some lectionary based programs for children:
like all catechetical resources, they come with a caveat, they are not perfect, they are starting off points for the catechist who must be knowledgeable enough to supply deficiencies.
Pflaum Gospel weeklys, by grade level, with leader guides and support materials on their website. downside is you have to purchase a magazine for each child.
the most complete for a parish-wide program is the Word to Go (formerly Celebrating the Lectionary) upside is these are reproducible.
Footprints (23rd publications, reproducible, not a stand-alone program, an aide to memorizing and meditation on gospel)
Celebrating the Gospels (Liguori, goes along with Journey of Faith for Children RCIA program)
Complete Children’s Liturgy book cycles A B & C (23rd pubs)
Sunday Weekly Leader guide and support resources, from Treehaus Communications (this is a CLOW resource but contains resource for teaching on the gospel
the chapter study method you describe above is way over the heads of most elementary school children, and should not be introduced until 6th grade or for advanced 5th graders. this is the traditional recommendation of the Church. I would be extremely wary of any method or resource used in a non-CAtholic setting since it will encourage and expect private interpretation.
You also want to have a clear idea in your mind, or for your program, on what you are trying to accomplish.
Do you want teaching based on the Sunday Gospel?
Do you want faith sharing with the Gospel and other readings?
Do you want a guided meditation based on the Gospel and other readings, whereby you will gradually introduce the method of prayer with scripture called lectio divina?
Do you want to foster meditative reading and prayer with scripture?
Do you want an intensive study of one portion, verse, chapter, book or topical readings from scripture, using reference works and research tools?
choose your resources accordingly.
there is another warning I should offer as well. Your friend should begin with asking her DRE what is the curriculum and syllabus for 3rd grade in her parish, and what is the diocesan requirements for teaching 3rd grade?