separate the hour and the minutes?

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.

Application Use question prompts regarding the data.

Picture and bar graphs are introduced in 2nd 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.

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FIRST GRADE

MATH

Standards

Bloom’s

Taxonomy

Specific Instructions

Pacing

Guide

Performance Tasks

G.1

Distinguish between defining attributes (e.g., triangles are closed and three-sided) versus non-defining attributes (e.g., color, orientation, overall size) for a wide variety of shapes; build and draw shapes to possess defining attributes.

Synthesis Students must know the difference between defining attributes and non-defining attributes.

See Comparing 3D Shapes writing template:

http://www.k- 5mathteachingresources.com/geometry-activities.html

Using a list of defining attributes and non-defining 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.

Synthesis Students do not need to learn formal names such as “right rectangular prism.”

Students create their new shapes using two-dimensional shapes or three-dimensional 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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