Unit 1 integers test

If there are 103 Skittles in a bag, how many bags would be needed for 1 million Skittles? Be mindful of labels and to show your thinking.

1,000,000 (skittles) divided by 103 in each bag = 9,708.7378 bags

If there are 103 Skittles in a bag, how many bags would be needed for 1 billion Skittles? Be mindful of labels and to show your thinking.

1,000,000,000 (skittles) divided by 103 in each bag= 9,708,737.8 bags

fill in the blank 1. 62,589,632,000 =(in words) 2. Four hundred ninety-three million, five hundred sixty-eight thousand, one hundred two= (in numeral) 3. 500,983,001,539= (in words) 4. Three hundred three trillion, seven hundred eighty-eight million, two hundred thirty-three= (in numeral)

1. sixty two billion, five hundred eighty-nine million, six hundred thirty-two thousand 2. 493,568,102 3. five hundred billion, nine hundred eighty-three million, one thousand, five hundred thirty-nine 4. 303,000,788,000,233

What are the skills required to count meaningfully? *3 things

1.students need to know their counting sequence 2. their one-to-one correspondence (knowing each item has a number with it) 3. cardinality ( knowing if I count 3, there are only 3)

Know how to write, in both numeral and words, numbers up to quadrillion. write sixty quadrillion, seven billion, four hundred million, six hundred ninety thousand

60,000,007,400,690,000

What are Number Talks and what is the purpose of them? What are the benefits?

a specific daily routine that engages students on number sense for 5-8 minutes daily. Benefits= daily math routine, expands students' view of what math is, normalizes "revising" thinking.

What role does "base ten language" play in the teaching of place value?

base ten language (e groups of hundred), helps emphasize that each individual numeral has a place value. It connects the concrete to the more abstract way that we frequently say numbers.

Why are oral counting different than writing numbers?

children tend to learn their numbers before writing them. Therefore, this challenges them when they have to write them out, because after 10, the pattern stops, then picks up again.

What is meant by the phrase: "developing a child's number sense?"

developing their intuition about umber relationships. It includes flexibility with numbers, exploring them, and visualizing them in all sorts of contexts.

What is an algorithm and why don't we start with teaching students' algorithms?

it is step by step procedures for producing the correct result every time. we don't start with them because they are very difficult to understand.

James was asked to count the connecting cubes. There were fourteen on the table. As he counted he pointed to each cube and stated a number "one, two, three, four, five, ....." He got to fourteen and then counted them again saying, "fourteen, fifteen, sixteen, seventeen,...." He stopped at nineteen and proudly announced "nineteen blocks." What did James know how to do? What kind of error did James make?

james knows one-to-one correspondence, because he knows each cube is associated with a number. He does not know cardinality, knowing he counted 14 blocks, so there are only 14 blocks.

Money can be a very motivating context that students really connect to in contextual problems. Why would coins be a challenging manipulative to use for teaching base-ten concepts?

not all coins represent the values of base-ten. ex. a nickel is 5 cents and 5 is not represented as a base ten block. also, the size isn't proportional to the value. for example, a dime is worth 10 cents while a nickel is worth five and is bigger than a dime.

What types of activities can cultivate a child's number sense?

number talk activities, which will promote counting, discussing numbers and seeing them differently. For example, ten frame games and counting games

What is "subitizing" and how can it be promoted in a math classroom?

recognizing the value in a set without physically counting the items. items like ten frame promote subitizing, because we often look at the absent spaces first. As well as number talks activities with dots in different formations (like in class).

show 536 in the following ways: standard language: standard written form: base-ten language: expanded written form: base 10 blocks:

standard language: five hundred thirty-six standard written form: 536 base-ten language: five hundreds three tens six ones expanded written form: 500+30+6 base 10 blocks: 5 flats 3 longs 6 units

Identify characteristics of concrete models and manipulatives used to teach grouping and place value concepts (i.e. proportional models, groupable, etc.). What are the benefits and disadvantage of each?

--Non-Proportional models, such as the place value mat, can often be used to help students see connections with how we write numbers, as they model that well, including making the "zero" obvious as a place holder. However, they can be tricky because 10 is not ten times larger than 1. So larger numbers may use a smaller quantity of cubes than smaller numbers, which can be confusing when comparing numbers. --Groupable models, such as using popsicle sticks or straw, allow for students to decide how they want to group items. It allows them to see the need for "grouping", especially for large numbers. They are proportional. However, they can be cumbersome and depending on the number, impractical (4,563 for example...) ---Pre-grouped models, such as base ten blocks, are a proportional model where they are already grouped into easy to identify groups. They are a great way to introduce base-ten concepts because they are pre-grouped and fit the place value while still representing the size each place value, accentuating the relationship between each.

In the numeral 826422, there are three 2's. How are they different from each other?

Each 2 has the same "face value" meaning that they tell you the same number is needed of each place value. However, they are all in different place values, one two is a ten-thousand, meaning that it requires two ten-thousands, etc.

How are the different place values related to each other?

Each place value is ten times larger than the previous place value and ten times smaller the place value to the left.

How are numbers used differently in the following scenarios? a. Julie counts out six bags of cookies for her friends. b. Michael is "it" and counts to twenty before chasing after his friends in tag. c. Maria counted that she has four cookies and her older sister has eight. Maria knows that it isn't fair. d. Juan's basketball jersey has a "42" on the back.

In this situation, Julie is counting a set. Using one-to-one correspondence and cardinality to know how many bags she has. In this situation, Michael is purely using oral counting skills and reciting the number sequence from 1-20. In this situation, Maria is counting a set. Using one-to-one correspondence and cardinality to know how many cookies she and her sister have. Further, Maria has an understanding of larger and smaller numbers and can compare who has "more" In this situation, Juan is recognizing a written number.