Exam 2- Math 210

Addition: Combine Scenario

2 collections of objects are combined

subtraction: take away scenario

objects are removed from a group

subtraction: missing addend scenario

additional objects are needed to reach a desired total

subtraction: comparison scenario

one group is matched against another

multiplication: repeated addition scenario

groups of identical size are combined

multiplication: array/area scenario

a grid or rectangle is created

multiplication: cartesian product scenario

different types of items are “mixed and matched”

division- repeated subtraction scenario

objects are separated into groups of known size

Division- Partitioning scenario:

objects are separated into a known number of groups

What scenario is this? Jeff has 8 apples and Carrie has 6. How many do they have together?

addition: combine scenario

What scenario is this? Jeff had 5 apples and gave Carrie 2. How many does he have left?

Subtraction: Take-away scenario

What scenario is this? Carrie has 2 apples and needs 5 for a recipe. How many more does she need?

Subtraction: Missing Addend Scenario

What scenario is this? Carrie has 5 apples and Jeff has 2. How many more does she have than he does?

Subtraction: Comparison scenario

What scenario is this? Shawn has 4 bags of 6 marbles. How many marbles does he have altogether?

Multiplication: Repeated addition scenario

What scenario is this? Belinda’s classroom has 6 rows of 4 desks. How many desks are there altogether?

Multiplication: Array/Area Scenario

What scenario is this? Belinda has 6 blouses and 4 skirts that go together. How many different outfits can she make?

Multiplication: Cartesian Product scenario

What scenario is this? Shawn has 12 cookies to put into bags of 3. How many bags can he make?

Division: Repeated subtraction scenario

What scenario is this? Shawn has 12 cookies to give to 3 friends. How many will each friend get?

Division: Partitioning Scenario

Algorithms

step by step process for doing something

For repeated subtraction, what two things are the same kind?

dividend and divisor

For partitioning scenario, what two things are the same kind?

dividend and quotient

manipulatives

physical objets we can handle and move to act out/represent math processes

What are the three main types of manipulatives for working with place value?

1) Concrete: see physical trades- base 10 blocks

2) Abacus (representational)

3) Place value card- blank piece of paper with columns representing each place value

Algorithms for adding whole #s

standard, scratch, base 10 blocks, place value cards

Algorithms for subtracting whole #s

standard and balancing (equal addends)

Algorithms for multiplication

standard, area model, lattice, partial products

scenario

setting/context

-for word problem that helps child choose whether to add or subtract or divide or multiply with the numbers they see

numeration system

set of rules for how to write #s (numerals)

state what key features hindu arabic has

10 digits

uses place value

number

idea of how many

numeral

how we write a number

place value

means where a digit occurs in an numeral-offsets how much it is worth

base ten

digit to the left is worth 10x as much to the right

egyptian numeration key features

7 digits

uses a variation of base 10

Egyptian numeral for one

| :staff

Egyptian numeral for ten

n: heel bone

Egyptian numeral for hundred

scroll

Egyptian numeral for thousands

lotus flower

Egyptian numeral for ten thousand

pointing finger

Egyptian numeral for hundred thousand

tadpole

Egyptian numeral for million

astonished person

x-2y=8 is what

equation

3-5+7=5 is what

number sentence

3-5+7 is what

expression

an equality does what

gives an answers

an equation does what

gives an answer and uses variables

a number sentence does what

gives an answer and only shows numbers

an expression does what

not show an answer