Place Value
Mathematics
Grade 1
Everyday Mathematics Teacher’s Lesson Guide, Volume 1
Unit Goals:
Develop an understanding of numbers and numeracy up to 100.
Develop an understanding values of numbers up to 100.
Pennsylvania Department of Education State Standards
Subject Area - : Mathematics
Grade Level - 1st Grade
Standard Area – 2.1: Numbers, number systems and Relationships
Standard
2.1.1.A: Demonstrate the relationship between numbers and quantities, including place value, one-to-one correspondence, rote counting, counting by twos to 20, counting by tens and fives and comparing values of whole numbers up to 100.
2.1.1.B: Represent equivalent forms of the same number through the use of pictures and concrete objects (including penny, nickel, dime, and quarter), up to 100.
2.1.1.D: Apply place value concepts and base-ten numeration to order and compare whole numbers up to 100.
Prior Kindergarten Level Knowledge from the Kindergarten Pennsylvania Learning Standards for Early Childhood. Office of Child Development and Early Learning (2009).
1. Rote count by whole numbers to 100 by ones.
2. Count by tens to 100.
3. Count up to 20 objects using one-to-one correspondence.
4. Use basic numbers and counting.
5. Use vocabulary independently to compare numbers of objects.
6. Use concrete objects to represent quantities up to and including twenty.
7. Identify penny, nickel, dime.
8. Represent equivalent forms of the same number the use of concrete objects and drawings up to and including twenty.
9. Group objects into sets of tens.
Content Skills and Concepts Being Taught During the Unit
1. Identify place value in two-digit numbers.
2. Name the values of groups of tens and ones represented in different ways, including dimes and pennies.
3. Find equivalent names for numbers.
4. Represent the value of the number 100 in one way.
5. Make exchanges among the place vales of tens and ones.
6. Compare numbers, including money values, using the symbols <, >, and =.
Future Use of Content Skills Taught in This Unit (Bell. 2004, pp. 798-811).
1. Practice and review of the skills taught in this unit during the next units.
2. Read and write three-digit numbers.
3. Make and solve number grid problems.
4. Use dollars and cents notation.
5. Identify equivalencies and make coin exchanges.
6. Identify pennies and dimes as fractional parts.
7. Calculate the value of coin combinations.
8. Solve two-digit addition and subtraction problems.
9. Count by numbers greater than ten.
Learning Targets for 1st Grade Unit on Place Value of Two-Digit Numbers
1. Knowledge and Simple Understanding
· Students will write two-digit numbers that are represented by drawings, and words, including dimes and pennies, on six problems accurately on paper and/or response boards throughout the unit (Examples: DDDPP = _____, l l l l • = _____,
8 tens and 5 ones = ___).
2. Deep Understanding and Reasoning
· Students will compare values of two two-digit numbers by writing the correct symbols (<, >, =) between them on paper in six number models accurately(Example:
23 61).
· Students accurately will verbally or in writing explain their reasoning for their answer to one number model in which they must write the correct symbol as the example above.
· Through observation and charting or on paper or response boards, students will show two different accurate representations for five two-digit numbers by exchanging tens and ones using drawings, and base ten blocks, or using dimes and pennies.
3. Skills
· Through observation and charting students will be evaluated on how well they represent values of two-digit numbers and/or the number 100 using drawings, and base ten blocks, including dimes and pennies. Student will show accurate representation on six two-digit numbers or the number 100.
4. Products
· While role playing that they are consumers that are comparative shopping and deciding which would be the better buys by comparing “prices only”, students will self-check their responses to see if they have made five good buys.
· While role playing that they are in various situations in which more money “in their banks” would be the best option, students will circle the higher value of two monetary values which are limited to totals below one dollar on paper or response boards.
· Students will accurately count and write three peers’ representations of one hundred on charts created by their teacher.
5. Affect
· Students will indicate in which way they feel most comfortable or the way in which they most enjoy showing representation of two-digit number by a show of choice: with base ten blocks, with coins, by drawing longs and cubes, or by drawing coins.
Lesson 1: Introduction to Base Ten Blocks
Standard: Pennsylvania Learning Standards for Early Childhood: First Grade: 2.1.C.: Represent equivalent forms of the same number through the use of concrete objects, drawings, word names and symbols to 100.
Objective: Students will be able to name the base ten blocks as longs and cubes and will state the value of a long and cube.
Activity 1: The teacher will introduce the cube and the long. Teacher and students will count how many blocks in each cube and long and state their values. Students will each be given a bag of 10 longs and 10 cubes. Students will show that a ten is equivalent to 10 cubes by placing 10 cubes beside a long. The teacher will ask the student to place a given number of longs or cubes or a combination on their desk. The students will state what is in front of them (Example: 3 longs) and ask the students how much is in each.
Activity2: Students will be given time to build a structure with the base ten blocks (p. 288, SRA/McGraw-Hill, 2004). Students will tell a peer how many longs and cubes are in their structures.
Assessment: Students will take a pre-assessment on place value.
Preassessment
The preassessment will be given at the end of Lesson 1: Introduction to Base Ten Blocks. It can be given orally or on paper. It includes counting by tens, identification and value of a dime and penny, writing the two-digit number equal to the values represented, and writing the values of the digits of two-digit numbers.
Preassessment for 1st Grade Place Value: This should be read orally to students one question at a time.
Modifications or accommodations should be written on this after each section.
Name______
Date______
1. Count by 10’s from 0 to 100.
0, ______, ______, ______, ______,
______, ______, ______, ______, ______,
______.
2. Which coin is this ?
a. A penny
b. A nickel
c. A dime
d. A quarter
3. How much is this coin worth ?
a. 1¢
b. 5¢
c. 10¢
d. 25¢
4. Which coin is this ?
a. A penny
b. A nickel
c. A dime
d. A quarter
5. How much is this coin worth ?
a. 1¢
b. 5¢
c. 10¢
d. 25¢
6. How much do the following values equal?
2 tens and 4 ones = ______
7 tens and 9 ones = ______
6 tens = ______
5 ones = ______
= ______
I I I I I • • • = ______
7. Show the values of the following numbers.
92 = ______tens and ______ones
63 = ______tens and ______ones
8. Show the value of these numbers by drawing pictures for the values.
27 = ______
51 = ______
Preassessment for 1st Grade Place Value: Answer Key
1. 0, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100
2. c.
3. c.
4. a.
5. a.
6. 24
79
60
5
42
53
7. 9, 2
6,3
8. Students should draw 2 tens and 7 ones.
Students should draw 5 tens and 1 one.
Scoring:
Prior Knowledge / Points / CommentsCan count by 10’s to 100 / _____/10
Identified a dime / _____/1
Knows value of a dime / _____/1
Identifies a penny / _____/1
Knows the value of a penny / _____/1
Writes the number equal to given values / _____/6
Writes how many tens and ones in a given number / _____/4
Shows representations of given numbers / _____/2
Lesson 2: Place Value with Tens and Ones
Standard: Pennsylvania Learning Standards for Early Childhood: First Grade: 2.1.C.: Represent equivalent forms of the same number through the use of concrete objects, drawings, word names and symbols to 100.
Objective: Students will explore place value concepts for tens and ones.
Activity 1: Students will review what was learned yesterday: a cube is a one and a long has 10 cubes or ones in it. The teacher will rename the long as a ten. Longs and tens are the same. Students will be given Tens-and Ones Mats. The teacher will use an overhead projector or Smartboard to show models of placing the base ten blocks on the mat and naming the number. She will ask the students to place longs, cubes, tens, ones and combinations on the mat and name the numbers. Students instead of the teacher can take turns naming the base ten blocks to place on the mats to name numbers.
Activity 2: On the board the teacher will write the place value blocks to use in order to guess a number (Example: 4 cubes and 2 longs. What number am I?) Students will write their answers on a response board. Several of these types of problems will be solved.
Differentiation for anyone who needs more practice placing tens and one accurately on mats at Pearson Fact Monster Knowledge Box Math @ http://sf.factmonster.com/math/knowledgebox/player.html?movie=sfw44801
Assessment: Students will complete Student Math Journal, Volume 1, p. 97 #1-4. Example: Tens and Ones Riddles: 3 cubes and 2 longs. What am I?(p. 336, SRA/McGraw-Hill, 2004) Advanced students can complete Student Math Journal, Volume 1, #5-6.
Tens and Ones Riddles
Directions: Solve the riddles. Use your base ten blocks to help you.
(An example is given:
3 illustration of a cube and 2 illustration of a long. What am I? __23___)
1. 5 cubes and 6 longs. What am I?_____
2. 2 longs and 7 cubes. What am I? _____
3. 4 cubes and 6 longs. What am I? ______
4. 7 longs and 0 cubes. What am I? ______
The following are for Advanced Learners:
5. 1 long and 11 cubes. What am I? _____
6. 14 cubes and 2 longs. What am I? _____
7. Make up your own riddle. Ask a friend to solve your riddle.
Answer Key:
1. 65
2. 27
3. 64
4. 70
5. 21
6. 34
7. A riddle is constructed in the same format as the above riddles with the correct answer.
Differentiation: Below Level Learners could work with the teacher in a small group to solve these problems. Students especially may need assistance with reading.
Observation Checklist: Students could earn up to 6 tallies for Writing the Number Represented.
Observation Checklist for Assessments on 1st grade Place Value Unit which will be used for most lessons.
Directions: Make a tally for each correct response observed solved by the students independently with no assistance. Show students their tallies earned at the end of the lesson (during restroom break.)
(The Observation Checklist can only fit in Landscape Orientation. It is attached separately.
Lesson 3: Representing Tens and One in Various Ways
Standard: Pennsylvania Department of Education State Standards: Mathematics, Grade 1: 2.1.1.B: Represent equivalent forms of the same number through the use of pictures and concrete objects (including penny, nickel, dime, and quarter), up to 100.
Objective: Students will show the values of two digit numbers using pictures, words, or manipulatives.
Activity 1: Students will be given whiteboards and base ten blocks. Students will be asked to make their whiteboards into a place value mat by drawing a line down the middle and writing the words tens and ones at the tops of the appropriate columns. The teacher will write a two-digit number on the board. Students will form the amount by placing base ten blocks on their whiteboards to match the numbers written by the teacher. The teacher will demonstrate how to count the base ten blocks starting with the tens and adding on the ones. The students will repeat counting and touching their base ten blocks the same way. The teacher and students will continue to practice several of these types of problems, but with the students can take turns writing the numbers on the board. Students will put their base ten blocks in their bags at the end of the lesson.
Activity 2: The teacher will ask a student to state a number to write on the board. The teacher will ask a student, “How many tens are in that number?” The teacher will draw sticks to represent the tens under the tens column. Then the teacher will ask, “How many ones are in that number?” The teacher will represent the ones with dots. (She will demonstrate how to make a dot that will show up.) The teacher will ask for another two-digit number. This time the students will draw the same type of representations for the tens and ones. After drawing several of these problems, the teacher will ask the students to erase their columns on their white boards and draw several two-digit numbers without the columns and value headers using sticks and dots.
Differentiation in readiness:
The following websites can be used be more practice and visuals for Below Level or Struggling Learners:
To demonstrate how to count tens and one with longs and cubes.: Schooltube: Place Value by Stephen@ http://www.schooltube.com/video/532c077c1645424ea8e3/Place-Value-by-Stephen
To practice matching the values of numbers.: ict Games: Dinosaur Place Value@
http://www.ictgames.com/dinoplacevalue.html
To practice identifying the tens and ones values of numbers.: AAA Math: Finding Place Values@ http://www.aaamath.com/B/g12b_px1.htm#section2
Assessment: Build a structure that is worth 62 with base ten blocks.
Observation Checklist: Students could earn 1 tally for Shows Representation of a Number One Way Accurately.
Lesson 4: Dimes and Pennies