Stage 1 Desired Results

Kathryn MoodyUbD Final DraftStage 1 Desired Results

Content Standard(s):

1. 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.

1. 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.

1. 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.

Understanding (s)/goals

Students will understand that:

Values are represented with the digits 0-9. Position of the digits in numbers, or place value, determine the quantity that the number represents.

There is a pattern to the formation of numbers. Understanding of place value can be applied to operations for mental math.Essential Question(s):For the following three questions, 28 can be replaced with any number up to and including 100

In the number 28, what amount does the 2 represent?

What amount does the 8 represent? If I changed the order of the digits, would this represent the same amount?

What pattern do you notice when you count?

What pattern do you notice in the columns of the hundred chart? What stays the same? What changes?

Student objectives:

Students will know That the digit in the tens place represents how many groups of ten would be needed to model a number, and the digit in the ones place represents how many ones would be needed to model a number.

That ten more or ten less than a given number will change the digit in the tens place only.

That adding or subtracting a multiple of ten will not change the digit in the ones place of a number.

Mentally, how to determine ten more or ten less than any given number under 100

Student objectives (continued):

Students will be able to Count to 120

Demonstrate ten more and ten less on a number line, ten frame, hundred chart, and with tens and ones (manipulatives and pictures)

Mentally determine ten more or ten less than a given number under 100.

Stage 2 Assessment Evidence

Performance Task(s):

In small, heterogeneous-ability groups, students pick two cards out of a stack containing the digits 0-9 and are instructed to make and record the largest number that they can make with their two digits, and the smallest number they can make with their two digits. Students then have to explain their reasoning.

In small, heterogeneous ability groups, students will solve word problems that address adding and subtracting increments of ten, as well as modeling the word problems in a hundred chart, number line, and ten frame. Students will share and discuss their methods and solutions and point out any patterns that they noticed in the numbers involved in their word problems.Other Evidence:

Pre-assessment

Listening to students count to 100, individually.

Student completion of a blank hundred chart.

Student completion of a blank number line.Formative Assessments

Teacher observation of individual contributions to performance tasks.

Asking for mental ten more or ten less of any given number, via a game of Around the World, a whole class review game in which two students compete to mentally answer teacher given questions. The first to correctly answer moves on to the next student. The questions move around the room, the goal being for one student to make it all the way around. Students modeling jumps of ten by coloring in on a hundred chart.Summative Assessments Students asked individually to orally count to 120. Students asked to state ten more or ten less of any given number, without counting. Student completion of a (read-aloud) word problem requiring subtraction of a multiple of ten, showing their thinking with pictures, numbers, or words.

Stage 3 Learning Plan

Learning Activities:

The teacher will gather students on the carpet and ask who would like to take a guess at how many pockets there are in the room. Decide as a class to figure out this problem by allowing each student to place a connector cube in a tub for each pocket that they are wearing. The teacher will model this with his or her own outfit. After all students have placed their cubes in the tub, the teacher will ask students to think about how the class should go about counting such a large number of cubes. Start by counting by ones. The teacher will (purposefully but carefully) spill the contents onto the carpet and sloppily count the cubes, purposefully losing count. The teacher will ask students to think of some things that might make the counting more efficient, or easier. The teacher will then ask the class to think of some ways that would be easier to count than by ones and try these until grouping by tens is suggested. At the conclusion, ask students what worked well and what did not. W, H, E1 After counting along and moving with Let's Get Fit | Counting to 100 by 1's | Kids Songs | Jack Hartmann (http://www.youtube.com/watch?v=0TgLtF3PMOc) students will work individually while sitting at their table groups to count out an assigned two-digit number (for example, 47) of colored bears (or another commercial math manipulative) from the large tub containing many of the manipulatives. While students count out the assigned amount, the teacher will circulate among desks to note any grouping strategies that students use while counting. Teacher will allow students two minutes to play, as is recommended for this age (with students reminded of their expectations for utilizing manipulatives). Once all students have gathered their amount, discuss the following questions: What worked well when counting that many bears? What did not work well? Did anyone group their bears? How did you group them? How did you arrange them? W, H, E1 In a similar manner to the previous lesson, students count out an assigned two-digit number while the teacher circulates among desks to note counting strategies. The teacher will give students a work mat containing 10 blank ten frames. Students record in their math journals how many groups of tens and how many left overs their number made, and the process with two more ten-digit numbers, each ten more than the last number (for example, 34, 44, and 54). Students will have different numbers to count out and arrange on their ten frames. The teacher will lead the students in a discussion about what they noticed about their numbers and what those numbers looked like on their ten frames. Students will also discuss what their recorded information looked like (how many full ten frames and how many left over). W, E1, R *See attachment 1 for ten frame mat. Students will work in pairs to travel around the room to different stations. Each station will have a collection of items in a plastic bag. Students will count out the set and write both the number and the number word for their collection amount in the corresponding location on a teacher-made table. Student pairs will then sort the objects in their collections into groups of tens. Students will record the amount of groups of ten and the left over amount in the appropriate column of the same table. After rotating to all stations, the teacher will lead students in comparing results as a class. Students will discuss again what they noticed about these amounts and numbers and any related discoveries about what the number looks and sounds like and what the recorded groups of tens and left-overs reveal. R, E2, T *See attachment 2 for table. Students will count and move along with Let's Get Fit | Counting to 100 by 1's | Kids Songs | Jack Hartmann (same as previous lesson). Students will gather with the teacher where a hundred chart is displayed. Students will count along while the teacher points to the corresponding number on the hundred chart. The teacher will then lead students in a discussion about what they know already about the hundred chart. Students will be invited to share any patterns that they notice on the chart. The teacher will synthesize and restate student discoveries, inviting other students to share. H, E1, O Students will work in small heterogeneous ability groups to solve a word problem with a subtraction of a multiple of ten. Students will be instructed to illustrate their thinking on a blank hundred chart and on blank ten frames how they solved their problem. Students will share their thinking with the class and students will discuss what they noticed about the illustrations. R, E2, T Students will use their math notebooks to record the amounts that they see in a quick-show activity. Using a document camera, the teacher will quickly display a 10 x 10 dot array. Using two pieces of paper to partially cover rows and columns (column changing only for the last row to signify ones), the teacher can display different amounts of dots. The goal for students is to relate the amount of rows displayed to groups of tens, and the remaining partially covered row to the ones place of the amount. Students will compete against each other to get as many amounts correct as possible. The teacher will then show all amounts and count the correct amount with each one. The teacher will discuss with students their strategies for quick counting. R, E2 *See attachment 3 for dot array example. Students will work as a whole group to fill in nearly blank hundred chart (only border numbers, 25, and 75 filled in) and with the teacher beginning with the number 25 to invite children to tell the numbers neighbors. In this manner, fill in the rest of the hundred chart, making sure that the answers are student-directed and encouraging the use of noticed patterns in the hundred chart. E1, R, O *See attachment 4 for hundred chart.

Students will then work independently with individual complete hundred charts, counters, and connector cubes to model teacher-determined numbers with the cubes, as well as cover the corresponding number on their hundred charts with a counter. The teacher will then ask students to cover ten more than that number and ten less than that number. The teacher will write all three numbers on the white-board and encourage students to note the patterns, continuing to wonder aloud whether the pattern will be the same each time. The teacher will continue to direct students to cover any three sequential numbers in a column and noting whether the pattern continues. R, E2, O

After review of concepts and discussion of learning activities and student discoveries, students individually complete summative assessment tasks. Individually, students will be asked to orally count to 120, state ten more and ten less than three given numbers between 20 and 100, without counting, and complete a (read-aloud) word problem requiring subtraction of a multiple of ten, showing their thinking with pictures, numbers, or words. E2

References

Hartman, J. (May 7, 2014). Lets Get Fit | Counting to 100 by 1s | Kids Songs | Jack

Hartmann. YouTube. Retrieved from http://www.youtube.com/watch?v=0TgLtF3PMOc.Attachment 1- Blank Ten Frame Mat

Attachment 2-Groups of Ten Recording TableName: ________________Bag of

How many?Number wordHow many groups of ten?

Example:

34thirty-fourGroups of ten: 3Leftovers: 4

Groups of ten:Leftovers:

Groups of ten:

Leftovers:

Groups of ten:

Leftovers:

Groups of ten:

Leftovers:

Attachment 3-10x10 Dot Array with Quick Show Example

This is an example of a quick-show number. The blue and gray rectangles represent movable pieces of paper covering partial rows and columns of a 10x10 dot array. This example is showing the number 55.Attachment 4-Partial Hundred Chart Name: ____________________

1

2345678910

11

20

21

2530

31

40

41

50

51

60

61

70

71

7580

81

90

91

9293949596979899100

Reflection