Entrance TaskSession 3

• Use the beans at your tables to complete the Place Value sheet.

• What mathematics is highlighted as you do this work?

• When you’ve completed the sheet…– Turn to Donna’s Case 12 on pages 47-50 in your DMI

books (Lines 82-166).– Read and skim the case.– What connections can you make between your

experience and the one she describes?

• Record your thoughts in your journals.

Think About It….

Thinking deeply about what we are doing leads us to ask better questions, break out of fruitless routines, make unexpected connections and experiment with fresh ideas.

Ron Brandt

Session 3Goals

• Content Process Community

BIG IDEA!

• There is tremendous complexity involved in making sense of our written and spoken number systems. Our systems are not intuitive or obvious to novices. Many of these ideas that children express make sense in light of this complexity. Reflect on the importance of tens and their relationship to other numbers:

What is ten?When is ten ones a ten?How can I break up a ten?Why would I want to?

Case Discussion Chapter 3

• As you work through the case you are assigned, look for elements of logic and where a students thinking goes awry.

• What are some of the children’s new insights? Cite evidence.

• Does this raise any questions about the way children make sense of our number system?

• Have you ever noticed children thinking this way in your own classes?

Merging of the Minds

• Merge with the other group who focused on the same case.

• Work together to complete the Graphic Organizer.

• Select at least 2 individuals (preferably one from each group) to present your information to the whole group.

• Did you have any new insights about our number system?

View and Discuss A Video• Watch the 12 minute video of a taped interview with a student named Chris• As you watch the interview, focus on the teacher’s moves…

• What types of questions is she asking?• What do you think her goals are?• How is she accomplishing this?• What evidence from this interview do you have to

support these statements?• What other questions or tasks would you have

included?

• Record your thoughts in your journals

Key Understanding 4

The whole numbers are in a particular order, and there are patterns in the way we say them which help us to remember the order.

Mathematics

Key Understanding 5

• Place value is the key to understanding how we say, read, write and calculate with whole numbers.– The order of the digits makes a difference– The position of a digit tells us the quantity it

represents– Zero is used as a place holder– There is a constant multiplicative relationship between

the places with the values of the position increasing in powers of ten from right to left

– The value of the digit multiplied by the value of the place tells us the quantity a digit represents

Mathematics

An Interview with Hannah

• Read through the interview with Hannah• In your groups determine Hannah’s rules for

writing large numbers

*Note…this material is from Australia. In Australia they use the word “and” to indicate a place value change and not decimals.

Mathematics

Place Value Tasks

Work with your grade level teams to select a place value task that you

would like to administer between now and January 16th.

43 Lollies Task

• Purpose– To find out whether students can produce and

use standard and non-standard place value partitioning.

• Procedure:– Give worksheet to students and ask them to

count the lollies.

Mathematics

43 Lollies Task

Mathematics

The Dinosaur Task

• Purpose– To examine children’s understanding of the meaning of the

individual digits in a two-digit number.

• Procedure– Give the worksheet and two different colored pencils or pens. – Ask, ”How many dinosaurs are on this page?”– When everyone agrees there are 35 dinosaurs, point to the 5

and say, “use a green pencil and put a circle around what this part of the number means in the set of dinosaurs”.

– Then point to the 3 and say “use a red pencil and put a circle around what this part of the number means in the set of dinosaurs”.

Mathematics

DinosaursMathematics

Up to and through the hundredsPurpose

To see if children know the patterns in the way we say and write numbers up to and through the hundreds.

Procedure

Provide each child with the grid and ask them to provide the missing numbers.

The 800 GamePurposeTo see the extent of children’s understanding of the relationship between the places. ProcedureThis can be played as a whole group or small group activity.Each person makes a number with the cards they were given.Decide how you could change the value of the 8 in your number so that it will equal the value of your partner’s 8.Use a calculator to try out your idea.Try other ways.Talk to other players. Are they doing it the same way as you?How do you account for any differences?

Circle the Biggest

PurposeTo see if children can compare numbers using multiplicative relationships. ProcedureDistribute the worksheet and ask students to write a full explanation of their reasoning on each choice they make. You may need to get clarification from a few students if their reasoning is questionable or unclear.

Wipe out

• Enter a number such as 256 into the calculator. Ask:– “How can we make the 5 a zero?” (Subtract 50)– “Why did you do that?” “What number have we got

now?”– “How can we make the 2 a zero?” “What number have

we got now?”– “How can we make the 6 a zero?”

• Students play wipe out in pairs taking turns to give each other the instructions.

Mathematics

Typical Place Value Work Sheet Questions

1. Fill in the missing numbers3486 = ____ thousands + ____ hundreds + _____ tens + _____ ones

546 = _____ hundreds + _____ tens + _____ ones

2. Complete the chart

Mathematics

Six thousand nine hundred and seventy three6 973

136

Twenty five

Write the number in words

Model with MAB

Draw what you used

Number

EXIT Cards• What Place Value misconceptions are most common in your

grade level?• Do you have any insights to share or questions to ask?

Homework• Read Chapter 4• Administer one of the First Steps Place Value tasks with your

class between now and our January 16th session.

Think About It….

If we only give experiences with things in groups of ten—children never get to see when the pattern doesn’t hold.