4.7 - Geometry and measurement. The
student applies mathematical process standards to solve problems involving
angles less than or equal to 180 degrees. The student is expected to:
4.7.A - illustrate the measure of an
angle as the part of a circle whose center is at the vertex of the angle that
is "cut out" by the rays of the angle. Angle measures are limited to
whole numbers;
4.7.C - determine
the approximate measures of angles in degrees to the nearest whole number using
a protractor;
4.7.D - draw
an angle with a given measure; and
4.7.E - determine
the measure of an unknown angle formed by two non-overlapping adjacent angles
given one or both angle measures.
This week our kiddos have to measure angles with protractors.
The way I remember complementary and supplementary angles is that it feels RIGHT to give a complement and supplementary and STRAIGHT both start with S.
Before I start my post... A great website to find angle worksheets. Big Idea The student will apply the knowledge of lines and angles
to identify types of triangles (acute, obtuse, and right). The student will classify
two dimensional figures based on lines, angles, and symmetry.
The student will understand and apply the characteristics of angles and angle
measure. The student will use knowledge of points, lines, and angles to
determine the measure of an unknown angle formed by two non-overlapping
adjacent angles.
The student will use a spreadsheet to collect data into a table and produce a
line graph forecasting the trends of angle measurements.
Guiding Questions How are 2D shapes formed? (types of lines and angles) What attributes are used to sort and classify 2D shapes? How can you check if a figure has symmetry?
How
can you relate angles to fractional part of a circle? How can you
determine the measure of an angle separated into parts?
How can you use technology to analyze data?
Some old vocabulary words reappeared! Reasonable and estimate.
I had a question about adding fractions and I wanted to explain the way I teach it.
Numerator- the number on top that tells me how many parts I have
Denominator- the number on the bottom that tells me how many parts make one whole
When you add fractions you ONLY add the numerators, because the amount that it takes to make one whole would still be the same.
For example... If I had two pies that were cut into six slices each, and I had four of those slices.. the fraction is 4/6. The the next week I have 3 slices, the fraction sentence would be 4/6 + 3/6 = 7/6
7/6 is an improper fraction because the numerator is greater than the denominator.
If I wanted to change it into a mixed number, I would have to write how many WHOLES I have, as well as the fractional part.
6/6 is one whole, so in 7/6 I have one whole and 1/6 left over.
Drawing pictures is so helpful for these concepts. I am constantly drawing circles and cutting them up.
Fractions can also be parts of a group.
For example. I have a class of 17 students. 8 of those students are boys. The fraction of boys in my classroom is 8/17. If I add the fraction of boys 8/17 plus the fraction for girls 9/17, I get one whole class!
If I have 17 kids make up one class, but then I have three more students who aren't in my class show up... My fraction is 17/17 plus 3/17 = 20/17 because now I have more kids than make up one class.
Our next unit is all about angles and symmetry and geometry.
I wanted to start off with going over what they should already know from previous years.
Types of polygons, what makes a polygon a polygon, sides, angles, vertices,
TEKS
4.6 - Geometry and measurement. The
student applies mathematical process standards to analyze geometric attributes
in order to develop generalizations about their properties. The student is
expected to:
4.6.A - identify
points, lines, line segments, rays, angles, and perpendicular and parallel
lines;
4.6.B - identify
and draw one or more lines of symmetry, if they exist, for a two-dimensional
figure;
4.6.C - apply
knowledge of right angles to identify acute, right, and obtuse triangles; and
4.6.D - classify
two-dimensional figures based on the presence or absence of parallel or
perpendicular lines or the presence or absence of angles of a specified size
4.1 - Mathematical process standards.
The student uses mathematical processes to acquire and demonstrate mathematical
understanding. The student is expected to:
4.1.A - apply
mathematics to problems arising in everyday life, society, and the workplace;
4.1.E - create and
use representations to organize, record, and communicate mathematical ideas;
4.1.F - analyze
mathematical relationships to connect and communicate mathematical ideas;
4.1.G - display, explain, and justify mathematical ideas and arguments using
precise mathematical language in written or oral communication.
4.1 - Creativity and innovation. The student uses creative thinking
and innovative processes to construct knowledge and develop digital products.
The student is expected to:
4.1.A - create original products using a variety of resources 4.1.B- analyze trends and
forecast possibilities, developing steps for the creation of an innovative
process or product 4.1.C - use virtual environments to explore systems and
issues.
We are ending our unit by talking about adding and subtracting fractions with the same denominator, and comparing fractions with different denominators. We also have talked about a mixed number and an improper fraction.
An improper fraction is a fraction where the numerator is greater than the denominator.
A mixed number has both a whole number and a fraction.
We're so grateful for the donation of yoga balls!!
Here are all the TEKS that we covered:
TEKS
4.3 - Number and operations. The
student applies mathematical process standards to represent and generate
fractions to solve problems. The student is expected to:
4.3.C - determine
if two given fractions are equivalent using a variety of methods;
4.3.D - compare
two fractions with different numerators and different denominators and
represent the comparison using the symbols >, =, or <;
4.3.G - represent
fractions and decimals to the tenths or hundredths as distances from zero on a
number line.
4.2 - Number and operations. The
student applies mathematical process standards to represent, compare, and order
whole numbers and decimals and understand relationships related to place value.
The student is expected to:
4.2.G - relate
decimals to fractions that name tenths and hundredths; and
4.9 - Data analysis. The student
applies mathematical process standards to solve problems by collecting,
organizing, displaying, and interpreting data. The student is expected to:
4.9.A - represent
data on a frequency table, dot plot, or stem-and-leaf plot marked with whole
numbers and fractions; and
4.9.B - solve
one- and two-step problems using data in whole number, decimal, and fraction
form in a frequency table, dot plot, or stem-and-leaf plot.
4.3 - Number and operations. The
student applies mathematical process standards to represent and generate
fractions to solve problems. The student is expected to:
4.3.A - represent a
fraction a/b as a sum of fractions 1/b, where a and b are whole numbers and b
> 0, including when a > b;
4.3.B - decompose
a fraction in more than one way into a sum of fractions with the same
denominator using concrete and pictorial models and recording results with
symbolic representations;
4.3 - Number and operations. The
student applies mathematical process standards to represent and generate
fractions to solve problems. The student is expected to:
4.3.E
- represent and solve addition and subtraction of
fractions with equal denominators using objects and pictorial models that build
to the number line and properties of operations;
4.3.F - evaluate
the reasonableness of sums and differences of fractions using benchmark
fractions 0, 1/4, 1/2, 3/4, and 1, referring to the same whole; and
I have decided that as a teacher it is not the activity that the kiddos are doing, it's the questions that go with the activity that matters.
Here's a lesson that I thought really worked well for my kiddos.
All it was was a bunch of different colored tiles in a baggy. If you don't have tiles, M&Ms would work.
They had to name the fractions, compare the fractions, understand unit fractions, denominator, decimals, and expanded form.
Plus it was hands on, and the kiddos had to work together with their partner. It's definitely a lesson I will be doing again next year!
Plus when the kiddos were done they were able to create a bar graph of their data. There are tons of different ways to extend this activity which is perfect for my GT students.
4.3.G - represent
fractions and decimals to the tenths or hundredths as distances from zero on a
number line.
Fractions on a numberline is a tricky concept. Honestly, regular numbers on a numberline is tricky! When I had my kiddos do decimals on a number line each child got a sticky note with a decimal (that was less than one). They had to do the the fraction, decimal, picture, word form, and expanded notation for that decimal. Then they had to place it on the number line.
It was tricky to remember that 0.11 goes right after 0.1.
Because 0.1 = 0.10
Today for fractions on a number line, I did this lesson. It was pretty great and it gave us an opportunity to see equivalent fractions and unit fractions.
We have started Bundle Three which is all about DECIMALS and fractions!!
Developing fluency with efficient use of the four arithmetic operations
on whole numbers and using this knowledge to solve problems
Students add, subtract, multiply, and divide whole numbers fluently; justify
these procedures; and use them to solve problems, including developing formulas
for perimeter and area. 4.4A-H; 4.5A-D; 4.8A-C; 4.9A-B
Understanding decimals and addition and
subtraction of decimals
Students use understanding of base-10 place value and equivalent fractions to
develop understanding of decimals as numbers and of procedures for adding and
subtracting decimals. 4.2A-H; 4.3G; 4.4A; 4.9A-B
Building foundations for addition and
subtraction of fractions
Students use their understanding of fractions as numbers along with their
understanding of addition and subtraction to develop understanding of and
procedures for adding and subtracting fractions with like denominators.
Students use these understandings and procedures to solve problems. 4.3A-G; 4.9A-B I started decimals by talking about a familiar concept... money. Now we're moving on to straight up decimals and fractions.
