DI Math- Chapter 7 Quiz

What is the wording suggested for explaining how renaming is done? AKA what is the prompt to carry?

"I cannot have a tens in the ones column, I must rename."

Associative law.

(4 + 2) + 5 = (2 + 5) + 4 (Reverse the order and reverse the grouping (to make the problem easier) and still get the same sum.)

What are the two types of complex addition facts?

1. A single digit number is added to a teen number and the total is 19 or less. 2. A single digit number is added to a teen number and the total is 20 or more.

When would addition the fast way be introduced?

1. After students have mastered "addition the slow way" 2. At least 80% correct

What are the two stages in teaching addition?

1. Concrete (use manipulatives) 2. Abstract (fading prompts)

What do the authors recommend the use of lines to represent the members of sets in initial addition strategies? Name at least 4.

1. Easy to use, 2. Readily accessible, 3. Provide a written record of student strategies, 4. Make diagnosis of errors easier, 5. Monitor active responding in students, 6. Teaches a concrete understanding of equality

What are the addends in 5 + 2 = 7?

2 & 5

What does an equation with a missing addend look like?

3 + ____ = 7 (The missing addend is 4.)

Show the cumulative law.

4 + 3 = 3 + 4 (Reverse the addends and get the same sum.)

What new pre-skill needs to be taught before addition problems with renaming are introduced?

Adding three single digit numbers with a sum below 10.

What is the identity element?

Adding zero to any number.

During the beginning stage students are taught two strategies for solving addition problems. What are they (show examples)?

Addition the slow way (based on equality). 1. Kids should draw counters under addends 2. Kids count number of counters 3. Draw same number of counters under answer box 4. Count the number of counters and write numeral in box Addition the fast way (transition from concrete to abstract understanding) 1. Draw counters under second addend 2. "Count on" from first addend 3. Write the numeral answer in the box

When should complex addition facts be introduced?

After the student knows about 50 (or half) of the basic addition facts.

What error are students most likely to make when mentally adding 3 single digit numbers?

After the students have added the first two digits- the student incorrectly responds with the sum of the second and third digit.

Describe the wording the teacher uses when leading the students through adding tens numbers.

Begin with the ones column- student adds the ones and then tens writing the sum for each column When adding the tens- the teacher asks about the number ten rather than the quantity represented by the 10s number.

What is renaming?

Carrying over a number to the next column. For example: if there is 10 or more in the ones column you must rename the 10 and carry the one over to the tens column.

What is a pre-skill for counting addition the fast way?

Counting starting from numbers other than 1.

Addition

II + III = IIIII

When is the concrete stage of addition introduced?

Kindergarten/first grade

Show and describe the basic strategy students are taught to work problems with missing addends during stage (based on equality).

Missing addend: Show and describe the steps to complete a problem (Model). (Example- 3 + ___ = 5) Put counters under the given addend (3) and the sum (5). Begin counting at the counters under three- "Starting at three, count-on." (Stop counting at the answer.) Continue under the box, and write counters as you count ("four" "five") Count the counters under the box and write the corresponding numeral in the box.

What is regrouping? How does it differ from renaming?

Regrouping is like renaming but it is concrete. Regrouping uses tangibles like unifix cubes.

What is a pre-skill for many renaming problems with three or more multi-digit numbers?

Students must mentally add a single digit number to a two-digit number (Example: 4 + 8 = 12 (two-digit #), then mentally add 12 + 6 (1-digit #) = 18, Then: Write the 8 in the ones, rename the 10 ones as a ten and carry to the tens column).

What is the difference between the two stages of addition?

The first stage is employs semi concrete and concrete objects, The second stage uses symbolic representations

What is the sum?

The sum is the answer of an addition problem

What should the teachers reaction be to a intermediate student who is using their fingers to figure out basic facts.

The teacher should make sure that the students are using their fingers accurately and as efficiently as possible.

When is abstract addition taught?

Typically taught towards the end of first grade

What is the difference between examples selected in the structured and less structured parts of a format?

When presenting the structured board and worksheet parts of a format, the teacher should use only examples of the type being introduced. When presenting the less structured and supervised parts of the format, the teacher should give the students a cumulative review worksheet with a mixture of current and past problem types.

Define equality

You must end with the same number on one side of the equal sign as the other.