Download Math-4-Parents Fall Workshops K-4

Math-4-Parents
Fall Workshops
K-4
Central School
Tammy Fisch, Math teacher
October 2014
• Discuss math content, language, and teaching methods
that are being used in classrooms today
• Increase understanding of why our children are
learning various strategies
• Explore hands-on math activities using manipulatives
• Discuss games and activities to do at home to support
mathematical thinking
Kindergarten Overview
• Know number names and count to tell numbers of
objects.
• Compare groups of objects, up to 10
• Fluently add and subtract within 5
• Add within 10 using objects or drawings
• Decompose numbers to 10 into pairs in more than
one way
1st Grade Overview
•
Developing understand of addition and subtraction, and
strategies for addition and subtraction within 20
•
Developing understanding of whole number relationships
and place value, including grouping tens and ones
•
Developing understanding of linear measurement and
measuring lengths as iterating length units
•
Reasoning about attributes of, and composing and
decomposing geometric shapes
Daily Routines:
Building Number Sense
• Count days of school: 10 frames, place
value bundles
• Calendar
• Quick Images, Rekenreks
Represent
numbers
flexibly
Some
students may
know that this
frame has 5!
5
6, 7, 8
Number Bonds
• Number bonds help students see that numbers
can be "broken" into pieces to make computation
easier.
• Children experience multiple ways to
decompose the same number, rather than
memorizing.
• The part/part/whole mat and concrete practice are
used a LOT! This helps little ones really
understand how addition and subtraction are
related.
•Students can find combinations in a
systematic way by sliding one bead at a
time from one side to the other.
•Notice the part/part/total relationship
shown on the bracelet.
•Students should verbalize each
combination (0 and 3 make 3, 1 and 2
make 3, etc.).
The Power of 10
• 1st graders begin learning their basic addition facts and apply
that knowledge in a strategy known as "make a ten”.
• This helps make sense of facts that might otherwise be hard
to memorize, such as 8 + 4 or 9 + 5.
• Students decompose one of the addends to make a ten from
the other. In the example pictured below, the 4 is
decomposed (split) into 3 and 1. The 3 is combined with the 7
to make 10, and then the 1 is added for 11.
Understanding the
Problems
•What is happening in the story?
•Can you tell the story without numbers?
•Visualize/act out the story.
•Draw or use manipulatives to show what
is happening.
Part-Part-Total Models
Kate and Nana baked some
cookies. They made 2 heart
cookies and some square
cookies. They baked 8
cookies altogether.
How many square
cookies did they bake?
There are 8 juice boxes on the
table. Some children drank
their juice. Now there are only
5 juice boxes. How many
juice boxes were taken from
the table?
Let’s take a peek!
nd
2
Grade Overview
• Extending understanding of base-ten (place
value)
• Building fluency with addition and subtraction
• Using standard units of measure
• Describing and analyzing shapes
Developing Place Value
Understanding
Students practice
counting & creating
“bundles” and
then represent numbers
in expanded form.
Stages of Representation
100 + 100 + 10 + 10 + 10 + 1 + 1 + 1 = 243
200
+
30
+
3
= 243
Concrete - Pictorial - Abstract
Read-Draw-Write
399 jars of baby food are sitting on the shelf at the
market. Some jars fall off and break. 389 jars are
still on the shelf. How many jars broke?
Concrete - Pictorial - Abstract
1.
2.
Ben and his dad have sold 60 chocolate chip cookies at the school
bake sale. If they baked 100 cookies, how many cookies do they
still need to sell?
Samantha is helping the teacher organize the pencils in her
classroom for the teacher. She finds 41 yellow pencils and 29
blue pencils. She threw away 12 that were too short. How many
pencils are left in all?
Lisa solves 166 – 48 vertically on her place value chart.
Explain what Lisa did correctly and what she needs to
fix.
The correct answer is not enough.
How you get the answer matters, too!
Hundreds
100’s
Tens
10’s
Ones
1’s
Use math drawings to
represent additions with
up to two compositions
and relate drawings to a
written method.
As students write
addition problems
vertically and make math
drawings, they are
reminded to be precise
in aligning the digits and
in drawing their dots in
neat
5-groups.
3rd Grade Overview
• Developing understanding of multiplication
and division and strategies for multiplication
and division within 100
• Developing understanding of the structure of
rectangular arrays and of area
• Developing understanding of fractions
• Describing and analyzing two-dimensional
shapes
Tape Diagrams or Bar Models
The use of the rectangular bars and the identification of the unknown quantity with a
question mark help students visualize the problem and know what operations to perform—
in short, viewing all problems from an algebraic perspective beginning in early elementary
grade levels.
―drawing a picture‖ usually this entails drawing objects, animals, or counters. It is not very
efficient when you move to larger numbers. When you use bar modeling, students learn to
represent these objects with rectangles that enable them to see the number relationships,
rather than focusing on the objects of the problems. Rectangles are used because they are
easy to draw, divide, represent larger numbers, and display proportional relationships.
There are 21 fish in a bowl. Fifteen are from a
student. The rest are from the school. How
many are from the school.
Grant buys 345 fruit bars. Ken buys 230 more
fruit bars than Grant. How many fruit bars does
Ken buy?
Read-Draw-Write
Red, orange, and blue scarves are on sale for $4
each. Nina buys 2 scarves of each color. She also
buys a hat that costs $4. How much does she
spend altogether?
Arrays
7 x 5 = ( 5 x 4 ) + ( 5 x 3 )
35 =
20
+
15
2x4=4x2
4+4=2+2+2+2
Commutative Property of Multiplication
states that changing the order of factors
does not change the product.
Four groups of 2 is the same as two groups
of 4, but one is more efficient. Students
begin to apply this property when solving
multiplication problems.
Distributive Property of
Multiplication states that the
product of a number is equal to the
sum of the individual products and
the number.
I can use the distributive property to
solve multiplication problems I don’t
know more efficiently.
8x8=?
(8 x 4) + (8 x 4) = ?
32 + 32 = 64
Number Bonds
4
sixes
2
sixes
2
sixes
2 sixes + 2 sixes = 4 sixes
4x6
4 groups of 6
4x6
2x6
2x6
( 2 x 6 ) + ( 2 x 6 ) = 24
Area of Figures
The tile floor in Brandon’s living room has a rug on it as shown
below. How many square tiles are on the floor, including the
tiles under the rug?
th
4
Grade Overview
(1) Developing understanding and fluency with multi-digit
multiplication, and developing understanding of dividing
to find quotients involving multi-digit dividends;
(2) Developing an understanding of fraction equivalence,
addition and subtraction of fractions with like
denominators, and multiplication of fractions by whole
numbers;
(3) Understanding that geometric figures can be analyzed
and classified based on their properties, such as having
parallel sides, perpendicular sides, particular angle
measures, and symmetry.
Word Problems & Tape Diagrams
Jennifer texted 5,849 times in January. In February , she texted
1,263 more times than she did in January. What was the total
number of text messages that Jennifer sent in the two months
combined? Explain how you would check the reasonableness of
your answer.
X and
÷ by 10
A rectangle is 1 inch wide. It is 3 times
as long as it is wide. Use square tiles to
find its length.
1‖
1‖
1‖
1‖
“ ___ times as many”
The basketball team is selling t-shirts for $9 each. On Monday, they sell 4 tshirts. On Tuesday, they sell 5 times as many t-shirts as on Monday. How
much money did the team earn altogether on Monday and Tuesday?
Multiplication Models
•Students learn to decompose numbers into base ten units in order to find
products of single-digit by multi-digit numbers.
•Students use the distributive property and multiply using number disks to
model.
•Students bridge partial products to the recording of multiplication via the
standard algorithm.
Division Models
• Students represent division with single-digit divisors using arrays
and the area model, followed by the place value disks.
• The standard division algorithm is taught using students’
knowledge of place value, decomposing unit by unit.
Why Does the Algorithm Work?
Emma takes 57 stickers from her collection and divides them
up equally between 4 of her friends. How many stickers will
each friend receive? Emma puts the remaining stickers back
in her collection. How many stickers will Emma return to her
collection?
Algorithm – step by step
Providing Support at Home
• Supporting work habits instead of work
–
–
–
–
What is the question asking?
What information do we need to solve?
What is a reasonable answer? Why?
What steps do we need in order to solve the problem?
• Don’t provide too much support. Homework is an important
assessment tool for the teacher.
• Provide tools to help your child solve problems.
• Focus more on the why and how than simply getting the correct
answer.
How can we bring math
into our children’s worlds?
•
•
•
•
•
•
•
Count everything!
Play games
Talk about math
Talk about our thinking
Explain why something works
Explore new ideas and make generalizations
Take a risk, It’s OK to make a mistake and struggle!
It’s the questions that
drive mathematics.
• Encourage them to explain their thinking.
• By expressing wonder and amazement at what
they are figuring out!
• “Can you show me how you got that answer?”
•
•
•
•
“How do you know? Can you show me?”
“Interesting, can you prove it?”
“Do you think it will always work?”
“What do you think it would look like if we put it on paper?”
Educate Yourself
Math Module Parent Letters
Play, Play , Play!
Math Resources
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