Math Tips and Strategies
Greetings, everyone! Some parents have expressed interest in learning about the various strategies that the children are learning in math, so rather than just leave this in the middle of my weekly update, I decided to create a new page for you.
Numbers, Number Words, and Ordinals.
Vocabulary
Cardinal Number Words:
one, two, three, four, five, six, seven, eight, nine, ten, eleven, twelve.
2 is less than 3; also expressed as 2<3.
3 is equal to 3; also expressed as 3=3.
4 is greater than 3; also expressed as 4>3.
We call the symbols < and > "Goldie Gold Fish," who "likes to gobble the greater number." Picture the point of the symbol as the hinge of her mouth, and the wide end as her open mouth, pointing toward the greater number.
Strategies
*Counting On: If I am trying to solve 2+3=?, I touch or start at 2 on the number line, then count on for 3 more, which will leave me at 5. If I do it "in my head," I tap my forehead and say "2," then hold up 3 fingers and count on "3, 4, 5."
*Act It Out: Use counters (manipulatives, such as pennies, buttons, M&M's, etc.) to demonstrate what is happening in the problem. Sometimes, the children may get up and do the activity, such as stand in a line to see who is first, fourth, etc.
*Draw a Picture: That means just what it says, so I would draw 2 circles (or whatever), then 3 more, and count them to arrive at 5.
Addition Strategies and Facts to 12.
Vocabulary
4 plus 5 equals 9
addend + addend = sum
addition fact 5+2=7
related addition facts
3 + 5 = 8
5 + 3 = 8
4 + 6 = 10
part + part = whole
doubles fact 3+3=6
doubles + 1 3+4=7
Strategies
*Use a Tens Frame That means to use a rectangular frame with ten spaces, five on the top row, five on the bottom. Counters are placed in the spaces, filling from left to right, top row first, to show how close to ten a group is. It may also be used vertically, filling the left-hand column, top-to-bottom, then the right-hand column.
*Equivalent Sums Related to doubles and doubles + 1, in using equivalent sums, the children are encouraged to break down a problem into easier pieces, such as changing 3+4 to 3+3+1=7
*Bar Model A bar model is used when trying to find an unknown, such as 6 + ? = 10. The bar model looks like a domino, with the known number (6) shown with dots on one side, the unknown number (?) shown as a blank on the other side, and the sum written on a bracketed line across the top. The task is to count on from the known number (6) while drawing the dots needed in the blank half (4), so that the total matches the sum written above: 6 + 4 = 10.
Some children may be very comfortable with the addition facts at this level. While they may not need to use counters all the time because they know the facts, they do need to know how to use the counters/strategies to check/show/draw a solution to problems.
Subtraction Strategies and Facts to 12
Vocabulary
subtraction sentence
8 - 3 = 5
subtraction facts
7 - 4 = 3 7
-4 In each of these facts, 3 is the difference.
3
related subtraction facts
9 - 7 = 2 9 - 2 = 7
fact family (uses the same 3 numbers)
9 - 3 = 6 9 - 6 = 3
3 + 6 = 9 6 + 3 = 9
pattern pattern rule
2, 4, 6... + 2
Data and Graphs: Using Operations
Vocabulary
bar graph-a graphic organizer that uses horizontal or vertical bars to represent data.
data-a collection of information; results of a survey.
key-used in a pictograph to tell how many each symbol stands for.
median-the median of a set of numbers is the middle number after the numbers are arranged in order.
mode-the mode of a set of numbers is the number that appears most frequently in the set.
pictograph-a form of picture graph that uses a repeating symbol to show data and a key to tell the symbol's meaning.
picture graph-a graphic organizer in which pictures represent data.
range-the range of a set of numbers is the difference between the greatest and the least numbers in the set.
real graph-a hands-on graphic organizer in which models, such as cubes or buttons, represent data.
tally chart-a two-column table with tall marks used to indicate quantities of listed items.
tally marks-simple lines used to record counting.
survey-to ask people their opinion, which is then recorded and presented in an organized way.
symbol-a picture that means the same thing each time it appears in a pictograph.
Place Value to 100
Vocabulary
2-digit number-a number, from 10 to 99 inclusively, that consists of a given number of tens and ones.
estimate-to make a thoughtful guess; to suggest a number that can be rounded or close to the exact amount.
value-numerical worth of a digit based on its position in a number.
digit- a single numeral from 0 though 9.
expanded form-a way to write a number as the sum of its place values, for example,
45 = 4 tens + 5 ones = 40 + 5.
compare-to look at things side by side to determine how they are alike and how they differ.
hundred chart-grid of 100 boxes (10 rows of 10 boxes per row) for displaying the numbers 1 to 100 in counting order.
10 less-describing a number with one fewer group of 10 but the same number of ones; for example, 67 is 10 less than 77.
10 more-describing a number with one more group of 10 but the same number ones; for example, 67 is 10 more than 57.
even number-the set (0,2,4,6,8,...) that can be separated into equal groups of two with none left over.
odd number-the set (1,3,5,7,...) that when separated into equal groups of two always has 1 left over.
count by 5s-to count on by a constant value of 5, resulting in a number pattern.
count by 2s-to count on by a constant value of 2, resulting in a number pattern
Check back for more as we move on!