# 1.2 - Place Value, Comparing & Ordering Numbers

The student, given up to 110 objects, will

a) group a collection into tens and ones and write the corresponding numeral;

b)  compare two numbers between 0 and 110 represented pictorially or with concrete objects, using the words greater than, less than or equal to;and

c)  order three or fewer sets from least to greatest and greatest to least.

### BIG IDEAS

• So that by grouping objects in tens and ones, I will begin to  understand place value for tens and ones
• So that by using objects and pictures, I can begin to understand place value
• So that by ordering sets I will understand more than, less than and equal to
• So that I can use pictures and objects to represent numbers

### UNDERSTANDING THE STANDARD

 Conservation of number is applied when students understand that a group of 10 objects is still 10 objects regardless of whether they are arranged in a cup, group, stack, etc.Unitizing is the concept that a group of objects can be counted as one unit (e.g., 10 ones can be counted as 1 ten).The number system is based on a pattern of tens where each place has 10 times the value of the place to its right.  This is known as the ten-to-one concept of place value.Opportunities to experience the relationships among tens and ones through hands-on experiences with manipulatives are essential to developing the ten-to-one place value concept of our number system and to understanding the value of each digit in a two-digit number.Models that clearly illustrate the relationships among tens and ones as physically proportional are most appropriate for this grade (e.g., the tens piece is 10 times larger than the ones piece).Knowledge of place value is essential when comparing numbers.Students are generally familiar with the concept of more and have limited experience with the term less. It is important to use the terms together to build understanding of their relationship.  For example, when asking which group has more, follow by asking which group has fewer.Recording the numeral when using physical and pictorial models leads to an understanding that the position of each digit in a numeral determines the size of the group it represents.Manipulatives that can be physically connected and separated into groups of tens and leftover ones, such as connecting or snap cubes, beans on craft sticks, pennies in cups, bundle of sticks, or beads on pipe cleaners should be used.Ten-to-one trading activities with manipulatives on place value mats and base-ten blocks are more appropriate in grade two.

### ESSENTIALS

 The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to Group a collection of up to 110 objects into sets of tens and ones. (a)Write the numeral that corresponds to the total number of objects in a given collection of up to 110 objects that have been grouped into sets of tens and ones. (a)Identify the place and value of each digit in a two-digit numeral (e.g., in the number 23, the 2 is in the tens place and the value of the 2 is 20). (a)Identify the number of tens and ones that can be made from any number up to 100 (e.g., 47 is 47 ones or can also be grouped into 4 tens with 7 ones left over).  (a)Compare two numbers between 0 and 110 represented pictorially or with concrete objects, using the words greater than, less than or equal to. (b)Order three or fewer sets, each set containing up to 110 objects, from least to greatest and greatest to least. (c)

### KEY VOCABULARY

Updated: Aug 22, 2018