Here’s a minds-on to introduce fractions in a fun way using LEGO blocks.
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Grade 4: Number Sense and Numeration
– represent fractions using concrete materials,
words, and standard fractional notation,
and explain the meaning of the denominator
as the number of the fractional parts
of a whole or a set, and the numerator as
the number of fractional parts being
considered;
– compare and order fractions (i.e., halves,
thirds, fourths, fifths, tenths) by considering
the size and the number of fractional parts
-demonstrate and explain the relationship
between equivalent fractions, using concrete
materials
The National Library of Virtual Manipulatives is an excellent site for teachers and students. It offers online lessons and practice on all strands of mathematics for JK to grade 12. We see here how part of the screen for number sense and numeracy looks like.
We see here and example of a subtraction problem using a number line.
Students are going skating this week. It is a good idea to look at what the rink looks like and identify the shapes on the rink, and their size. We can easily code what we learned in this investigation.
Update: with some reflection, we can add circling variables to this program to make them count up and down each turn of the skating rink.
For example, we can have one skater starting at 0 and going up by 50 each turn of the rink. The numbers generated would be: 0, 50, 100, 150, 200, 250, 300 and so on, each turn of the rink.
We can have another skater starting at 10,000 and going down by say 50 each turn of the rink. The numbers generated would be: 10, 000, 9950, 9900, 9850, 9800 and so on, each turn of the rink.
After spending some time looking at number lines, this would be an excellent way to see the progression of regular addition and regular subtraction.
Here is what the updated screen look and the code for the subtraction.
What is nice about this type of activity is that students are having fun and do not necessarily realize how much mathematics they are doing while coding.
This program relates to several Ontario grade 4 Mathematics strands and mathematical processes.
If the students are to write in a journal after they complete the program, all the mathematical processes are addressed by coding a program like this.
Mathematical Processes expectations:
• develop, select, and apply problem-solving strategies as they pose and solve problems and
conduct investigations, to help deepen their mathematical understanding;
• develop and apply reasoning skills (e.g., classification, recognition of relationships, use
of counter-examples) to make and investigate conjectures and construct and defend
arguments;
• demonstrate that they are reflecting on and monitoring their thinking to help clarify their
understanding as they complete an investigation or solve a problem (e.g., by comparing
and adjusting strategies used, by explaining why they think their results are reasonable, by
recording their thinking in a math journal);
• select and use a variety of concrete, visual, and electronic learning tools and appropriate
computational strategies to investigate mathematical ideas and to solve problems;
• make connections among mathematical concepts and procedures, and relate mathematical
ideas to situations or phenomena drawn from other contexts (e.g., other curriculum areas,
daily life, sports);
• create a variety of representations of mathematical ideas (e.g., by using physical models,
pictures, numbers, variables, diagrams, graphs, onscreen dynamic representations), make
connections among them, and apply them to solve problems;
• communicate mathematical thinking orally, visually, and in writing, using everyday language,
a basic mathematical vocabulary, and a variety of representations, and observing
basic mathematical conventions.
From Grade 4: number sense and numeration. The specific expectations addressed:
– represent, compare, and order whole
numbers to 10 000, using a variety of
tools (e.g., drawings of base ten materials,
number lines with increments of 100 or
other appropriate amounts);
– demonstrate an understanding of place
value in whole numbers and decimal
numbers from 0.1 to 10 000, using a
variety of tools and strategies (e.g., use
base ten materials to represent 9307 as
9000 + 300 + 0 + 7) (Sample problem:
Use the digits 1, 9, 5, 4 to create the greatest
number and the least number possible,
and explain your thinking.);
– read and print in words whole numbers to
one thousand, using meaningful contexts
(e.g., books, highway distance signs);
– round four-digit whole numbers to the
nearest ten, hundred, and thousand, in
problems arising from real-life situations;
– solve problems that arise from real-life
situations and that relate to the magnitude
of whole numbers up to 10 000
From Grade 4: Measurement
– estimate, measure, and record length,
height, and distance, using standard units
(i.e., millimetre, centimetre, metre, kilometre)
(e.g., a pencil that is 75 mm long);
– draw items using a ruler, given specific
lengths in millimetres or centimetres
(Sample problem: Use estimation to draw
a line that is 115 mm long. Beside it, use a
ruler to draw a line that is 115 mm long.
Compare the lengths of the lines.);
– estimate, measure using a variety of tools
(e.g., centimetre grid paper, geoboard) and
strategies, and record the perimeter and
area of polygons;
– determine, through investigation, the relationship
between the side lengths of a
rectangle and its perimeter and area
(Sample problem: Create a variety of rectangles
on a geoboard. Record the length,
width, area, and perimeter of each rectangle
on a chart. Identify relationships.);
– pose and solve meaningful problems that
require the ability to distinguish perimeter
and area (e.g.,“I need to know about area
when I cover a bulletin board with construction
paper. I need to know about
perimeter when I make the border.”);
Grade 4: Geometry and Spatial Sense
– draw the lines of symmetry of twodimensional
shapes, through investigation
using a variety of tools (e.g., Mira, grid
paper) and strategies (e.g., paper folding)
(Sample problem: Use paper folding to
compare the symmetry of a rectangle with
the symmetry of a square.);
identify and describe the general location
of an object using a grid system (e.g.,“The
library is located at A3 on the map.”);
– create a number pattern involving addition,
subtraction, or multiplication, given
a pattern rule expressed in words (e.g., the
pattern rule “start at 1 and multiply each
term by 2 to get the next term” generates
the sequence 1, 2, 4, 8, 16, 32, 64, …);
In addition to using coding as a tool to teach math, I am thinking of using another program, Nearpod, with BYOD to teach mathematics.
In the classroom, we have 2 computers, my iPad that I can use for teaching purposes and some student’s iPad. With 5 devices, one for teaching and 4 others, one for each table group, we can have a mathematics discussion with Nearpod.
Talking mathematics visually using Nearpod
Mathematics teachers often face the challenge of teaching complex mathematics ideas to students who have mathematics anxieties or speak little English. Communicating mathematics concepts visually with sometimes only one picture can be the source of deep mathematics understanding. The Nearpod app allows teacher and students to have live conversations with technology. Teachers can prepare their own visual lessons where students can comment live by filling a bubble, or writing text using their own device. Using examples from a grade 4 class, we will discuss how to introduce math concepts using technology that ignites curiosity and get students talking.
Discuter mathématique de façon visuelle avec Nearpod
Les professeurs de mathématiques font souvent face au défi d’enseigner des concepts mathématiques complexes à des étudiants qui ont l’angoisse des mathématiques ou à ceux qui parlent très peu le français. Communiquer de façon visuelle avec souvent une seule image peut être la source d’une excellente compréhension de la part des élèves. L’application Nearpod permet aux professeurs et aux étudiants d’avoir une communication instantanée avec la technologie. Le prof peut préparer une leçon visuelle et les élèves peuvent répondre en direct et à leur propre rhythme en choisissant une bulle ou en écrivant une phrase depuis leur propre appareil. En utilisant des exemples d’une classe de 4ième année, nous allons discuter comment introduire des concepts de mathématiques en utilisant la technologie afin de les rendre curieux et de susciter leur intérêt.
Students learned to use variables. We had a drama session where we mentioned that a variable is like a box that we place numbers in. We did 2 simulations. One where we counted hands that were up based on a question and we placed a rod in the box for each count. In simulation number 2, we did the Fibonacci sequence modelling, still in drama. Students had access to the code I wrote.
Some decided to create their own work, counting by 5s or 10s, using variables. Others did the Fibonacci sequence in drawing with their own creative decorations.