##
* *Reflection: Diverse Entry Points
Manipulation Central - Section 2: Practice, Practice, Practice

It would be great if all students progressed at the same rate, or understood things the same way, but as teachers we know that this is not ever the case. Each student processes material differently and makes connections to prior knowledge in a different way. It is our job to scaffold new ideas onto previous learning.

In this lesson some of the children had been struggling with the concept of tens and ones. They knew the terms, but still were not clear about why the digit in the tens place could not be added to the digit in the ones place. The tens frames made this very clear. It was exciting to watch the students quickly count out the tens and then the ones, and realize if they had more than 10 ones on the frame, they could count those as an extra 10 and then put the ones with it to form a 2 digit number.

Students need to see things in different ways. For some children this just made sense. We need to make sure that we present things in different ways if we want all children to understand what we are trying to present.

*Understanding Ones, Tens and Hundreds*

*Diverse Entry Points: Understanding Ones, Tens and Hundreds*

# Manipulation Central

Lesson 5 of 10

## Objective: Students will use different manipulatives to solve addition and subtraction problems using base ten strategies.

## Big Idea: Not everyone solves a problem in the same way. Reinforcing that different strategies can be used effectively is the goal of this lesson.

*60 minutes*

#### Warm Up

*15 min*

I put 4 number sentences on the board written vertically because at this point I am trying to move students from the horizontal perspective to the vertical as they get ready to add and subtract using place value columns. Some of the problems are purposefully incorrect. I want to see if students can notice my place value mistakes. I ask them to check the problems and see if I did them right. Here students do not have all of the manipulatives so I am asking them to reason abstractly as they look at what I have done (MP5).

The problems are:

63 - 29 = 46 28 + 28 = 416 37 + 24 = 61 41 - 18 = 37

In the first problem I have flipped the ones around and solved 9 - 3, rather than 3 - 9 which would require borrowing or trading. In the second problem I added 8 + 8 = 16 and wrote the 16 in the ones column and then 2 tens plus 2 tens = 4 tens, writing the 4 in the tens column. The third problem is correct and in the 4th problem I again flipped the ones and solved 8 - 1 rather than 1 - 8. These are common mistakes for second graders as they begin to grasp how numbers work.

By having students correct my work they will need to attend to precision and look for and make use of structure (MP 2 and MP7), as they attempt to determine whether what I did was correct or incorrect.

I give students time to check the problems and then I ask volunteers to come up and mark my problem right, or show me what I did wrong.

We discuss what I might have done that gave me the answer I got.

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#### Practice, Practice, Practice

*30 min*

Today I create 3 centers for students to work through. I have 2 sets of problems, with one being word problems for the students who are more secure, and one being numerical problems for those who need more practice using different strategies.

I tell students that they will rotate through the 3 centers to complete the problems on their pages. At each center they will find a set of tools. They will need to use those tools to complete the problems, or if they prefer to do the problems another way, they need to use those tools to check their work. I tell them I will be rotating around to watch how they use the tools they have available.

Today I group the children into homogeneous groups. This way I can concentrate on the students who are having more difficulty, and provide scaffolding to groups of students at the same time who may need the same type of assistance. Students will stay at each center for 10 minutes.

The first group has ten frames to use for adding and subtracting of 2 digit numbers. I make sure to remind students how to use the tens frames to help them with their work. I use pre-filled ten frames as well as blank ten frames with colored chips so students can manipulate the ones place as needed.

The second group has place value houses (or place value mats) and base ten blocks. They will build each number on the house, and then add or subtract, trading as needed to get their answers.

The last group will be using drawings to complete the work. They can draw base 10 blocks or open number lines to assist them in doing their work.

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#### Closing

*15 min*

I ask students to return to their seats. I ask them to write on their papers the method that they liked best today (the words are at the top of the page so they just need to circle their favorite) and then write why they liked it.

Now I put one problem on the board. I ask them to use their favorite method to solve the problem (they may return to a center if they need the manipulatives). I ask for one person to demonstrate at each center how they solved the problem.

We close by reminding ourselves that there are many different ways to solve a problem and that students should use the method that is best for them. I tell them that after I correct today's work, I will return it to add to their math suitcases as a reminder of a way they like to solve problems.

*expand content*

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- UNIT 1: What and Where is Math?
- UNIT 2: Adding and Subtracting the Basics
- UNIT 3: Sensible Numbers
- UNIT 4: Sensible Numbers
- UNIT 5: Everything In Its Place
- UNIT 6: Everything in Its Place
- UNIT 7: Place Value
- UNIT 8: Numbers Have Patterns
- UNIT 9: Fractions
- UNIT 10: Money
- UNIT 11: The Numbers Are Getting Bigger
- UNIT 12: More Complex Numbers and Operations
- UNIT 13: Area, Perimeter and More Measurement
- UNIT 14: Length
- UNIT 15: Geometry
- UNIT 16: Getting Ready to Multiply
- UNIT 17: Getting Better at Addition and Subtraction
- UNIT 18: Strategies That Work

- LESSON 1: Where Are Our Understandings
- LESSON 2: Students As Teachers
- LESSON 3: Students as Teachers Part II
- LESSON 4: Kindness Day Math
- LESSON 5: Manipulation Central
- LESSON 6: More Than One Way to Solve A Problem
- LESSON 7: How Big Is One Thousand
- LESSON 8: Let's Compare
- LESSON 9: Assessment
- LESSON 10: Missing Numbers in Japanese